The influence of climate on the
numerical response of a predator
(Canis latrans: coyote) population to its
prey (Lepus americanus: snowshoe hare) in
the Canadian boreal forest
Berlinda Joy Bowler, BEnvSc
Institute for Applied Ecology
University of Canberra
A thesis submitted in partial fulfillment of the requirements for the degree of
Bachelor of Applied Science (Honours) at the University of Canberra
December 2010
Winter is what determines all the life here…
Liz Hofer, Kluane, 9 August 2010
i
Abstract
Predation is an important ecosystem function and much work has been done across
trophic levels to elicit the often complex relationships between predators and their prey.
The influence of climate on predator-prey relationships, however, remains poorly
understood, particularly for terrestrial mammalian predators and their mammalian prey.
The aim of this study was to evaluate evidence of an effect of climate on the coyote
(Canis latrans) numerical response to their keystone prey snowshoe hares (Lepus
americanus) in a Canadian boreal forest ecosystem. A set of a priori hypotheses of
coyote numerical response were developed that postulated linear, non-linear, additive,
and interactive effects of prey and climate. Models separately incorporated four largescale climate indices (the North Atlantic Oscillation, the El Niño-Southern Oscillation,
the Pacific/North Atlantic, and the North Pacific Index) and eight local scale climate
variables (a range of temperature measures, precipitation, rain, and snow). Model
selection procedures estimated which climate variables most influenced the coyote
numerical response.
The North Atlantic Oscillation (NAO) had the strongest effect on coyote numerical
response via its interaction with snowshoe hare density, while other large-scale and
local climate indices had relatively weak or no effects. The coyote numerical response
was positively influenced by the negative phase of the NAO and, contrary to
expectations, negatively influenced by increased local winter temperatures. It is
proposed that the coyote numerical response is ultimately determined by the coyote
functional response (hunting ability, efficiency, and success) influenced by favourable
or otherwise winter conditions determined by the NAO. In a time of climate change and
a prevailing trend for a positive phase of the NAO, the results of this study have
potential longer-term implications for boreal forest coyote populations, as well as for
snowshoe hare populations, other snowshoe hare predators, and hence, boreal forest
community dynamics.
In conclusion, this study provides strong support for the inclusion of climate into
models of the predator numerical response. Further, this study illustrates how a largescale climate index can better help explain an ecological process than local climate
variables.
ii
Certificate of authorship
Except as specifically indicated in footnotes and quotations, I certify that I am the sole
author of the thesis submitted today entitled: The influence of climate on the numerical
response of a predator (Canis latrans: coyote) population to its prey (Lepus
americanus: snowshoe hare) in the Canadian boreal forest, in terms of the Statement of
Requirements for a thesis issued by the University Research Degrees Committee.
Signature of Author
_______________________________
Date
_______________________________
iii
Acknowledgements
A very special and sincere thanks to my primary supervisor Professor Jim Hone for his
continued advice, guidance, encouragement, and support throughout the course of the
year. A very sincere thanks also to my secondary supervisor Professor Charles Krebs for
his invaluable advice and insights into the boreal forest community the subject of this
thesis, and for sponsoring my field trip to Canada.
I sincerely thank Alice Kenny and Liz Hoffer for taking me on as their understudy in the
field. Sharing with them their experiences and insights into the climatic and ecological
processes at play in the boreal forest ecosystem allowed me to put my research into an
ecosystem specific context and enabled me to directly relate to the true biological and
ecological consequences of my findings. I further wish to thank Mark O’Donoghue for
his enthusiasm for my study, and for the provision of invaluable advice on coyote habits
and data collection methods.
I would like to thank Bill Danaher, Kimberley Edwards, Maria Boyle, and Wendy
Dimond for their extremely useful comments on draft thesis chapters. I would also like
to thank my honours buddy Matt Young for his continued motivational support over the
course of the year.
Very special thanks are due to Bill, Joy, Nicole and Cody Danaher. I wish to thank them
for always being there to provide me with much love, support and encouragement, as
well as cake and coffee, especially on those days I needed it the most.
This thesis would not be possible without the unrelenting love and support from my
husband Denis and our son Lawrence. Denis, you provided me with the energy and
inspiration I needed to undertake this journey, and stood close by me every step of the
way. I dedicate this thesis to you.
iv
TABLE OF CONTENTS
CHAPTER 1: INTRODUCTION ..........................................................................1
1.1 Predation............................................................................................................................................... 1
1.1.1 What is predation?.......................................................................................................................... 1
1.1.2 The ups, downs, and cycles of predator and prey populations ....................................................... 1
1.1.3 Time-lags in the response of predators to their prey....................................................................... 3
1.2 The influence of climate on predator-prey dynamics........................................................................ 4
1.2.1 Defining climate ............................................................................................................................. 4
1.2.2 Climate and predator-prey dynamics.............................................................................................. 4
1.3 Canids: a fascinating, but unfortunate, family of predators ............................................................ 6
1.4 The predator: Coyote (Canis latrans) ................................................................................................. 7
1.5 The prey: Snowshoe hare (Lepus americanus)................................................................................... 8
1.6 The dynamic duo: Predation dynamics between coyotes and snowshoe hares ............................. 10
1.6.1 Coyote prey preferences ............................................................................................................... 10
1.6.2 Are coyotes specialist or generalist predators?............................................................................. 11
1.6.3 Environmental influences on coyote predation of hares............................................................... 12
1.6.4 The responses of coyotes to changing hare densities.................................................................... 12
1.7 Significance of this study ................................................................................................................... 12
1.8 Aims and objectives............................................................................................................................ 13
1.9 Thesis structure .................................................................................................................................. 14
CHAPTER 2: THE RESPONSES OF PREDATORS TO THEIR PREY ...........15
2.1 Introduction ........................................................................................................................................ 15
2.2 Numerical response ............................................................................................................................ 15
2.3 Functional response............................................................................................................................ 17
2.4 The measurement of numerical and functional responses of canids: shortfalls and pitfalls ....... 18
2.5 The numerical and functional responses of Canadian coyotes to their prey: A review ............... 21
2.6 Summary............................................................................................................................................. 24
CHAPTER 3: MODELS ....................................................................................25
3.1 Model development ............................................................................................................................ 25
3.1.1 Description and assumptions ........................................................................................................ 25
3.1.2 Ecological context: Historical background................................................................................... 26
3.1.3 Ecological context: The current state of knowledge..................................................................... 27
3.1.4 Justification for climate indices .................................................................................................... 28
3.2 Candidate models ............................................................................................................................... 35
3.3 Model selection ................................................................................................................................... 39
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CHAPTER 4: METHODS .................................................................................41
4.1 Study area ........................................................................................................................................... 41
4.1.1 Location........................................................................................................................................ 41
4.1.2 Vegetation .................................................................................................................................... 42
4.1.3 Climate ......................................................................................................................................... 43
4.2 Coyote and snowshoe hare data ........................................................................................................ 45
4.2.1 Estimation of snowshoe hare density ........................................................................................... 45
4.2.2 Estimation of coyote density ........................................................................................................ 46
4.3 Climate data........................................................................................................................................ 48
4.3.1 North Atlantic Oscillation ............................................................................................................ 48
4.3.2 El Niño-Southern Oscillation (Southern Oscillation Index) ......................................................... 48
4.3.3 Pacific/North American................................................................................................................ 48
4.3.4 North Pacific Index....................................................................................................................... 49
4.3.5 Local climate data......................................................................................................................... 52
4.4 Partial correlation analyses ............................................................................................................... 54
CHAPTER 5: RESULTS—RELATIVE MODEL SUPPORT BY CLIMATE
VARIABLE........................................................................................................55
5.1 Observed coyote and snowshoe density............................................................................................ 55
5.2 Coyote numerical response and large-scale climate indices ........................................................... 58
5.2.1 North Atlantic Oscillation (NAO) ................................................................................................ 58
5.2.2 El Niño-Southern Oscillation (SOI) ............................................................................................. 63
5.2.3 Pacific/North American (PNA) .................................................................................................... 68
5.2.4 North Pacific Index (NPI) ............................................................................................................ 73
5.3 Coyote numerical response and local climate variables.................................................................. 78
5.3.1 Extreme maximum winter temperature ........................................................................................ 78
5.3.2 Extreme minimum winter temperature......................................................................................... 81
5.3.3 Precipitation.................................................................................................................................. 84
5.3.4 Rain .............................................................................................................................................. 87
5.3.5 Snow............................................................................................................................................. 90
5.3.6 Mean minimum winter temperature ............................................................................................. 93
5.3.7 Mean winter temperature.............................................................................................................. 96
5.3.8 Mean maximum winter temperature............................................................................................. 99
5.3.9 Reconstructions of coyote density using local climate variables................................................ 102
5.4 Summary of Akaike weight values (ωi) for each climate variable ............................................... 108
CHAPTER 6: RESULTS—RELATIVE SUPPORT FOR EACH CLIMATE
VARIABLE BY MODEL..................................................................................109
6.1 Model 2 (Ct = a + bHt-1 + dWt-1×Ht-1) .............................................................................................. 109
6.2 Model 3 (Ct = f + bHt-1 + gWt-1) ....................................................................................................... 110
6.3 Model 5 (Ct = a + cHt-1h + dWt-1×Ht-1h)............................................................................................ 111
6.4 Model 6 (Ct = f + bHt-1h + gWt-1)...................................................................................................... 112
6.5 Summary of Akaike weight values (ωi) by model.......................................................................... 113
6.6 Relationships between the NAO and the local climate variables ................................................. 113
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CHAPTER 7: DISCUSSION ...........................................................................115
7.1 The influence of climate on the coyote numerical response.......................................................... 115
7.2 The influence of climate on snowshoe hares .................................................................................. 117
7.3 Comparisons to other predator–prey studies with the NAO........................................................ 119
7.4 The relationship between the NAO and local climate variables................................................... 122
7.5 Why was there little support for models with local climate variables? ....................................... 123
7.6 What are the extra effects on coyote density not explained by the effects of snowshoe hare
density and climate?............................................................................................................................... 124
7.6.1 Population demography and social structure .............................................................................. 125
7.6.2 Density and phase dependencies ................................................................................................ 126
7.6.3 Alternative prey .......................................................................................................................... 127
7.6.4 Interspecific competition with other predators ........................................................................... 127
7.6.5 Human harvest and disease......................................................................................................... 129
7.7 Synopsis............................................................................................................................................. 130
7.8 Implications of the study.................................................................................................................. 131
7.9 Conclusions ....................................................................................................................................... 132
References.....................................................................................................133
APPENDIX 1: Regression analysis of local climate variables: Burwash
Landing and Whitehorse, Yukon .................................................................146
APPENDIX 2: Partial correlation coefficients and P-values for coyote track
counts and climate, correcting for coyote population estimate ...............148
APPENDIX 3: Regression analysis of the winter North Atlantic Oscillation
index and local climate variables ................................................................149
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LIST OF FIGURES
Figure 2.1 Examples of numerical response forms ................................................................................. 16
Figure 2.2 Predator functional response types......................................................................................... 17
Figure 2.3 A comparison of the Caughley-type numerical response of barn owls to field voles, estimated
by two methods ...................................................................................................................... 20
Figure 2.4 Numerical response of (a) coyotes and (b) lynx to snowshoe hares in the Yukon, Canada... 23
Figure 3.1 The three climatic regions of Canada based on spatial influences of the NAO ..................... 31
Figure 3.2 Composite difference in the frequency of winter warm spells across Canada between the
positive and negative phases of the NAO during winter........................................................ 31
Figure 3.3 Graphical hypotheses (models 1 to 6) of coyote numerical response .................................... 38
Figure 4.1 Location of the Kluane study area, in the Yukon Territory Canada ...................................... 41
Figure 4.2 Total amount of rain (mm) for the winter months of October to March inclusive 1985–2007
for Burwash Landing. ............................................................................................................ 44
Figure 4.3 Total amount of snow (cm) for the months of October to March inclusive 1985–2007 for
Burwash Landing ................................................................................................................... 44
Figure 4.4 Mean winter temperatures (°C) for the months of October to March inclusive 1985–2007 for
Burwash Landing ................................................................................................................... 45
Figure 4.5 Layout of snowshoe hare trapping grid.................................................................................. 46
Figure 4.6 Comparison of track counts and population estimates of Kluane coyotes ............................. 47
Figure 4.7 Changes in the winter North Atlantic Oscillation index for the years 1986/87 to 2008/09 ... 50
Figure 4.8 Changes in the winter Southern Oscillation Index for the years 1986/87 to 2008/09............ 50
Figure 4.9 Changes in the winter Pacific/North American index for the years 1986/87 to 2008/09....... 51
Figure 4.10 Changes in the winter North Pacific Index for the years 1986/87 to 2008/09. ...................... 51
Figure 5.1 Changes in the estimated mean number of coyote tracks per track night per 100 km of
Kluane coyotes for the period 1987/88 to 2009/10 ................................................................ 56
Figure 5.2 Changes in the estimated density of Kluane snowshoe hares for the period 1986 to 2009.... 56
Figure 5.3 Coyote density (Ct) and snowshoe hare density (Ht-1) for the period 1986/87–2009/10........ 57
Figure 5.4 (a) Coyote density against NAO the same year; (b) coyote density against NAO the year
before; and (c) hare density against NAO the year preceding hare data collection ............... 58
Figure 5.5 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and the second ranked model 5 () using the NAO ................. 61
Figure 5.6 Influence of NAOt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with model 2 parameter estimates ................................................................... 62
Figure 5.7 (a) Coyote density against SOI the same year; (b) coyote density against SOI the year before;
and (c) hare density against SOI the year preceding hare data collection.............................. 63
viii
Figure 5.8 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 2 () using the SOI.................... 66
Figure 5.9 Influence of SOIt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates ............................................................. 67
Figure 5.10 (a) Coyote density against PNA the same year; (b) coyote density against PNA the year
before; and (c) hare density against PNA the year preceding hare data collection ................ 68
Figure 5.11 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 2 () using the PNA .................. 71
Figure 5.12 Influence of PNAt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates ............................................................. 72
Figure 5.13 (a) Coyote density against NPI the same year; (b) coyote density against NPI the year before;
and (c) hare density against NPI the year preceding hare data collection .............................. 73
Figure 5.14 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and the second ranked model 1 () using the NPI.................... 76
Figure 5.15 Influence of NPIt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates ............................................................. 77
Figure 5.16 (a) Coyote density against mean extreme maximum winter temperature (EmaxTEM) the
same year; (b) coyote density against EmaxTEM the year before; and (c) hare density against
EmaxTEM the year preceding hare data collection ............................................................... 78
Figure 5.17 (a) Coyote density against mean extreme minimim winter temperature (EminTEM) the same
year; (b) coyote density against EminTEM the year before; and (c) hare density against
EminTEM the year preceding hare data collection ................................................................ 81
Figure 5.18 (a) Coyote density against total winter precipitation (PREC) the same year; (b) coyote density
against PREC the year before; and (c) hare density against PREC the year preceding hare
data collection ........................................................................................................................ 84
Figure 5.19 (a) Coyote density against total winter rain (RAIN) the same year; (b) coyote density against
RAIN the year before; and (c) hare density against RAIN the year preceding hare data
collection................................................................................................................................ 87
Figure 5.20 (a) Coyote density against total snow (SNOW) the same year; (b) coyote density against
SNOW the year before; and (c) hare density against SNOW the year preceding hare data
collection................................................................................................................................ 90
Figure 5.21 (a) Coyote density against mean minimum winter temperature (minTEM) the same year;
(b) coyote density against minTEM the year before; and (c) hare density against minTEM the
year preceding hare data collection........................................................................................ 93
Figure 5.22 (a) Coyote density against mean winter temperature (TEM) the same year; (b) coyote density
against TEM the year before; and (c) hare density against TEM the year preceding hare data
collection................................................................................................................................ 96
Figure 5.23 (a) Coyote density against mean maximum winter temperature (maxTEM) the same year;
(b) coyote density against maxTEM the year before; and (c) hare density against maxTEM
the year preceding hare data collection .................................................................................. 99
Figure 5.24 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and second ranked model 3 () using EmaxTEM .................. 102
ix
Figure 5.25 Influence of EmaxTEMt-1 on coyote numerical response (Ct) to snowshoe hare density
(Ht-1), reconstructed with the model 2 parameter estimates ................................................. 103
Figure 5.26 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 3 () using EminTEM ............. 104
Figure 5.27 (a) Precipitation, (b) rain and (c) snow. Observed data (solid line) and estimates (broken
lines) of coyote density reconstructed from the first ranked model 1 (○) and second ranked
model 2 ().......................................................................................................................... 106
Figure 5.28 (a) Minimum, (b) mean and (c) maximum winter temperatures. Observed data (solid line)
and estimates (broken lines) of coyote density reconstructed from the first ranked model (○),
and second ranked model (). For (a) mean minimum winter temperature ○=model 1 and
=model 3; for (b) mean winter temperature ○=model 3 and =model 1; and for (c) mean
maximum winter temperature ○=model 3 and =model 2.................................................. 107
Figure 7.1 Model of factors influencing the coyote numerical response............................................... 130
Figure A1 Local climate variable correlations for Burwash Landing and Whitehorse ......................... 146
Figure A3 North Atlantic Oscillation and local climate variable correlations for Burwash Landing,
Yukon .................................................................................................................................. 149
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LIST OF TABLES
Table 3.1
Coefficients of determination (R2) between large-scale climate indices. NAO=North Atlantic
Oscillation; SOI=El Niño-Southern Oscillation; PNA=Pacific/North American; NPI=North
Pacific Index .......................................................................................................................... 34
Table 4.1
Local climate variables examined in this study ..................................................................... 52
Table 4.2
Local weather variable outliers removed prior to correlation analysis to predict missing
Burwash Landing values........................................................................................................ 53
Table 5.1
The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of the North Atlantic Oscillation (NAOt-1)............................................................. 60
Table 5.2
Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and NAOt-1 .................................................................................................................... 60
Table 5.3
The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of the El Niño-Southern Oscillation (SOIt-1) .......................................................... 65
Table 5.4
Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and SOIt-1. ..................................................................................................................... 65
Table 5.5
The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of the Pacific/North American (PNAt-1)................................................................. 70
Table 5.6
Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and PNAt-1 .................................................................................................................... 70
Table 5.7
The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of the North Pacific Index (NPIt-1) ......................................................................... 75
Table 5.8
Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and NPIt-1 ...................................................................................................................... 75
Table 5.9
The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of mean extreme maximum winter temperature (EmaxTEMt-1) ............................ 80
Table 5.10 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and mean extreme maximum temperature (EmaxTEMt-1)............................................ 80
Table 5.11 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of mean extreme minimum temperature (EminTEMt-1) ......................................... 83
Table 5.12 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and mean extreme minimum temperature (EminTEMt-1) ............................................. 83
Table 5.13 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of total precipitation (PRECt-1)............................................................................... 86
Table 5.14 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and PRECt-1 .................................................................................................................. 86
Table 5.15 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of total rain (RAINt-1)............................................................................................. 89
Table 5.16 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and RAINt-1................................................................................................................... 89
xi
Table 5.17 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of total snow (SNOWt-1) ........................................................................................ 92
Table 5.18 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and SNOWt-1 ................................................................................................................. 92
Table 5.19 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of mean minimum temperature (minTEMt-1) ......................................................... 95
Table 5.20 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and mean minimum temperature (minTEMt-1) ............................................................. 95
Table 5.21 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of mean temperature (TEMt-1)................................................................................ 98
Table 5.22 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and TEMt-1 .................................................................................................................... 98
Table 5.23 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of mean maximum temperature (maxTEMt-1)...................................................... 101
Table 5.24 Parameter estimates for models of the numerical response of coyote density (Ct) to hares
(Ht-1) and mean maximum temperature (maxTEMt-1).......................................................... 101
Table 5.25 Summary of Akaike weights for each model for large-scale and local climate variables.... 108
Table 6.1
The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
interactive effect of each climate variable (Wt-1) for model 2.............................................. 109
Table 6.2
The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
additive effect of each climate variable (Wt-1) for model 3.................................................. 110
Table 6.3
The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
interactive effect of each climate variable (Wt-1) for model 5.............................................. 111
Table 6.4
The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
additive effect of each climate variable (Wt-1) for model 6.................................................. 112
Table 6.5
Summary of Akaike weights (ωi) for each large-scale climate variable by model. The climate
variable with the most support for each model is shown in bold ......................................... 114
Table 6.6
Summary of Akaike weights (ωi) for each local climate variable by model ........................ 114
Table A1
Correlation by least-squares regression analysis between each local climate variable for
Burwash Landing and Whitehorse, Yukon to allow for prediction of five missing Burwash
Landing values ..................................................................................................................... 146
Table A2
Partial correlation coefficients and P-values for coyote track counts and climate, correcting
for coyote population estimate ............................................................................................. 148
Table A3
Correlation by least-squares regression analysis between the winter NAO index and each
local climate variable for Burwash Landing, Yukon ........................................................... 149
1
CHAPTER 1: INTRODUCTION
1.1 Predation
1.1.1 What is predation?
Predation is an ecological interaction that can be defined as occurring when individuals
eat all or part of other live individuals, and encompasses herbivory, parasitism,
carnivory, and cannibalism (Taylor, 1984; Sinclair et al., 2006). Predation usually
involves interactions between trophic levels where one species negatively affects
another and will often, but not always, result in the killing of the prey species (Sinclair
et al., 2006; Krebs, 2009).
Predation is an important ecosystem process as it influences the distribution and
abundance of prey species, influences community organisation, and acts as a major
selective force in terms of the evolutionary adaptation of organisms (Bonsall and
Hassell, 2007; Krebs, 2009). The interactions between predators and their prey is a topic
of increasing interest and importance in the fields of wildlife ecology, management, and
conservation, and much work has been done across trophic levels to elicit the often
complex relationships between predators and their prey (Sinclair et al., 2006).
1.1.2 The ups, downs, and cycles of predator and prey populations
A common feature of predator-prey interactions is the tendency of both populations to
fluctuate, that is, the increase and decrease of predator populations in response to the
respective increase and decrease of their prey populations (Bonsall and Hassell, 2007).
As prey populations increase in size, more predators survive and reproduce or migrate
to areas of abundant prey. Conversely, as prey becomes scarce, there is less food
available to predators, and their survival and reproduction rates are reduced, or they
migrate out of the area in search of food (Sinclair et al., 2006; Bonsall and Hassell,
2007; Krebs, 2009). This predator-prey dynamic is consistent with the mechanistic
paradigm of population regulation defined by Krebs (1995; 2002; 2009) and Sibly and
Hone (2002). The mechanistic paradigm identifies the limiting effects of ecological
factors (such as food, predators, parasites, and disease) and extrinsic factors (such as
climate) on a population’s abundance and growth rate.
2
There is also an inherent tendency for some predator-prey systems to result in coupled
population oscillations or cycles in abundance (Begon et al., 2006; Bonsall and Hassell,
2007). The defining feature of a population cycle is regularity: a peak (or trough) in
abundance every x years (Begon et al., 2006). Coupled cycles in predator-prey
abundance have been demonstrated with bacteria, protists, algae, and invertebrates in
laboratory microcosms (for example Utida, 1957; Huffaker, 1963), but are also present
in the wild. Coupled predator-prey cycles have been found between a range of wild
mammalian and avian predators and their prey in Fennoscandia, Finland, North
America, Greenland, Siberia, Japan, and central Europe (Lindström, 1989; Akcakaya,
1992; Angerbjörn et al., 1999; Krebs et al., 2001b; Ims and Fuglei, 2005).
There are two commonly observed cycle periods in terrestrial mammalian predator-prey
systems. The first are 3–5 year cycles exhibited by the microtine rodents (lemmings
Lemmus and Dicrostonyx spp., and voles Clethrionomys and Microtus spp.) and their
predators in the Arctic tundra regions (Lindström, 1989; Akcakaya, 1992; Angerbjörn et
al., 1999; Ims and Fuglei, 2005). The second are 9–11 year cycles exhibited by hares
and jackrabbits (Lepus spp.) and their predators inhabiting the boreal forests of Canada
(Akcakaya, 1992).
The classic ‘text-book’ example of a coupled predator-prey oscillation can be seen with
the regular snowshoe hare (Lepus americanus)–Canada lynx (Lynx canadensis) cycle
(Trostel et al., 1987; Hodges et al., 2001; Krebs et al., 2001a; O'Donoghue et al., 2001).
The dramatic cyclic interaction between these mammal species, where both the
snowshoe hare and lynx exhibit closely linked 10-year cycles in abundance, has
historically been held to epitomise natural predator-prey cycles (Begon et al., 2006;
Bonsall and Hassell, 2007).
Despite some predators and their prey exhibiting closely linked cycles in abundance,
it is difficult to isolate exclusive predator-prey cycles (Begon et al., 2006; Bonsall and
Hassell, 2007). In nature predation does not occur independently but takes place in the
context of other biotic and abiotic processes, such as competition and environmental
fluctuations (Begon et al., 2006; Krebs, 2009). In regard to the snowshoe hare–lynx
cycle, it is now known that other factors are involved in the cyclic population dynamics.
These are: the quality of the hare’s own food supply (Krebs et al., 1995; Hodges et al.,
2001; Krebs et al., 2001a); other mammalian and avian predators which act both
3
directly on hares and indirectly on lynx via exploitative competition (Stenseth et al.,
1997; Tyson et al., 2010); and the effect of climate on lynx hunting ability (Stenseth et
al., 2004b). It has further been postulated that the snowshoe hare’s population cycle
could be modulated indirectly by solar (sunspot) activity which is known to influence
broad weather patterns by amplifying climate cycles (Sinclair et al., 1993). Stenseth
et al. (2004b) hypothesised that the hare–lynx interaction is influenced by properties of
snow (hardness and depth resulting from temperature changes) that can, in turn,
influence lynx hunting efficiency and success (Stenseth et al., 2004b). Hence, predator–
prey cycles can be the product of a number of intrinsic and/or extrinsic factors operating
across trophic levels.
1.1.3 Time-lags in the response of predators to their prey
Predator numbers do not respond instantaneously to changes in prey density. Predator
populations can increase when there are more food resources available to support a
larger predator population but this increase takes time, i.e. prey are not immediately
‘converted’ into new predators (Bonsall and Hassell, 2007). Thus, a time lag between
changes in abundance of a predator in response to changes in abundance of its prey
species is commonly seen in cyclic predator-prey systems. This ‘predator lag’ can be
defined as the time between the peak (maximum abundance) of the prey cycle, and the
subsequent peak of the predator cycle (Taylor, 1984; Tyson et al., 2010). When a prey
population peaks, the abundance of prey can be in excess of a predator population’s
needs. The prey population must subsequently decrease sufficiently below the needs of
the increased number of predators before predators are adversely affected (Keith et al.,
1977).
Predator lags of one year have been reported for: both lynx and coyotes (Canis latrans)
to snowshoe hare cycles in Canada (Keith et al., 1977; Todd and Keith, 1983;
O'Donoghue et al., 1997); coyotes to jackrabbit (Lepus californicus) populations in
Idaho, USA; red foxes (Vulpes vulpes) to vole cycles in Sweden (Lindström, 1989); and
arctic foxes (Alopex lagopus) to lemming cycles in northern Siberia (Angerbjörn et al.,
1999).
4
1.2 The influence of climate on predator-prey dynamics
1.2.1 Defining climate
Atmospheric phenomena are typically classified as ‘weather’ or ‘climate’. Weather is
defined as the pronounced atmospheric fluctuations occurring from hour to hour, day to
day, and is described by local parameters of temperature, air pressure, humidity,
cloudiness, precipitation, snow, and wind (Stenseth et al., 2003). Climate is defined as
the synthesis of all the weather recorded over a long period of time, and describes both
the average conditions and the variations and distributions of weather conditions for
some particular geographical locality or region (Stenseth et al., 2003; Bureau of
Meteorology 2010b). The ecological effects of climate operate through local weather
parameters, as well as interactions among these and biotic factors (Stenseth et al., 2002;
Mysterud et al., 2003; Krebs, 2009). In the past decade there has been an increasing
interest in studying the effects of large-scale climate phenomena such as the North
Atlantic Oscillation and the El Niño-Southern Oscillation on population dynamics, as
these and other climate patterns (or modes) have also been found to influence ecological
processes (Stenseth et al., 2003).
1.2.2 Climate and predator-prey dynamics
Climate directly affects the distribution and abundance of all organisms and influences a
variety of ecological processes (Stenseth et al., 2002; Krebs and Berteaux, 2006; Krebs,
2009). As such, its effects have been a topic of great interest in ecology for nearly a
century (Turesson, 1925; Hallett et al., 2004; Krebs, 2009). Among long-lived
vertebrates, the influence of climate has most clearly been demonstrated through its
effects on body condition, population growth rate, fecundity, reproductive success and
early survival, recruitment, and migration patterns across both spatial and temporal
scales (Mech et al., 1987; Ottersen et al., 2001; Stenseth et al., 2002; Durant et al.,
2003).
In the current environment of global climate change, there has been a marked increase
in interest in evaluating population and ecosystem response to changes in climatic
variability, and much research has been undertaken to elicit such relationships (Walther
et al., 2002; Fischlin et al., 2007). Despite this, the influence of climate on predator-
5
prey interactions remains poorly studied. Most studies that link the effects of climate to
predation dynamics tend to focus on invertebrate or aquatic populations (for example
Ottersen et al., 2001; Lusseau et al., 2004; Baier and Terazaki, 2005), the prey species
only (for example Patterson and Power, 2002), or the interactions between plant
(pasture biomass in response to rainfall; quality of forage) and herbivore trophic levels
(for example Bayliss, 1987; Forchhammer et al., 1998; Aanes et al., 2002; Bayliss and
Choquenot, 2002; Davis et al., 2002; Hone and Clutton-Brock, 2007). Therefore, the
effect of climate on terrestrial mammalian predator-prey interactions, and specifically
the effect of climate on predator responses to their prey, remains poorly understood (but
see Post and Stenseth, 1998; Post et al., 1999; Stenseth et al., 1999; 2004a; 2004b).
Stenseth et al. (2004a; 2004b) found the dynamics of lynx populations across Canada to
be strongly influenced by climate. Specifically lynx–snowshoe hare interactions were
found to be influenced by the properties of snow, which results from temperature
changes correlated with the North Atlantic Oscillation (NAO). In particular, snow
surface hardness, determined by the frequency of warm spells, influenced lynx hunting
success of hares (measured by lynx killing rate) due to the snow sinking depth.
Specifically, it was proposed that increased warm spells which cause snow thawrefreeze events led to harder snow surfaces, which in turn, resulted in increased
(more successful) killing rate of hares by lynx (Stenseth et al., 2004b).
Studies by Post and Stenseth (1998) and Post et al. (1999) found a strong influence of
climate on the predator-prey dynamics between grey wolves (Canis lupus) and their
main prey moose (Alces alces) on Isle Royale, northeast USA. Grey wolf predation
dynamics were found to be not only related to population levels of moose, but also
mediated by large-scale climatic fluctuations in snowfall and winter temperatures
determined by the NAO. Wolves were found to change their predation behaviour in
response to changes in climate. Principally, wolves were disadvantaged in years of
increased winter snow and responded by increasing pack size, thereby increasing
hunting success (predation rate on moose) (Post and Stenseth, 1998; Post et al., 1999;
Stenseth et al., 2004a).
6
1.3 Canids: a fascinating, but unfortunate, family of predators
The Canidae family of carnivorous predators which includes foxes, wolves, coyotes,
jackals and dogs are a fascinating family to study biologically, ecologically, and
socially, and have thus been at the forefront of such research for over a century (Bekoff,
1978; Pitt et al., 2003; Sillero-Zubiri and Macdonald, 2004). As human populations
have expanded, however, the management of canid populations has met with conflicting
pest control–conservation objectives.
Across much of their range canids are considered serious agricultural pests or
commercial commodities (i.e. the fur trade) and are subject to intensive human control
and harvest (Corbett, 1995; Conover, 2001; Macdonald and Sillero-Zubiri, 2004;
Sillero-Zubiri et al., 2004). However, the removal of canid predators from ecosystems
has been implicated in loss of biodiversity and increased threat to, or local extinction of,
lower trophic level species by way of mesopredator release (Crooks and Soulé, 1999;
Henke and Bryant, 1999; Mezquida et al., 2006; Gehrt and Prange, 2007; Glen et al.,
2007; Letnic et al., 2009). The mesopredator release hypothesis predicts that reduced
abundance or loss of a large predator results in the ecological release (increased
abundance or activity) of smaller (meso) predators, which in turn, has a detrimental
impact on the prey of those mesopredators (Crooks and Soulé, 1999; Letnic et al.,
2009).
Changing social attitudes have seen an increase in support for the conservation of canid
species, some of which are at serious risk of extinction due to human persecution
(Sillero-Zubiri et al., 2004). An important step in addressing such wildlife management
dilemmas is the ability to identify and understand predator-prey interactions including
the effect predators have on prey density, how predators respond to prey densities, and
what factors influence those responses (Sinclair et al., 2006). Consideration of such
interactions is important when determining how predator and prey populations may
respond to environmental, climatic, or human induced changes.
7
1.4 The predator: Coyote (Canis latrans)
The coyote is a medium sized mammalian carnivore from the Canidae family. Adult
coyotes have an average length and height of 80 cm and 62 cm respectively, and can
weigh between 8 and 22 kg (Macdonald and Sillero-Zubiri, 2004; Reid, 2006). Coyotes
are the most primitive member of their genus in the North American region, having
evolved during the Pleistocene epoch around 1.5 million years ago (Bekoff, 1978;
Macdonald and Sillero-Zubiri, 2004). Prior to modern European settlement of North
America coyotes were restricted predominantly to the south-west region and plains of
the continent, although the exact southern, northern, and eastern limits of their historical
range are not known (Bekoff, 1978; Macdonald and Sillero-Zubiri, 2004). A marked
change in distribution following modern European settlement has seen coyotes expand
their range into all of the United States including Alaska and almost all of Canada, as
well as south into all of Mexico and Central America (Bekoff, 1978; Macdonald and
Sillero-Zubiri, 2004). As such, coyotes are relatively recent colonisers of the
northwestern region of Canada.
The coyote is considered the most versatile of all canids. Flexibility in behaviour, social
ecology and diet have allowed the species to exploit and thrive in almost all
environments altered by humans (Bekoff, 1978; Macdonald and Sillero-Zubiri, 2004).
Hence, modern European settlement and subsequent land-use change (logging, land
clearing, and the expansion of pastoral industries) has contributed to the expansion of
the coyote’s range in the last 100 years (Macdonald and Sillero-Zubiri, 2004). Aiding
the coyote’s expansion has been the removal by humans of wolves (Canis lupus and
C. rufus) from many areas allowing coyotes to exploit the prey and territorial niches
once occupied by these related canids (Bekoff, 1978; Mech, 1978).
Coyotes are harvested and subjected to intensive population control across much of their
North American range, but particularly so in the United States. They are a major
predator of domestic sheep and wild game species, and are therefore considered serious
pests (Mech, 1978; Conover, 2001; Bartel and Brunson, 2003; Gese and Bekoff, 2004).
Although coyotes have been found to cause significant damage to individual sheep
ranches in the United States, the actual economic value of losses to the agricultural
8
industry due to the coyote is a matter of some dispute (Mech, 1978; Conover, 2001;
Gese and Bekoff, 2004). Despite decades of intense control coyotes remain abundant
across much of their range, with reductions in local populations typically temporary in
nature. As such, there are no immediate threats to coyote populations (Gese and Bekoff,
2004; Macdonald and Sillero-Zubiri, 2004).
Notwithstanding the vast effort devoted to destroying the coyote, initially little research
was dedicated towards understanding it, or the impact of its removal on other species
(Mech, 1978). There has been in more recent times a marked change in social
consciousness with an increase in awareness of how little was known about the species,
despite its heavy persecution. Indeed, the coyote is increasingly becoming known as an
important (keystone) predator, whose removal, even if temporary, can be detrimental to
lower trophic levels (Crooks and Soulé, 1999; Henke and Bryant, 1999; Mezquida et
al., 2006; Letnic et al., 2009).
1.5 The prey: Snowshoe hare (Lepus americanus)
The snowshoe hare (also known as the ‘varying hare’) is a moderate sized lagomorph
from the Leporidae family of hares and rabbits. Adults have a total length of between
36 and 52 cm, and with their heavily furred, large hind feet of between 12 and 15 cm
long, are well adapted to winter life on the snow. Adult snowshoe hares weigh between
0.9 and 2.2 kg, and display camouflaging seasonal colouration: dark brown with white
flanks in summer and almost entirely white in winter (Reid, 2006; Murray and Smith,
2008). Snowshoe hares occur in the boreal and mixed deciduous forests of North
America, and are distributed across most of Canada, Alaska, and the north-western and
north-eastern United States (Reid, 2006; Murray and Smith, 2008). Across most of their
range, snowshoe hares are considered common, but some populations in the southern
most areas of their distribution have experienced a recent decline due to excessive
habitat loss and fragmentation (Murray and Smith, 2008).
The snowshoe hare is a critical (keystone) species across much of its boreal forest
range. The structure of plant and predator communities in North American boreal
forests is largely governed by the population dynamics of snowshoe hares, and loss of
hares from these ecosystems would see such systems substantially altered (Krebs et al.,
9
2001a). The snowshoe hare is also considered an economically important species, as it
provides important prey for many commercially valuable furbearer species (such as
coyotes and foxes), and is an alternative prey item for predators over commercially
important game species such as ruffed grouse (Bonasa umbellus) (United States Forest
Service, 2010). Despite their ecological importance, snowshoe hares can also be
considered agricultural pests across the Pacific Northwest regions of North America, as
they can potentially cause significant damage to managed and unmanaged conifer
stands. As such they are often subject to management control across those regions
(Giusti et al., 1992; United States Forest Service, 2010).
Across their range, and particularly in the boreal forests of Canada, snowshoe hare
populations exhibit predictable cyclic fluctuations in abundance, with peak densities
occurring every 8–11 years (Hodges et al., 2001). The changes in densities of snowshoe
hares over the course of a population cycle are quite dramatic, with fluctuations of
between 5 and 25-fold (Hodges et al., 2001). Snowshoe hares are typically the dominant
herbivore present in Canadian boreal forests. Thus, their cyclic fluctuations are
considered a dominant perturbation, with cycles having widespread ramifications across
trophic levels, including on their predators (Keith et al., 1977; Krebs et al., 1995;
Hodges et al., 2001; Krebs et al., 2001a; Tyson et al., 2010). Not surprisingly, the study
of community organisation around, and various species responses to, snowshoe hare and
other cyclic mammal populations has attracted much attention (Krebs et al., 2001b).
As snowshoe hares show such a wide variation in density over the course of their
population cycles, their predators become particularly good candidates for the
measurement of predator-prey dynamics (numerical and functional responses) (Boutin,
1995).
The snowshoe hare cycle in Canada has been traced back over 200 years through
meticulous commercial fur harvest records held by the Hudson’s Bay Company
(Sinclair et al., 1993). Cycles are largely synchronous across many of the boreal forests
of North America, and are associated with predictable changes in hare reproduction and
survival (Hodges et al., 1999; Hodges et al., 2001). The mechanisms underlying the
cause of the snowshoe hare cycle have been the subject of much debate. The two main
causal factors first postulated were food (plant–herbivore hypothesis) and predation
(predator–prey hypothesis), however, these factors considered alone were not sufficient
10
to explain hare population trends (Sinclair et al., 1993; Krebs et al., 1995; Boonstra et
al., 1998). Results of experimental field studies (manipulation of food and predator
abundance) undertaken as part of a long term ecological monitoring project in the
Yukon, Canada, showed that snowshoe hare cycles were a direct result of the interaction
between food and predation suggesting a three-trophic-level interaction (Krebs et al.,
1995; Krebs et al., 2001a). The impact of predation is the dominant process. It is largely
direct and is almost always the immediate cause of hare death. The influence of food
(predominantly felt in winter) is largely indirect and relates to food quality (as opposed
to quantity). When the nutritional quality of food is reduced, hare reproduction output
can be adversely affected (O'Donoghue, 1994; Krebs et al., 1995; Krebs et al., 2001a).
1.6 The dynamic duo: Predation dynamics between coyotes and
snowshoe hares
Two studies conducted in Canada have investigated the predation dynamics of coyotes
and snowshoe hares: one in central Alberta Province (Keith et al., 1977; Todd et al.,
1981; Todd and Keith, 1983) and the other in the Yukon Territory (O'Donoghue et al.,
1997; O'Donoghue et al., 1998a; O'Donoghue et al., 1998b). These studies are reviewed
in detail in Chapter 2, section 2.5. In brief, both studies demonstrated that: snowshoe
hares are a key prey item for coyotes; coyote populations cycled in response to cycling
snowshoe hare populations; and coyote populations exhibited a predator lag of one year.
Apart from these two studies, the coyote has received little attention in terms of its
interaction with snowshoe hares in northern North America, compared to its ecological
counterpart, the Canada lynx.
1.6.1 Coyote prey preferences
Typically coyotes exhibit a broad diet, but can show strong preferences for particular
mammalian prey. The main prey species for Canadian (and Alaskan) coyotes are
snowshoe hares (O'Donoghue et al., 1998a; O'Donoghue et al., 1998b; O'Donoghue et
al., 2001; Prugh, 2005) and white-tailed deer (Odocoileus virginianus) (Patterson et al.,
1998; Patterson and Messier, 2001). Agricultural carrion, where available, are also a key
prey item for coyotes (Nellis and Keith, 1976). Additionally, a range of alternative prey
are sought when densities of preferred prey are low, for example during the low and
11
increasing phases of the snowshoe hare population cycle (O'Donoghue et al., 1998a;
O'Donoghue et al., 1998b; Prugh, 2005).
In the Yukon Territory, coyotes increase their predation of red squirrels (Tamiasciurus
hudsonicus) and voles (Clethrionomys sp. and Microtus sp.) when snowshoe hares
become scarce (O'Donoghue et al., 1998a; O'Donoghue et al., 1998b). However, the
availability of these small mammals can be limited. Squirrels are able to escape
predation by climbing trees and spending much time in their arboreal nests, while voles
are somewhat protected in their nests under the snow (O'Donoghue et al., 1998a;
O'Donoghue et al., 1998b).
1.6.2 Are coyotes specialist or generalist predators?
A generalist predator is one that indiscriminately consumes a wide range of prey items,
typically in the same relative proportions as they are available. By contrast, a specialist
predator relies on one or a few prey species (Sinclair et al., 2006). These terms are
generally not well defined in their practical application to the predation habits of species
(Prugh, 2005). For example, a specialist predator may rely predominantly on one prey,
but will also consume a range of alternative prey. Thus, there remains uncertainty as to
how broad a predator’s diet must be in order for it to be considered a generalist (Prugh,
2005).
A dichotomy in opinion exists in relation to whether or not coyotes are generalist or
specialist predators. The characteristics of broad diet, opportunistic foraging, and
flexibility as predators are hallmarks of canids (Bekoff, 1978; Newsome et al., 1983;
Gese et al., 1996a; Conover, 2001; Macdonald and Sillero-Zubiri, 2004). As coyotes
commonly exhibit these traits, they have typically been classified as generalists. Despite
this, coyotes in Canada have shown strong specialisation for prey species, namely
snowshoe hares (Todd et al., 1981; O'Donoghue et al., 1997; O'Donoghue et al., 1998b)
and white-tailed deer (Patterson et al., 1998). Coyote prey specialisation is particularly
evident in low-diversity ecosystems such as those of the Canadian boreal forests where
choice of alternative prey is limited (Todd et al., 1981; O'Donoghue et al., 1997;
O'Donoghue et al., 1998a). In these ecosystems, coyotes have become known as
facultative (contingent) specialists (O'Donoghue et al., 1997; O'Donoghue et al., 1998b;
Prugh, 2005).
12
1.6.3 Environmental influences on coyote predation of hares
Particular winter conditions such as weather severity, snow depth, and snow hardness
have been shown to influence coyote hunting efficiency (Todd et al., 1981; Patterson et
al., 1998; Prugh, 2005). Coyotes can be disadvantaged in snow because they have a
high foot load (low foot-surface to body-weight ratio) and can readily sink if the snow is
too deep and soft. These conditions can adversely influence coyote foraging and hunting
ability and success in relation to snowshoe hares (Keith et al., 1977; Todd et al., 1981;
Murray and Boutin, 1991; O'Donoghue et al., 1998b). Conversely, increased snow
depth can increase the coyote’s predation success on white-tailed deer fawn, which
become vulnerable under these conditions (Patterson et al., 1998).
1.6.4 The responses of coyotes to changing hare densities
Predators exhibit two key responses to changes in densities of their prey and these are
termed the numerical response and the functional response. These responses and their
pertinence to coyotes are described in detail in Chapter 2.
1.7 Significance of this study
The influence of climate on terrestrial carnivorous predators and their mammalian prey
remains poorly understood. Further, there remains a lack of dedicated studies on the
mechanisms underlying the numerical response of the Canidae family of carnivores.
This study aims to address these knowledge gaps. The relationship between the
numerical response of predators to prey has been mathematically described (for
example see Hone and Clutton-Brock, 2007). Some studies have expanded further to
incorporate both prey density and predator density, lending support for the preydependent and predator-dependent hypothesis of predator dynamics (Hone et al., 2007).
These studies, however, have not fully investigated the extrinsic mechanisms underlying
those numerical responses and the addition of parameters into models to test for effects
of climate on predator-prey dynamics remains lacking. Indeed, very little theoretical
research appears to have been undertaken to investigate the effect of prey and climate
on the numerical response of predators, and this has not at all been undertaken for
coyotes.
13
This thesis extends the work of O’Donoghue et al. (1997) to investigate whether climate
as an extrinsic factor has an influence on the numerical response of coyotes in the
Kluane region of the Yukon Territory, Canada. Therefore, this thesis addresses the
above knowledge gaps. In addition, this study develops and evaluates mathematical
models to elicit these relationships and provides a novel and constructive example of the
model selection procedure, as applied to wildlife population dynamics.
By addressing these knowledge gaps and fulfilling the study’s aims, this research also
extends upon and provides an important contribution to a major renowned long-term
ecosystem scale study. The Kluane Ecological Monitoring Project (KEMP) investigates
the ecosystem dynamics of a boreal forest in Canada. The primary objectives of the
KEMP are to: (a) serve as an early warning system of significant changes taking place
to guide future management and research; (b) provide long-term baseline information
on an undisturbed forest site that is of value to many researchers and park and forest
management; and (c) document important long-term ecological interactions and
processes that drive the boreal forest ecosystem (Henry et al., 2007). By addressing
climate as an important extrinsic factor influencing the population dynamics of the
coyote in the Kluane ecosystem, this research fills an important knowledge gap in the
existing KEMP work. In particular it fulfills the KEMP objectives (a) and (c) above.
1.8 Aims and objectives
The overarching aim of this research is to evaluate the influence of climate on the
numerical response of a mammalian predator in the Canadian boreal forest, using the
coyote as the subject predator and snowshoe hares as the subject prey. Determining,
through model selection procedures, which climate variables most influence the coyote
numerical response and in what way, are key components of this aim. A further aim is
to examine the potential biological and ecological consequences of any such influences,
as knowing these may aid in determining the likely demographic mechanisms
underlying the predator’s numerical response.
14
The specific research objectives are:
1.
To develop a set of a priori hypotheses expressed mathematically as models to
investigate the influence of both large-scale and local climate variables on the
numerical response of coyotes to snowshoe hare abundance, and;
2.
To evaluate the hypotheses using model selection procedures to elicit any such
influences.
1.9 Thesis structure
This thesis follows an introduction, methods, results and discussion format. Following
this introductory chapter, chapter two (Responses) introduces the numerical and
functional responses of predators to their prey and examines some of the difficulties
often encountered in measuring these responses for highly mobile terrestrial predators
such as canids. It then provides a comprehensive review of the studies undertaken to
date on these responses for coyotes in Canada. Chapter three (Models) describes in
detail the ecological basis upon which hypotheses were developed, provides
justification for the selection and use of climate indices, presents the candidate set of
models, and describes the model selection methods. Chapter four (Methods) describes
the study site, the methods of field data collection, and the source and form of climate
data. Chapters five and six (Results) present the results of the model selection analyses
by climate variable and by candidate model respectively. Chapter seven (Discussion)
explores the significance of the results in the context of the theoretical and practical
implications of the study, addresses the stated aims and research objectives, and
articulates on further avenues for study.
15
CHAPTER 2: THE RESPONSES OF PREDATORS TO THEIR PREY
2.1 Introduction
Predators exhibit two key responses to differing prey densities: numerical response and
functional response (Holling, 1959). These responses form the basis of the theoretical
and empirical understanding of how predators and prey affect the population dynamics
of each other (Boutin, 1995; Sinclair et al., 2006). Central to this thesis is the numerical
response of coyotes to their key prey, snowshoe hares, and the influence of climate on
that relationship. Having an understanding of both responses, however, is pivotal to
interpreting the predator-prey interactions between the species. This chapter first
provides an explanation of both the numerical and functional responses. It examines the
difficulties inherent in defining these responses for mobile terrestrial mammals such as
coyotes, then provides a review of these responses as documented for Canadian coyote
populations.
2.2 Numerical response
The numerical response was first described as the increase in numbers of animals as
their resources increased (Solomon, 1949). The term has subsequently evolved to have
a number of definitions as authors have applied it to different relationships (Sibly and
Hone, 2002). For example, the term ‘numerical response’ has been used to describe: the
effect of food availability on fecundity (May, 1974 in Sibly and Hone, 2002); the effect
of food availability on the rate of amelioration of population decline (Caughley, 1976 in
Sibly and Hone, 2002); and the relationship between annual population growth rate and
food availability (Bayliss and Choquenot, 2002; Sinclair and Krebs, 2002; Hone et al.,
2007). One study expanded further on these concepts to describe the numerical response
of a predator as the relationship between predator population growth rate and both prey
density and predator density (Hone et al., 2007).
Notwithstanding the differing definitions of numerical response, two main forms are
recognised (Figure 2.1). The first is termed the ‘Solomon’ numerical response, the
general form of which is expressed as predator density as a function of prey or food
availability (Bayliss and Choquenot, 2002; Sinclair and Krebs, 2002) (Figure 2.1(a)).
16
The second is termed the ‘Caughley’ or ‘demographic’ numerical response, where
population growth rate is expressed as a function of prey or food availability (Bayliss
and Choquenot, 2002; Sibly and Hone, 2002; Sinclair and Krebs, 2002) (Figure 2.1(b)).
Central to this thesis is the Solomon form of the numerical response and the influence of
climate on that relationship.
(b)
Predator density
Population growth
rate
(a)
Prey density
Food availability
Figure 2.1 Examples of numerical response forms: (a) termed ‘Solomon’ where predator density is a
function of prey density; and (b) termed ‘Caughley’ or ‘demographic’ where predator population growth
rate is a function of food availability.
A numerical response can occur when there are changes in the rates of reproduction and
survival of predators in response to changes in prey density (O'Donoghue et al., 2001;
Sinclair et al., 2006; Krebs, 2009). A typical numerical response would be an increase
in predator density/population growth rate in response to an increased prey density.
As more prey are available, more predators survive and reproduce, which in turn, eat
more prey (Sinclair et al., 2006). Numerical responses tend to be more pronounced in
specialist predators due to the often strongly correlated predator–prey population
fluctuations (Crawley, 1975).
A further mechanism by which a numerical response can occur is by movement. This is
referred to as an aggregative response and results from movements or concentration of
highly mobile predators into areas of high prey density (Krebs, 2009). Such a response
has been demonstrated for coyotes preying on highly concentrated densities of
snowshoe hares in the Yukon Territory and the Alberta Province of Canada (Todd et al.,
1981; O'Donoghue et al., 2001).
17
2.3 Functional response
The functional response was defined by Holling (1959) as an increase in the number of
prey consumed per unit time in response to increasing prey population density. Hence,
the functional response is the feeding behaviour of individual predators, and measures
how many prey it eats in a given time period (Sinclair et al., 2006; Krebs, 2009). There
are three general types of functional responses recognised (Figure 2.2).
A Type I functional response (Figure 2.2) assumes a linear relationship between the
number of prey eaten per predator and prey density. This response assumes a predator
constantly searches for prey and has an unlimited appetite (Sinclair et al., 2006).
Despite some predators seeming to conform to a Type I response at lower prey
densities, the assumptions of this response are considered unrealistic as it is unlikely a
predator has an unlimited appetite, and in any event, still requires time to search for,
Prey eaten per predator
per unit time
kill, eat, and digest their prey (Sinclair et al., 2006).
Type II
Type III
Type I
Prey density
Figure 2.2 Predator functional response types: Type I assumes constant eating and no satiation point;
Type II and Type III assume satiation points at high prey densities. Axes values are hypothetical. (Figure
source: Ganter and Peterson, 2006).
18
A Type II functional response (Figure 2.2) involves an initial rapid increase in the
number of prey eaten per unit of time, rising to an asymptote at higher prey densities
(Sinclair et al., 2006). The response line plateaus out across some range of high prey
density, as the predator becomes satiated (Krebs, 2009). The Type II response is typical
of specialist predators: predators that rely predominantly on a few prey species.
A Type III functional response (Figure 2.2) is described by a sigmoidal curve and shows
an initial slow increase in the number of prey eaten per predator at low prey densities,
an increasing number of prey eaten at intermediate prey density, leveling off again at
higher densities (Sinclair et al., 2006). The Type III response is typical of generalist
predators, and can be described by a number of mechanisms including: prey switching
by predators; changes in the vulnerability or behaviour of prey; and/or increased
predation efficiency (skill) with increasing prey density (Keith et al., 1977; O'Donoghue
et al., 1998b; Sinclair et al., 2006).
2.4 The measurement of numerical and functional responses of canids:
shortfalls and pitfalls
To measure a numerical response, predator density or population growth rate is plotted
as a dependent variable against prey density or food availability at appropriate spatial
scales (O'Donoghue et al., 1997; Sinclair et al., 2006; Hone et al., 2007). Demographic
mechanisms (for example reproduction, survival, fecundity, movement) behind the
response are concurrently measured and used to explain any trend. Likewise, describing
the functional response requires that the number of prey killed per predator be known
(Boutin, 1995). As a predator’s functional response is influenced by predator travel
rates, reactive distances, capture success, and foraging and handling time, these factors
should also be measured (Boutin, 1995; O'Donoghue et al., 1998b; Sinclair et al., 2006).
Many predator response studies tend to infer the numerical or functional responses by
using scat count and scat and stomach content analysis, whereby it is assumed that a
change in scat density and food habits respectively represents a numerical or functional
response (for example Keith et al., 1977). As Boutin (1995) points out, however, the
methods of such studies can be biased, and their findings should therefore be interpreted
with caution. For example, although observed changes in the proportion of a given prey
19
item in the diet derived from scat and stomach content analysis may be a reasonable
indication of predatory dietary shifts over intermediate prey densities, it is less likely to
be so at high and low prey densities (Boutin, 1995). Hence, when a functional response
is derived from diet composition alone, it can affect the shape of the functional response
curve by lending support to predator satiation (Boutin, 1995).
Several dedicated studies on the numerical and functional responses of coyotes to
snowshoe hares in Canada have been undertaken (Keith et al., 1977; Todd et al., 1981;
Todd and Keith, 1983; O'Donoghue et al., 1997; O'Donoghue et al., 1998b). These
studies represent perhaps the first of their kind in respect of their aims to directly
quantify the true responses of this canid species, and describe the demographic and
behavioural mechanisms behind those responses. These studies were limited, however,
in their ability to obtain the demographic information required to explain the numerical
response trend. The factors described above that influence the numerical and functional
response are inherently difficult to obtain, largely due to the cryptic nature of canids and
the innate difficulties associated with field studies of large, highly mobile mammals
over large spatial and temporal scales. Further, there is often an inability to accurately
determine the shapes and significance of functional response curves due to the typically
low number of observations (small sample sizes) and lack of replication (Boutin, 1995;
O'Donoghue et al., 1998b; Marshal and Boutin, 1999).
Explicit demographic data are not, however, categorically required to measure a
predator’s numerical response. Hone and Sibly (2002) compared the Caughley-type
numerical response of a barn owl (Tyto alba) population to their food (field vole)
availability, estimated by two methods: the first using annual census (count) data, and
the second using demographic (annual adult survival, juvenile survival, and fecundity)
data. The results were very similar, showing strong support that a predator’s population
dynamics are directly linked to food via the population’s demographics (Figure 2.3).
Barn owl annual finite
population growth rate
20
Field vole abundance
Figure 2.3 A comparison of the Caughley-type numerical response of barn owls to field voles, estimated
by two methods: from census data (solid line); and demographic data (broken line) (from Hone and Sibly,
2002 p. 1175).
Marshal and Boutin (1999) evaluated the sample size required to soundly (statistically)
distinguish between the shapes of functional response curves (namely Types II and III)
in previously published grey wolf and moose predation data. They found that in order to
achieve adequate statistical power (defined as 1 – ß, where ß is the probability of failing
to reject the null hypothesis that both models fit the data set equally well), far less
variance and considerably larger sample sizes than that likely attainable for such wolfmoose predation studies are required. That is, sample sizes of no less than n=70 are
required, whereas currently published wolf-moose studies have sample sizes of
n=11 to 14 (Marshal and Boutin, 1999). Coyote predator dynamics studies are also
limited by small sample sizes (e.g. n=8).
Furthermore, Marshal and Boutin (1999) found that in many past studies looking at
predator functional response, the evaluation of the response type (i.e. the shape of the
curve) was commonly made by visual inspection of the data. Some authors have tried to
establish the inadequacy of a particular model shape by using least-squares methods to
fit a model, but then failed to reject the null hypothesis that the model does not fit the
data (Marshal and Boutin, 1999). Using this latter approach when dealing with highly
variable systems or small sample sizes—circumstances typical of canid predator-prey
studies—can lead to the erroneous conclusion that the model for the curve applied does
not fit the dataset, even if the underlying distribution can, in fact, be described by the
model (Marshal and Boutin, 1999).
21
2.5 The numerical and functional responses of Canadian coyotes to their
prey: A review
The first study to quantify the numerical and functional responses of coyotes in Canada
was that of Keith et al. (1977). The aim of that study was to specifically describe the
responses of coyotes (and a number of other predators) to fluctuating densities of
snowshoe hares over the course of an entire snowshoe hare cycle. The study was
undertaken in the boreal forest of the Rochester district (part agriculturally cleared),
central Alberta, and spanned 10 years. Coyote density was estimated from aerial survey
counts and trapping. Scat and stomach content analysis were used to obtain percent
biomass of snowshoe hare in the coyote diet, from which a kill rate (number of prey
individuals killed in a given time: functional response) was estimated (refer Keith et al.,
1977 p. 155–156 for formulae applied).
Coyotes showed strong numerical and functional responses to fluctuating snowshoe
hare densities (Keith et al., 1977). Coyote density increased 4-fold during the increase
phase of the hare cycle, and peaked concurrently with peak snowshoe hare density. The
coyote population then declined 6-fold, although with a lag, following snowshoe hare
decline. The marked numerical response of coyotes demonstrated in this study was in
keeping with the widely accepted view that cyclic fluctuations of snowshoe hares as key
prey items can be responsible for the respective comparable fluctuations of their
primary predators (Keith et al., 1977).
The population ecology and demographic mechanisms underlying the observed
numerical response of coyotes found by Keith et al. (1977) were described by Todd et
al. (1981) and Todd and Keith (1983). These studies measured coyote reproduction,
survival, and body condition to help explain the observed numerical response.
A progressive reduction in reproduction (ovulation rate, pregnancy rates, and litter
sizes), reduced recruitment, and lower body condition in the coyote population as
snowshoe hare numbers declined was found. As hare densities increased and peaked, an
aggregative response (movement) of coyotes was indicated (Todd et al., 1981; Todd and
Keith, 1983).
In terms of the functional response, Keith et al. (1977) found trends in percentage
biomass of hare in the coyote diet directly paralleled trends in hare density. That is,
22
coyotes responded to an increase in hare abundance with an increase in killing rates.
The functional response was found to be sigmoid in shape, and conform to a Type III
curve, in keeping with a generalist predator. The authors cited increased hunting
efficiency as responsible for the trend. As hare density increased, a network of wellpacked trails and runways were formed in the snow, facilitating increased traveling and
hunting efficiency (Keith et al., 1977). As hare density declined, a shift in diet to
livestock carrion in nearby agricultural lands (and hence, a shift in habitat use) was also
observed (Todd et al., 1981). Unfortunately, no statistical comparison (linear versus
curvilinear) was made of the fit obtained by Keith et al. (1977), and satiation was based
on a single critical point (Boutin, 1995). Further, the sample size of this study was small
(n=8). It is also pertinent to note that the kill rate estimate used to calculate the
functional response by Keith et al. (1977) may have been inaccurate as it assumed that
coyotes never scavenged or cached hares. Scavenging and caching of prey by canids,
including coyotes, has since been well documented (Bekoff, 1978; O'Donoghue et al.,
1998b; Macdonald and Sillero-Zubiri, 2004).
Other studies on the numerical and functional response of coyotes in Canada are those
of O’Donoghue et al. (1997) and O’Donoghue et al. (1998b). These studies were
undertaken as part of the Kluane Ecological Monitoring Project which over 25 years
ago set out to examine the vertebrate community dynamics of the boreal forest in
Canada (Krebs et al., 2001b). These studies were conducted in the southwest Yukon
Territory between 1986 and 1997 and measured the responses of both coyotes and
Canada lynx relative to a full snowshoe hare population cycle. Coyote population
density was estimated using snow-tracking, radio-tracking, and trapping (O'Donoghue
et al., 1997). Scat analysis was used to analyse diet, and calculation of the kill rate
(functional response) was made by incorporating predator travel rates and activity
patterns by tracking and telemetric monitoring (O'Donoghue et al., 1998b). These
studies appear to be the most explicit conducted to date in terms of the factors measured
and subsequently used to explain the observed responses.
Both coyotes and lynx in the Yukon demonstrated a strong numerical response to the
fluctuating snowshoe hare abundance, directly correlated with hare numbers the
previous year (O'Donoghue et al., 1997) (Figure 2.4). The overall amplitude of the
coyote population change over the cycle was 6-fold. Emigration rates and loss
23
(presumed emigrated) of radio-collared coyotes was found to be high, but no clear
relationship was found between emigration and prey abundance. Reproduction was
unable to be directly measured, however the authors observed reduced recruitment
associated with the decline of the coyote population (O'Donoghue et al., 1997).
Insufficient data were obtained to enable survival to be measured.
(b)
Lynx per 100 km
2
Coyotes per 100 km
2
(a)
Hares per 100 ha in previous winter
Hares per 100 ha in previous winter
Figure 2.4 Numerical response of (a) coyotes and (b) lynx to snowshoe hares in the Yukon, Canada,
showing strong correlation with hare density the previous winter. Numbers next to data points indicate
years (1987–1993). Source: O’Donoghue et al. (1997; Figures 5 and 6, p. 155).
Coyotes in the Yukon also exhibited a strong functional response to changes in
snowshoe hare abundance (O'Donoghue et al., 1998b). Coyotes responded to the
increasing snowshoe hare abundance with increased kill rates, and were shown to kill
more hares than was energetically required when hare abundance was high. Caching by
coyotes was common, particularly during the increase phase of the hare cycle. When
snowshoe hare abundance was low, coyotes increasingly preyed on alternative prey
(which were coincidently abundant) and scavenged cached hare carcasses. The
functional response of coyotes to snowshoe hares was shown to conform equally well to
both the Type I and Type II forms.
As with the study of Keith et al. (1977), no statistical comparison was made between
the shape of the functional response curves obtained by O’Donoghue et al. (1998b). The
inability to do so was a legacy of the experimental design, which was unable to
24
incorporate replication and had very few data points (n=8). Further to this was the
inability to calculate a measure of variance, and hence estimate the precision, of kill
rates used to devise the functional response (O'Donoghue et al., 1998b).
2.6 Summary
Notable research has been undertaken to elicit the numerical and functional responses of
Canadian coyotes to their key prey snowshoe hares. Such studies are inherently difficult
to carry out as they deal with a cryptic and highly mobile terrestrial mammal, and
require field studies over large spatial and temporal scales with little opportunity to gain
adequate sample sizes or replication. The legacy of these limitations to the experimental
design introduces bias and reduces the statistical power required to soundly differentiate
between functional response types.
Despite their limitations, the studies to date on coyote numerical and functional
responses represent perhaps the most comprehensive studies of their type for this Canis
species. These studies are novel examples of research that integrates both predator-prey
theory and real (empirical) data, and provide important benchmark information on the
predator-prey interactions of coyotes in the boreal forests of Canada.
Although the study of O’Donoghue et al. (1997) lacked in its ability to obtain the
information required to demographically explain coyote numerical response, changes in
coyote density have shown to be mechanistically related to variation in their food
supply (snowshoe hares). As was demonstrated by Hone and Sibly (2002), the use of
the demographic and mechanistic approaches to estimate a predator’s numerical
response can yield analogous results (Figure 2.3).
The study by O’Donoghue et al. (1997) is the foundation of this thesis, with the
reported numerical response of coyotes at Kluane in the Yukon Territory as the
ecological starting point. The following chapter describes the ecological context within
which this study’s hypotheses (models) of coyote numerical response, prey density, and
climate are developed, presents the candidate set of numerical response models, and
describes the model selection procedure applied.
25
CHAPTER 3: MODELS
3.1 Model development
3.1.1 Description and assumptions
A number of competing hypotheses expressed as mathematical models were developed
a priori. The use of model selection procedures to analyse data and make biological
inferences in the field of ecology has gained in popularity over recent time (Johnson and
Omland, 2004). Model selection provides a valid and robust alternative to traditional
null hypothesis testing, and allows a number of plausible competing hypotheses to be
tested simultaneously (Johnson and Omland, 2004; Anderson, 2008).
The ecological starting point for model development was the numerical response of
coyotes to changes in the abundance of their key prey, snowshoe hares (O'Donoghue et
al., 1997) (models 1 and 4 described below), and the effect of climate on that
relationship (models 2, 3, 5 and 6 described below). The use of the numerical response
in this study is an example of the mechanistic paradigm which identifies the effects of
an ecological factor (food) and an extrinsic factor (climate) on a predator population’s
abundance (Krebs, 2002). All models are based on the Solomon-type numerical
response with linear, non-linear, additive, and interactive (multiplicative) relationships
postulated between predator density, and prey density and climate. O’Donoghue et al.
(1997: Figure 5, p. 155) found coyote numbers to be strongly correlated with hare
numbers the previous year (Spearman rank correlation coefficient=1.00; P < 0.001).
Hence, models assume coyote density is related to hare density in this manner. A one
year delay between the forces associated with the climate variables of interest and the
ecological response is also assumed.
When applying an information-theoretic approach to make valid inferences from the
analysis of empirical data, it is pivotal to ensure candidate models have an ecological
basis—that is, they are well supported by underlying science (Burnham and Anderson,
2001; Johnson and Omland, 2004; Anderson, 2008). A key component of model
development, therefore, was to determine which climatic factors are likely to influence
the numerical response of the coyote relevant to its snowshoe hare prey, and how these
factors are expected to influence the relationship. Models were articulated based on an
26
understanding of the chosen climatic factors and their potential effect on the predatorprey interaction of interest.
The ecological context within which model development for this study took place
largely arose from past and present studies that investigated the influence of climate on
the Canada lynx. In the Yukon Territory coyotes and lynx are considered ecological
counterparts (O'Donoghue et al., 2001). Both are of similar size, rely heavily on
snowshoe hares as a key prey resource, and both show similar strong numerical and
functional responses to hares (O'Donoghue et al., 2001).
3.1.2 Ecological context: Historical background
An influence of climate on the Canada lynx cycle was initially proposed over five
decades ago (Moran, 1953a; Moran, 1953b). Moran (1953a) undertook statistical
analysis of the Canada lynx cycle using fur trapping records and found it to be a classic
predator-prey relationship: i.e. as the lynx feeds almost exclusively on snowshoe hares,
lynx population density was directly related to hare population density. Conceding that
this relationship alone cannot account for the strong synchronisation of lynx–hare cycles
across Canada, Moran further reasoned that the cycle must be somehow influenced by
large-scale climate phenomena (Moran, 1953b). He tested this and found a significant
negative effect of minimum winter temperatures on the lynx cycle. The potential
mechanisms underlying the relationship were not directly measured, but were
hypothesised by Moran (1953b) to be due to either a direct influence of temperature on
lynx birth and death rates, or the effect of climate on snowshoe hare survival via their
own food supply, and subsequently lynx food supply.
Watt (1973) later correlated Moran’s lynx data with an index of global mean
temperatures, and in so doing, demonstrated a statistical relationship between this index
and the lynx cycle. A negative effect of minimum global temperatures on lynx density
was indicated. The extreme minimum global temperatures plotted by Watt (1973) were
coincident with major volcanic eruptions. Watt surmised that: (i) minimum global
temperatures, and therefore increased snowfall, were forced by volcanic eruptions;
(ii) this increased snowfall had a negative impact on the survival of snowshoe hare
offspring; (iii) this in turn resulted in reduced hare prey available to the lynx; and
(iv) lynx populations declined as a result (Watt, 1973). Watt tested the assumption of
27
reduced hare survival due to increased snowfall by correlating log-transformed
snowshoe hare census data collected from Lake Alexander, Minnesota, USA by Green
and Evans (1940) with snowfall records obtained from two stations located 32 km and
201 km respectively from the hare census collection site. A trend of reduced juvenile
hare survival relative to increased total snowfall the year prior for both stations was
indicated. However, the significance or otherwise of the relationship was not stated, and
no explanation provided as to the possible mechanistic factors involved.
Despite this early interest in the potential effects of climate on lynx-snowshoe hare
dynamics, the topic received little subsequent attention, until recent times.
3.1.3 Ecological context: The current state of knowledge
Despite their status as a keystone species across their boreal forest range, and their longepitomised place in population ecology teachings, surprisingly little research has been
undertaken to investigate the potential influence of climate on snowshoe hare
population dynamics since that of Watt (1973) described above. The most notable
subsequent study is that of Sinclair et al. (1993), who found a strong correlation
between sunspot activity and snowshoe hare reproductive output in Yukon Territory
hare populations. The precise mechanism underlying this relationship remains unclear,
but it was hypothesised to relate to snow depth. Sunspots influence the weather in
northwestern Canada which, in turn, influences snow depth (Krebs and Berteaux, 2006).
Variation in snow depth could indirectly influence hare reproductive output in two
ways: either by influencing the availability or otherwise of food to the hares, thus,
affecting hare nutrition and reproduction; or by influencing predator (lynx and coyote)
hunting behaviour and success (Sinclair et al., 1993; Krebs and Berteaux, 2006).
Warmer winters may provide a longer vegetation growing season, which is typically
short in the Kluane region, and this may, in turn, influence hare reproduction and
survival through access to increased winter food supply. Although there is little
evidence to support the proposition that limited winter food supply alone limits
snowshoe hare populations, winter food supply does play an important role in hare
mortality and reproductive output at higher hare densities (Krebs et al., 2001).
With respect to predators, there is now strong evidence to show that both coyotes and
lynx can be affected directly by certain winter conditions. In particular, weather
28
severity, snow depth and hardness influenced by temperature, precipitation, and climatic
extremes of these have been shown to influence coyote and lynx hunting efficiency and
success (Bekoff, 1978; Todd et al., 1981; Murray and Boutin, 1991; Gese et al., 1996b;
O'Donoghue et al., 1998b; Patterson et al., 1998; Stenseth et al., 1999; Crête and
Larivière, 2003; Rueness et al., 2003; Macdonald and Sillero-Zubiri, 2004; Stenseth et
al., 2004a; Stenseth et al., 2004b; Prugh, 2005). Coyotes can be particularly
disadvantaged in snow because, unlike lynx which are morphologically adapted to the
far northern hemisphere winter conditions, they have a high foot load and can readily
sink if the snow is too deep and soft (Murray and Boutin, 1991). These conditions, in
turn, can adversely influence coyote foraging and hunting ability and success in relation
to snowshoe hares (Keith et al., 1977; Todd et al., 1981; Murray and Boutin, 1991;
O'Donoghue et al., 1998a; Thibault and Ouellet, 2005).
A negative effect of climate on coyote numerical response, therefore, may occur in
winters of increased snow depth. Such conditions can adversely influence coyote
hunting ability and, ultimately, coyote survival, reproductive output and fecundity.
A positive effect of climate on coyote numerical response might be seen with much
colder winters which may reduce snowfall and snow depth. Extreme maximum winter
temperatures could increase snow hardness by the process of thaw-refreeze, while
extreme minimum winter temperatures could limit the amount of snowfall and depth.
These conditions could, in turn, positively influence coyote hunting ability.
3.1.4 Justification for climate indices
The Yukon Territory climate is dominated by very cold winter conditions. The area
typically has continued snow coverage from October through May, though highpressure systems in winter tend to predominate and the resultant very cold weather can
limit the amount of snowfall (O'Donoghue et al., 1997; Krebs et al., 2001b). The
prevailing winter temperatures, and particularly the frequency and intensity of extreme
warm and cold spells, as well as precipitation, are important factors in determining
snow properties including its hardness (defined as resistance to penetration of an object
into; Colbeck et al., 1990). Local climate variables and large-scale climate indices were
chosen for evaluation, as both are known to directly or indirectly influence the
abundance and distribution of species and ecological processes (Stenseth et al., 2002;
Stenseth et al., 2003; Krebs, 2009). The local climate variables chosen for this study
29
were mean winter temperatures (including extreme minimum and maximum winter
temperatures), winter snow depth, winter rain, and winter precipitation.
Large-scale climate patterns (or modes) represent the dominant sources of global-scale
climate variation and are known to considerably influence ecological processes through
their often profound influence on weather and climate over much of the globe on an
interannual, interdecadal or longer time scale (Ottersen et al., 2001; Hurrell and Deser,
2009). In contrast to local climate variables which are quite specific, large-scale modes
imply information about temperature, wind, cloudiness, precipitation, storms—and
extremes of these—and, in the case of marine systems, hydrography. Therefore, such
modes provide an integrated measure or ‘package’ of weather (Aanes et al., 2002;
Stenseth et al., 2003; Hurrell and Deser, 2009). As such, they have the potential to be
linked more closely to the overall physical variability of a system than any individual
local variable (Hallett et al., 2004; Hurrell and Deser, 2009). Given populations are
likely to be affected by more than a single weather variable, large-scale climate modes
are increasingly becoming regarded as good proxies for overall climate condition.
Indeed, in some cases these modes have been found to be better predictors of ecological
processes than local climate (Ottersen et al., 2001; Aanes et al., 2002; Stenseth et al.,
2003; Hallett et al., 2004).
The large-scale climate phenomena selected for analyses were the North Atlantic
Oscillation (NAO), the El Niño-Southern Oscillation (ENSO), the Pacific/North
American (PNA), and the North Pacific Index (NPI). Each of these, described in detail
below, are known to influence the climate across Canada (Trenberth and Hurrell, 1994;
Hurrell, 1996; Stenseth et al., 1999; Ottersen et al., 2001; Stenseth et al., 2002; Stenseth
et al., 2003; Deser et al., 2004; Stenseth et al., 2004b; NOAA, 2005; NOAA, 2010;
Environment Canada, 2010a).
North Atlantic Oscillation (NAO)
The NAO refers to the redistribution of atmospheric mass (changes in the atmospheric
sea level pressure difference) between the Arctic and the subtropical Atlantic (Hurrell et
al., 2003). The NAO is one of the most prominent and recurrent teleconnections and,
thus, leading patterns of weather and climate variability over the northern hemisphere.
Patterns of the NAO are of largest amplitude during the boreal winter months (Hurrell
30
and Deser, 2009). The NAO exerts a dominant influence on wintertime temperatures,
and swings from a negative or positive phase to the other produce large changes in heat
and moisture transport, and intensity and frequency of wind, precipitation and storms
across much of the northern hemisphere including the USA and Canada (Hurrell et al.,
2003; Hurrell and Deser, 2009).
Three climatic regions of Canada were defined by Stenseth et al. (1999) based on the
spatial influences of the NAO: the Atlantic, Continental, and Pacific regions
(Figure 3.1). The NAO produces a differential effect of surface winter temperatures
from east to west across the Atlantic and Continental regions (Stenseth et al., 1999).
During the positive phase of the NAO (i.e. surface pressures are lower than normal near
Iceland and higher than normal over the subtropical Atlantic), eastern Canada
experiences cooler surface temperatures, while warmer surface anomalies are seen over
the Continental region, with opposite effects during the negative phase (Stenseth et al.,
1999; Mysterud et al., 2003).
Stenseth et al. (2004b) found a difference in climatic conditions across Canada between
the positive and negative phases of the NAO (Figure 3.2). A positive NAO phase leads
to a lower frequency of warm spells in the Atlantic region and a correspondingly higher
frequency of warm spells in the Continental region, with opposite effects during a
negative NAO phase (Stenseth et al., 2004b). This differentiation of climate conditions
between east and west Canada leads to a corresponding difference in snow surface
properties, namely hardness, as determined by the frequency or otherwise of warm
spells. Such differences in temperature and snow condition may act mechanistically to
influence the interaction between predator and prey (Stenseth et al., 2004b).
31
Difference in frequency of winter warm spells
between opposite polarity of the NAO.
Figure 3.1 The three climatic regions of Canada based on spatial influences of the NAO, defined by
Stenseth et al. (1999 p.1072).
Figure 3.2 Composite difference in the frequency of winter warm spells across Canada between the
positive and negative phases of the NAO during winter. X=locations (stations) that exhibited a
statistically significant (P<0.05) difference (from Stenseth et al., 2004b, p. 10633).
32
A difference in Canada lynx population dynamics across these three climatic regions,
and with region-specific winter conditions (namely surface temperatures and snow
condition) defined by the NAO, was hypothesised by Stenseth et al. (1999; 2004b).
They proposed that the climate influenced by the NAO was affecting lynx hunting
behaviour and success, suggestively through snow depth, hardness, and structure. As a
result, lynx population cycles were found to be more alike (i.e. had the closest related
dynamic structure) within each of the climatologically based regions shown in
Figure 3.1 (Stenseth et al., 1999; Mysterud et al., 2003; Stenseth et al., 2004b).
A genetic differentiation between Atlantic and Continental region lynx populations was
found by Rueness et al. (2003) despite the absence of any physical geographic barrier
between these regions. This further supports the proposition that lynx population
structuring is occurring along an environmental gradient due to differences in winter
conditions and snow properties (Rueness et al., 2003; Stenseth et al., 2004a; Stenseth et
al., 2004b). It is unknown whether coyotes exhibit a similar pattern of population
structuring across Canada.
El Niño-Southern Oscillation (ENSO)
The ENSO cycle is the most prominent source of interannual climatic variation on
Earth. It originates in the tropical Pacific and leads to global-scale exchanges (swings)
of atmospheric air masses between the eastern and western hemispheres (Stenseth et al.,
2002; McPhaden, 2004). The Southern Oscillation has two opposing phases known as
El Niño (positive warm phase) and La Niña (negative cool phase), and ENSO is the
term used to describe the oscillation between these phases (McPhaden, 2004; Bureau of
Meteorology, 2010a). When an El Niño event occurs extensive warming of the central
and eastern tropical Pacific Ocean leads to a major shift in weather patterns across the
Pacific (Stenseth et al., 2003; McPhaden, 2004). The opposite conditions prevail during
a La Niña event.
The effects of the ENSO are dramatic and global scale weather changes are triggered
when an El Niño event occurs (Stenseth et al., 2003; McPhaden, 2004; Krebs, 2009).
As such, the climatic changes associated with the ENSO can have profound impacts on
terrestrial ecosystems (Holmgren et al., 2001; Stenseth et al., 2002; Stenseth et al.,
2003; Letnic et al., 2009). During an El Niño event, drought conditions can prevail
across large areas (for example Australia, Indonesia, the Philippines, and northeastern
33
South America), whilst torrential rains might occur across others (for example the
central Pacific island states, and west coast of South Africa) (Holmgren et al., 2001;
Holmgren et al., 2006). Western Canada experiences warmer winters with less
precipitation, shallower snow depth, and less snow cover during El Niño events, with
the opposite cooler and wetter conditions seen with La Niña events (Environment
Canada, 2010a).
Pacific/North American (PNA)
The PNA is a large-scale northern hemisphere winter phenomenon which relates the
atmospheric circulation pattern in the central Pacific Ocean, with centres of action over
western Canada and the southeastern United States (Wallace and Gutzler, 1981;
Trenberth and Hurrell, 1994; NOAA, 2010). The PNA is one of the most prominent
modes of low-frequency variability in the northern hemisphere extratropics and the
large-scale atmospheric variability associated with the PNA has been shown to have
a major impact on surface climate, namely snowfall and temperature, over much of
central and western Canada (Brown and Braaten, 1998; Stenseth et al., 1999; NOAA,
2010). In particular, the positive phase of the PNA is associated with above average
temperatures over central and western Canada (NOAA, 2010). Like the NAO, patterns
of the PNA are of largest amplitude during boreal winter months (Hurrell and Deser,
2009). The PNA can be strongly influenced by the ENSO phenomenon, with the
positive PNA phase associated with El Niño episodes, and negative phase associated
with La Niña events (NOAA, 2010).
North Pacific Index (NPI)
The North Pacific is a strong teleconnection that links changes over the Pacific Ocean to
profound climatic changes over North America including Canada and Alaska (Trenberth
and Hurrell, 1994). The NPI is the measure of strength of this wintertime atmospheric
circulation and corresponds to the area-weighted sea level pressure over the north
Pacific region (Deser et al., 2004). Below normal (low) NPI values relate to a deeperthan-normal Aleutian low pressure system and are strongly associated with above
normal surface temperatures and precipitation across northwestern Canada (Trenberth
and Hurrell, 1994; Hurrell, 1996; Deser et al., 2004). Opposite conditions prevail for
above normal (high) NPI values. The NPI serves as a good proxy record for the PNA
34
teleconnection pattern, but is a much more robust measure of north Pacific circulation
(Trenberth and Hurrell, 1994; Deser et al., 2004).
Relationships between large-scale climate indices
To confirm the independence of the large-scale climate indices, correlation by leastsquares regression analysis was undertaken in SAS version 9.0 to test for any strong
relationships between them. There was a significant but weak positive relationship
(R2=0.29) between the SOI and NPI (F=8.72; df=1,21; P<0.05) and a significant but
weak negative relationship (R2=0.49) between PNA and NPI (F=20.22; df=1,21;
P<0.05) (Table 3.1).
Table 3.1 Coefficients of determination (R2) between large-scale climate indices.
NAO=North Atlantic Oscillation; SOI=El Niño-Southern Oscillation;
PNA=Pacific/North American; NPI=North Pacific Index. Degrees of freedom=1, 21.
Bold indicates significance (P<0.05).
SOI
PNA
NPI
NAO
0.01
0.07
0.09
SOI
–
0.03
0.29
PNA
–
–
0.49
35
3.2 Candidate models
Consistent with the principles of model-based inference outlined by Anderson and
Burnham (2002) and Anderson (2008), the aim was to evaluate a small number of
parsimonious models, each with a clear ecological basis. A set of six candidate models
are presented. Models contain the following symbols: Ct=coyote density at winter t;
Ht-1=hare density the autumn before winter t; Wt-1=climate variable the winter before
winter t; h=power curve exponent.
Model 1 (Figure 3.3(a)) is a linear model and assumes no effect of climate. It postulates
a simple positive relationship between coyote density (Ct) and hare density the previous
winter (Ht-1). Model 1 provides an ecological starting point against which competing
models that include an influence of climate can be compared.
Ct = a + bHt-1
(Model 1)
Model 2 (Figure 3.3(b)) assumes a positive linear effect of hare density on coyote
density, but with climate (W) influencing the slope of the relationship (for example
climate may influence hares via coyote hunting efficiency). Therefore, if
Ct = a + bHt-1
where
b = c + dWt-1
then
Ct = a + (c + dWt-1)Ht-1
therefore
Ct = a + cHt-1 + dWt-1×Ht-1
(Model 1)
(Model 2)
Hence, model 2 explores an interaction of hare density (H) and climate (W). A positive
effect of climate (i.e. d > 0) would lead to a positive influence on coyote density, while
a negative effect (i.e. d < 0) would lead to a negative influence on coyote density.
Where there is no effect of climate (i.e. d=0) model 2 reduces to model 1.
Model 3 (Figure 3.3(c)) is an additive model and assumes a linear positive effect of hare
density and climate on the intercept of the coyote-hare relationship. Hence, if
36
Ct = a + bHt-1
where
a = f + gWt-1
then
Ct = f + bHt-1 + gWt-1
(Model 1)
(Model 3)
Coyote density is positively influenced by hare density and favourable climatic
conditions, but note that the influence of climate may also be negative (i.e. g < 0), for
example related to reduced coyote hunting efficiency, and therefore, lower fitness and
reduced reproduction and survival.
Recognising that complex ecological interactions such as predator-prey dynamics may
not necessarily follow a purely linear form (May, 1986), non-linear models 4, 5 and 6
are derived by incorporating a power curve (or scaling) exponent variable (h) into linear
models 1, 2 and 3 respectively. The numerical response of coyotes to snowshoe hares in
the Yukon reported on by O’Donoghue et al. (1997, Figure 5, p. 155; Figure 2.4(a)
herein) suggested a positive curved (concave up) relationship, though this was not
formally tested. As hare density increased, so too did coyote density, but not in a strictly
linear manner.
Model 4 (Figure 3.3(d)) is a non-linear version of model 1 and also assumes no effect of
climate, but postulates a positive curved influence of hares on coyotes as indicated by
O’Donoghue et al. (1997) which is concave up if h > 1 and concave down if 0 < h < 1.
The numerical response can be curved, concave down, as shown in Figure 2.1(a).
Coyote social behaviour may generate the curve.
Ct = a + bHt-1h
(Model 4)
Model 5 (Figure 3.3(e)) takes model 2 and incorporates an exponent on both the hare
density and the interaction between climate and hare density. Model 5 postulates a
positive curved relationship between coyotes and hares, and the interaction between
hares and climate (i.e. concave up if h > 1 and concave down if 0 < h < 1). A positive
effect of climate may be a more rapid rate of coyote density increase due to increased
hunting efficiency.
Ct = a + cHt-1h + dWt-1×Ht-1h
(Model 5)
37
Model 6 (Figure 3.3(f)) assumes a positive curved effect of hares on coyote density and
an additive positive effect of climate. As with model 3, the effect of climate may also be
negative (i.e. g < 0) and may cause reduced coyote hunting efficiency resulting in
lowered fitness and survival.
Ct = f + bHt-1h + gWt-1
(Model 6)
In summary, the models capture the distinction between prey-dependent and prey-andclimate-dependent hypotheses of coyote numerical response. Models are represented
graphically in Figure 3.3.
38
(b)
Model 1
50
45
40
35
30
25
20
15
10
5
0
Ct
Ct
(a)
0
1
2
3
Positive
effect of
climate
50
45
40
35
30
25
20
15
10
5
0
4
Negative
effect of
climate
0
1
Ht-1
Model 3
(d)
Positive
effect of
climate
50
45
40
35
30
25
20
15
10
5
0
Negative
effect of
climate
0
1
2
3
4
0
1
Negative
effect of
climate
1
2
Ht-1
3
4
Ct
Ct
(f)
Positive
effect of
climate
0
4
3
4
Model 4
2
Ht-1
Model 5
50
45
40
35
30
25
20
15
10
5
0
3
50
45
40
35
30
25
20
15
10
5
0
Ht-1
(e)
2
Ht-1
Ct
Ct
(c)
Model 2
Model 6
50
45
40
35
30
25
20
15
10
5
0
Positive
effect of
climate
Negative
effect of
climate
0
1
2
3
4
Ht-1
Figure 3.3 Graphical hypotheses (models 1 to 6) of coyote numerical response. Ct=Coyote winter density
at year t; Ht-1=snowshoe hare autumn density at year t-1. Density values are hypothetical. Models 4, 5 and
6 show hypothesised concave up relationship (i.e. h > 1). Relationship will be concave down if 0 < h < 1.
39
3.3 Model selection
Model selection was used to identify the models from the candidate set that are best
supported by the given data. The residual sum of squares and parameter estimates for
each model were first obtained by least-squares regression analysis in SAS version 9.0.
Inspection of the distribution of residuals was undertaken in each case to ensure
homogeneity of variances and normality. Where a parameter estimate failed to converge
during the SAS PROC MODEL regression procedure, the SAS grid search function was
used to provide starting values in order to overcome non-convergence (SAS Institute
Inc. 2008).
Model selection was then undertaken in Microsoft Office Excel 2003 using informationtheoretic analyses, namely Akaike Information Criterion corrected for small sample
sizes (AICc) (Burnham and Anderson, 2001; Anderson, 2008). AICc analysis provides
an estimate of the Kullback-Leibler information: a measure of distance of the
approximating models from conceptual reality (i.e. the true processes that generated the
observed data) (Kullback and Leibler, 1951; Anderson, 2008). The model with the least
information loss is therefore sought (Anderson, 2008). The information-theoretic
paradigm, and therefore model selection, is partially grounded in the principle of
parsimony: the conceptual trade-off between squared bias and variance (uncertainty)
versus the number of estimable parameters in the model (Burnham and Anderson, 2001;
Anderson, 2008). The model with the lowest AICc is deemed to be the most
parsimonious and considered to be the ‘best fit’ model for the given data. Akaike
weights (denoted as ωi) are a measure of the relative likelihood or probability of a
model given the data (Anderson, 2008) and were used as weight of evidence in favour
of a given model. Akaike weights are scaled from 0 to 1 with 1 implying the strongest
level of support, given the data.
The results of AICc analyses are examined and presented from two perspectives. Firstly,
analyses were carried out to determine which model had the highest level of support for
each climate variable, i.e. the model with the highest Akaike weight. These results are
presented in Chapter 5. Secondly, for models that incorporated a climate parameter
(models 2, 3, 5 and 6), analyses were carried out to determine which climate variables
40
from each of the large-scale and local climate sets had the most support for each model,
i.e. the climate variable with the highest Akaike weight. This enabled a more direct
model-by-model comparison between the climate variables. These results are presented
in Chapter 6.
41
CHAPTER 4: METHODS
4.1 Study area
4.1.1 Location
The study area is approximately 350 km2 in size and located in Shakwak Trench,
a broad glacial valley situated in the boreal forest of the Kluane region, southwest
Yukon Territory, Canada (60° 57’ N, 138°12’ W) (Figure 4.1). The nearest population
centres are the townships of Burwash Landing (~60 km to the northwest) and Haines
Junction (~62 km to the southeast). The area is bounded to the north and south by alpine
tundra, to the west by Kluane Lake, and to the east by Kloo Lake and the Jarvis River.
Elevation in the area ranges from approximately 760 m to 1170 m (O'Donoghue et al.,
1997; Krebs et al., 2001b).
Figure 4.1 Location of the Kluane study area, in the Yukon Territory Canada (Krebs et al., 2001b).
42
Human disturbance in the area has been relatively minimal. Historical land use in the
region has been limited to placer (alluvial) gold mining and large game hunting. These
activities were all but eliminated in the region following the establishment of the nearby
Kluane National Park and Reserve in 1972. The study area itself is bisected by the
Alaska Highway. No commercial logging has occurred in the Shakwak Trench, but
some local-scale tree cutting for firewood takes place. The Kluane region has been
subjected to commercial fur trapping for many decades, the intensity of which generally
reflects return prices over time (Krebs et al., 2001b). Intensive fur trapping has not,
however, been undertaken in the immediate vicinity of the study area.
4.1.2 Vegetation
The study area vegetation is typical of the Kluane sector of the boreal forest, but differs
from surrounding regions because of the area’s relatively high elevation and location in
the climatic rain shadow of the St Elias Mountains (Krebs et al., 2001b). The area is
dominated by white spruce (Picea glauca) trees with scattered stands of aspen (Populus
tremuloides), with a willow (Salix glauca), bog birch (Betula glandulosa), and
soapberry (Shepherdia canadensis) understorey (O'Donoghue et al., 1997; Krebs et al.,
2001b). The vegetation differs along a gradient of increasing elevation and has been
classified into three ecological zones: montane valley bottom forests (760–1080 m);
subalpine forests (1080–1370 m); and alpine tundra (above 1370 m). The two lower
zones consist of white spruce, balsam poplar (Populus balsamifera), aspen stands, and
shrub dominated areas of willow and dwarf birch (Betula nana). The upper zone
consists largely of open canopy spruce mixed with tall willow shrubs (Krebs et al.,
2001b).
43
4.1.3 Climate
The climate in the region is dominated by the topographic effect of the St Elias
Mountains with their massive ice fields and alpine glaciers to the west and southwest,
along with the strong seasonality of the area’s high latitude. The area lies between two
major climate systems: that of the cold, dry Arctic air masses, and the warm Pacific air
masses from the west, modified in transit by the St Elias Mountains (Krebs et al.,
2001b). As such, the climate is variable and cold, and precipitation is low (less than
300 mm annually) making this region semi-arid. Most rain falls in summer, with an
average of just 2 mm total rainfall over the winter months (Figure 4.2).
Up to 50% of the precipitation falls as snow. On average 85 cm of snow falls over each
winter, with depth variation influenced by altitude within the study area (Figure 4.3).
Snow cover is usually continuous from October to May, and long-term cycles in snow
depths in the region are indicated (Krebs et al., 2001b) (Figure 4.3).
Temperature in the Kluane region varies considerably from year to year, with a more
recent general climatic trend toward warmer weather (Krebs et al., 2001b), in keeping
with general trends observed across northwestern Canada and Alaska (Field et al.,
2007). Mean winter temperatures for the region typically remain below 0 °C, but a
broad range of temperatures can occur between extreme minimum and extreme
maximum averages (Figure 4.4). A typically short vegetation growing season is the
result of the region’s cold climate (Krebs et al., 2001b). However, the length of the
vegetation growing season across Canada has increased by an average of two days per
decade since 1950, with most of the increase resulting from earlier spring warming
(Field et al., 2007).
44
11.0
10.0
Total winter rain (mm)
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
85
/8
86 6
/8
87 7
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
7
0.0
Winter
150
135
120
105
90
75
60
45
30
15
0
85
/8
86 6
/8
87 7
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
7
Total winter snow (cm)
Figure 4.2 Total amount of rain (mm) for the winter months of October to March inclusive 1985–2007
for Burwash Landing. Source: Environment Canada (2010b).
Winter
Figure 4.3 Total amount of snow (cm) for the months of October to March inclusive 1985–2007 for
Burwash Landing. Source: Environment Canada (2010b).
45
10.0
Mean winter temperatures °C
5.0
0.0
-5.0
-10.0
-15.0
-20.0
-25.0
-30.0
-35.0
-40.0
85
/8
86 6
/8
87 7
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
7
-45.0
Winter
Figure 4.4 Mean winter temperatures (°C) for the months of
October to March inclusive 1985–2007 for Burwash Landing.
Source: Environment Canada (2010b)
4.2 Coyote and snowshoe hare data
Coyote and snowshoe hare data were collected over the period 1986–2009 as part of the
Kluane Ecological Monitoring Project (KEMP). All KEMP monitoring data are
available online courtesy of Professor Charles Krebs, University of British Colombia at
http://www.zoology.ubc.ca/~krebs/kluane.html.
4.2.1 Estimation of snowshoe hare density
Snowshoe hare population density was estimated by applying the jackknife estimator
(the heterogeneity model defined in Pollock et al., 1990) in Program CAPTURE (White
et al., 1982) to live trapping (mark-recapture) data obtained in accordance with the
methods outlined by O’Donoghue et al. (1997) and the Yukon Ecological Monitoring
Protocols (Anonymous, 2007). Namely, snowshoe hares were live-trapped each autumn
46
(late September-October) on two 60 ha grids located within control (i.e. nonexperimental treatment) sites of 1 km2 (Figure 4.5). Each grid contains a minimum of
86 live-traps spaced 30 m apart. Hares were processed in accordance with the methods
outlined in the Yukon Ecological Monitoring Protocols (Anonymous, 2007) to reduce
trap and handling stress. The data are expressed as the mean density of hares per hectare
(ha). O’Donoghue et al. (1997) found coyote numbers to be strongly correlated with
hare numbers the previous winter. Hence, for the purpose of analysis, snowshoe hare
data are lagged by one year (Ht-1) relative to coyote data (Ct).
Figure 4.5 Layout of snowshoe hare trapping grid. Grid size 60 ha (Source: Krebs et al., 2001b).
4.2.2 Estimation of coyote density
Coyote population density was estimated using snow track counts in accordance with
the methods outlined by O’Donoghue et al. (1997). Namely, all tracks of coyotes along
a 25 km transect that traversed the study area were counted each winter. The transect
was run each day by snowmobile after fresh snowfalls from October to April inclusive,
continuing on subsequent days for as long as fresh tracks could be distinguished. Every
track that crossed the transect that could not be visually connected to another crossing
was recorded. Track count data were then analysed by calculating least-squares means
for each year in an analysis of covariance model. Covariates were included in the model
(transect segment, date, days since last snowfall, temperature, and cloud cover the night
47
before) to control for time, year, weather and location. The data are expressed as the
mean number of tracks per track night per 100 km. Such track counts were found by
O’Donoghue et al. (1997) to be highly correlated (Spearman rank correlation
coefficient=0.88; P=0.01) with population estimates obtained by other means, namely
telemetry and extensive snow-tracking, over the course of the first recorded population
cycle (1987–1996) (O'Donoghue et al., 1997: Figure 2, p. 153-155) (Figure 4.6). Hence,
the mean number of coyote tracks is being used herein as a proxy (linear index) for
2
Coyote tracks per night
per 100 km (■)
Coyotes per 100 km (●)
coyote density.
86/87
88/89
90/91
92/93
94/95
Figure 4.6 Comparison of track counts and population estimates of Kluane coyotes from 1986 to 1995.
From O’Donoghue et al. (1997).
48
4.3 Climate data
4.3.1 North Atlantic Oscillation
NAO data were obtained from the Climate Analysis Section of the National Center for
Atmospheric Research (USA) website (Hurrell, 1995a). The NAO winter (December to
March) station based index for the period 1986/87 to 2008/09 inclusive was used
(Figure 4.7). The winter index data are based on the difference of normalised sea level
pressure between Lisbon, Portugal and Stykkisholmur/Reykjavik, Iceland since 1864
(Hurrell, 1995a).
4.3.2 El Niño-Southern Oscillation (Southern Oscillation Index)
The Southern Oscillation Index (SOI) is an important ENSO index (Stenseth et al.,
2003). It is a monthly index calculated from the standardised anomaly of the mean sea
level pressure difference between Tahiti in the Southern Pacific Ocean, and Darwin,
Australia (Stenseth et al., 2003; Bureau of Meteorology 2010a). SOI data were obtained
from the Australian Government’s Bureau of Meteorology website (Bureau of
Meteorology, 2010c). For the purposes of analysis, mean winter SOI values were
obtained by calculating the average of the monthly SOI values for October to March
(i.e. Canadian winter coyote tracking months) for the years 1986/87 to 2008/09
inclusive (Figure 4.8).
4.3.3 Pacific/North American
PNA data (standardised monthly mean values) were obtained from the National Oceanic
and Atmospheric Administration’s National Weather Service website (NOAA, 2010).
For the purposes of analysis, mean winter PNA values were obtained by calculating the
average of the monthly PNA values for October to March (i.e. the Canadian winter
coyote tracking months) for the years 1986/87 to 2008/09 inclusive (Figure 4.9).
49
4.3.4 North Pacific Index
The NPI is the area-weighted mean sea level pressure over the North Pacific region,
with a geographic coverage extending over Alaska and western Canada (Trenberth and
Hurrell, 1994). NPI data were obtained from the Climate Analysis Section of the
National Center for Atmospheric Research (USA) website (Hurrell, 1995a). The winter
(November to March) index was used for years 1986/87 to 2008/09 inclusive
(Figure 4.10).
50
6.00
5.00
4.00
Winter NAO
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
-4.00
-5.00
7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
/8 /8 /8 /9 /9 /9 /9 /9 /9 /9 /9 /9 /9 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0
86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08
Year
Figure 4.7 Changes in the winter North Atlantic Oscillation index for the years 1986/87 to 2008/09.
15
10
Winter SOI
5
0
-5
-10
-15
-20
86
/8
87 7
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
07 7
/0
08 8
/0
9
-25
Year
Figure 4.8 Changes in the winter Southern Oscillation Index for the years 1986/87 to 2008/09. Winter
SOI value=mean of the monthly SOI values for October to March inclusive.
51
1.00
0.80
Winter PNA
0.60
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9
/8 /8 /8 /9 /9 /9 /9 /9 /9 /9 /9 /9 /9 /0 /0 /0 /0 /0 /0 /0 /0 /0 /0
86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08
Year
Figure 4.9 Changes in the winter Pacific/North American index for the years 1986/87 to 2008/09. Winter
PNA value=mean of the monthly PNA values for October to March inclusive.
16
14
Winter NPI
12
10
8
6
4
2
86
/8
87 7
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
07 7
/0
08 8
/0
9
0
Year
Figure 4.10 Changes in the winter North Pacific Index for the years 1986/87 to 2008/09.
52
4.3.5 Local climate data
Local climate data were obtained from the Canadian Government’s environment
website (Environment Canada, 2010b). Monthly climatological data for the Yukon
Territory beyond February 2007 are no longer available for many weather stations, and
those which are available have not been adequately quality controlled (G. Bramwell,
Climatologist and C. Barnes, Climate Services Specialist, Environment Canada,
personal communications). Therefore, only local climate data up to February 2007 were
analysed. Climate variables analysed were: mean, minimum, maximum, and extreme
minimum and maximum temperatures; and precipitation, rain, and snow (Table 4.1).
Mean (for temperatures) and total (for rain, snow and precipitation) winter values for
each variable were calculated on the monthly October to March data for the years
1986/87 to 2005/06 inclusive, while the monthly October to February data were used for
the year 2006/07. These were the values used in the model selection analyses.
Table 4.1 Local climate variables examined in this study and definitions provided by Environment
Canada (2010b).
Local climate variable
Definition
Mean temperature
°C
The mean temperature for each month is the average of daily
mean temperature values, being the average of the maximum
and minimum temperature during the day
Mean minimum temperature
°C
The average minimum temperature across a month—the sum
of daily minimum values divided by the number of days in the
month
Mean maximum temperature
°C
The average maximum temperature across a month—the sum
of daily maximum values divided by the number of days in the
month
Extreme minimum temperature
°C
The lowest recorded temperature during the entire month
Extreme maximum temperature
°C
The highest recorded temperature during the entire month
Precipitation
mm
The sum of the total rainfall and the water equivalent of the
total snowfall observed during the month
Rain
mm
The total rainfall, or amount of all liquid precipitation such as
rain, drizzle, freezing rain, and hail, observed during the month
Snow
cm
The total snowfall, or amount of frozen (solid) precipitation
such as snow and ice pellets, observed during the month
53
The three closest weather stations to the study area are Haines Junction, Burwash
Landing, and Whitehorse (Figure 4.1). There is very little continuous meteorological
data available for Haines Junction for the period in question and therefore data from this
station were not able to be used. Burwash Landing presents as the next suitable station,
given its location in the Shakwak Trench and proximity to the study area. There are no
data available for Burwash Landing for the winter months: October 1987; January,
February, and March 2002; and October 2005. Correlation by least-squares regression
analysis was undertaken in SAS version 9.0 on the Burwash Landing and Whitehorse
climate data (Burwash = a + bWhitehorse) to allow prediction of the five missing
Burwash Landing values for each climate variable (Appendix 1). A small number of
outliers were removed prior to this regression analysis (Table 4.2). This was required to
normalise the residuals and strengthen the significance of the correlation for the purpose
of estimating the missing values. Outliers were replaced prior to model selection
analysis. Correlation was undertaken on the data for the winter months only (October to
March inclusive), as it was found by excluding the summer months from the correlation
analysis, the multiplicative effect of the regression equation on higher values was
reduced, and so to were the total number of missing values to be estimated. Hence,
missing Burwash Landing values for the months of October 1987, January, February,
and March 2002, and October 2005 were predicted from the resultant regression
equations and substituted into the Burwash Landing data.
Table 4.2 Local weather variable outliers removed prior to correlation analysis to predict missing
Burwash Landing values.
Station
Month and Year
Variable
Value
Whitehorse
January 1996
Extreme minimum temperature
-25.5 °C
Burwash Landing
October 1999
Total snow
66 cm
Burwash Landing
October 1999
Total precipitation
63 mm
Burwash Landing
January 2004
Extreme maximum temperature
-10 °C
54
4.4 Partial correlation analyses
Given the relationship between the coyote track count and population estimate data
(Figure 4.6), it was necessary to demonstrate that track counts beyond the first
population cycle were a valid index for coyote population density, and not an artifact of
the climate variable in question. Therefore, partial correlation analyses were carried out
between coyote track count data and each climate variable, controlling for the effect of
the coyote population estimate for the period 1987–1996 (the first population cycle).
Analyses were undertaken in SAS version 9.0.
The relationship between track count and each climate variable after removing the effect
of the population estimate variation were non-significant (P>0.05), except for the
climate variables North Pacific Index (r=-0.71; P=0.05) and local mean extreme
maximum winter temperature (r=-0.79; P=0.02) (Appendix 2). Both correlations
indicated a negative relationship with coyote snow track count. The relationship
between track count and NPI was barely significant (i.e. the exact level for significance
cutoff). The significant relationship between track count and mean extreme maximum
winter temperature was considered spurious. This is because the probability of a Type I
error (the probability of incorrectly rejecting the null hypothesis when it is true) being
made is determined by the significance level of α set for the test, usually 0.05 (or 1 in 20
times the incorrect conclusion about the significance is reached) (Benjamini and
Hochberg, 1995; Anderson et al., 2001; Ottersen et al., 2001; Stevens, 2001). Hence, up
to one spurious result could be expected given 12 hypotheses tests were undertaken. The
assiduous manner in which the track data are collected further support this assessment
of a spurious correlation. Snow track count surveys only occur when conditions are
ideal, namely immediately following fresh snowfalls, and only while tracks remain
distinguishable and uncompromised by too much coyote activity or thaw events caused
by extreme maximum temperatures (O'Donoghue et al., 1998b; Mark O’Donoghue and
Liz Hofer, Kluane senior field technician and coyote and lynx track surveyor, personal
communications).
55
CHAPTER 5: RESULTS—RELATIVE MODEL SUPPORT BY CLIMATE
VARIABLE
5.1 Observed coyote and snowshoe density
Over the period 1987 to 2010, coyote density (defined as the mean number of tracks per
track night per 100 km) peaked three times in the winters of 1991/92, 1999/2000 and
2007/08 (Figure 5.1). There was a mean coyote density of 14.08 (± 12.12), with a
minimum of 0.59 in the winter of 1993/94 and a maximum of 41.68 in the winter of
1999/2000 (Figure 5.1). Snowshoe hare densities peaked three times in the autumns of
1988, 1998 and 2006 (Figure 5.2). The mean hare density for the entire period was 0.91
(± 0.81) per ha, with a minimum of 0.07 per ha in the autumn of 2001, and a maximum
of 2.73 per ha in the autumn of 1998 (Figure 5.2). The population densities of both
coyotes and hares in the most recent cycle (i.e. from 2003) did not reach previous cyclic
peak densities (Figures 5.1 and 5.2).
Mean coyote tracks per track night per 100 km
56
60
50
40
30
20
10
0
8
9
0
4
3
2
1
5
6
7
0
9
8
1
2
3
7
6
5
4
8
9
0
/8 8/8 9/9 0 /9 1 /9 2 /9 3 /9 4/9 5/9 6/9 7 /9 8 /9 9 /0 0/0 1/0 2/0 3 /0 4 /0 5 /0 6 /0 7/0 8/0 9/1
87
8
8
9
9
9
9
9
9
9
9
9
9
0
0
0
0
0
0
0
0
0
0
Winter
Figure 5.1 Changes in the estimated mean number of coyote tracks per track night per 100 km (proxy for
density) of Kluane coyotes for the period 1987/88 to 2009/10. Vertical bars=95% confidence intervals.
Snowshoe hare density per ha
3.5
3.0
2.5
2.0
1.5
1.0
0.5
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
0.0
Autumn
Figure 5.2 Changes in the estimated density of Kluane snowshoe hares for the period 1986 to 2009.
Vertical bars=95% confidence intervals.
57
There was a significant positive linear relationship between coyote density (Ct) and
snowshoe hare density the previous year (Ht-1) (F=13.07; df=1, 21; P=0.0016) (model 1;
Figure 5.3; Table 5.1). The regression equation for the model is:
Ct = 5.472 + 9.439Ht-1
Only 38% of variation in coyote density could be explained by changes in snowshoe
hare density alone (R2=0.38). The estimated intercept (ß0) of 5.47 was not significantly
different from zero (Table 5.2).
Figure 5.3 Coyote density (Ct) and snowshoe hare density (Ht-1) (model 1, Table 5.2) for the period
1986/87–2009/10. Solid line shows significant fitted regression.
58
5.2 Coyote numerical response and large-scale climate indices
5.2.1 North Atlantic Oscillation (NAO)
There was no direct significant relationship between coyote density (Ct) and the NAO
the same year (NAOt) (P>0.05; R2=0.002), Ct and the NAO the previous year
(NAOt-1) (P>0.05; R2=0.059), nor hare density (Ht) and the NAO the year preceding the
autumn of hare density data collection (i.e. NAOt-1 relative to Ht) (P>0.05; R2=0.005)
(Figure 5.4).
(a)
(b)
(c)
Figure 5.4 (a) Coyote density against NAO the same year; (b) coyote density against NAO the year
before; and (c) hare density against NAO the year preceding hare data collection. NAO=winter
(December to March) station based index. Data are for the period 1985/86–2009/10.
59
The AICc analysis of coyote density against hare density and the NAO demonstrated
that the model with the lowest AICc and highest Akaike weight (ω2=0.78) was model 2
(Table 5.1). Model 2 had a highly significant and positive effect of hare density (ß1) and
a highly significant negative effect of NAO and hare density (ß3) (Table 5.2). The
intercept (ß0) was not significantly different from zero (Table 5.2). The overall
regression was highly significant (F=32.00; df=2,20; P<0.0001) with R2= 0.76.
The regression equation for the fitted model 2 is:
Ct = 2.725 + 18.272Ht-1 – 3.233NAOt-1×Ht-1
The second ranked model was model 5 (Table 5.1). The overall regression was highly
significant (F=21.08; df=3,19; P<0.0001) and indicated a positive effect of hare density
on coyote density, and a negative effect of the interaction between hares and NAO. The
AICc difference for model 5 was low (∆AICc=2.61;Table 5.1) showing support for this
model as an alternative to model 2 given the data, however the Akaike weight was low
(ω5=0.212) indicating a low level of relative support. Model 5 parameters ß1 and ß3
were significant, but the intercept (ß0) was not different to zero (Table 5.2). The power
curve exponent parameter (ß4) was not significantly different from 1.0. The regression
equation for the fitted model 5 is:
Ct = 4.373 + 15.467Ht-11.216 – 2.914NAOt-1×Ht-11.216
The remaining models (models 1, 3, 4, and 6) had the lowest support from the AICc
analysis with consistently low Akaike weights (ωi). The sum of ωi for the remaining
models was ∑ ωi=0.0055 (Table 5.1).
60
Table 5.1 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with
the effect of the North Atlantic Oscillation (NAOt-1). RSS=residual sum of squares; R2= coefficient of
determination; K=number of parameters; ωi=Akaike weight; na=not applicable. The model with the most
support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2057.948
0.38
3
110.6245
18.91927
0.0001
2
Ct = a + cHt-1 + dNAO t-1×Ht-1
794.913
0.76
4
91.70521
0
0.7826
3
Ct = f + bHt-1 + gNAO t-1
1243.538
0.63
4
101.9973
10.29211
0.0046
4
Ct = a + bHt-1h
2053.600
na
4
113.5349
21.82968
0.0000
5
Ct = a + cHt-1h + dNAO t-1×Ht-1h
771.300
na
5
94.31883
2.613612
0.2118
6
Ct = f + bHt-1h + gNAO t-1
1243.400
na
5
105.302
13.59674
0.0009
Table 5.2 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and NAOt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for NAOt-1; ß3=regression coefficient for interaction between NAOt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.4723
3.1506
1.7400
0.0971
2.7249
2.0648
1.3200
0.2019
6.4509
2.5241
2.5600
0.0188
9.4389
2.6107
3.6200
0.0016
18.2722
2.2847
8.0000
<0.0001
12.2901
2.2237
5.5300
<0.0001
na
na
na
na
na
na
na
na
-3.0731
0.8491
-3.6200
0.0017
na
na
na
na
-3.2325
0.5734
-5.6400
<0.0001
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
4.3193
7.4310
0.5813
0.5670
4.3728
2.7945
1.5648
0.1319
11.0879
9.5690
1.1587
0.2590
15.4673
4.1473
3.7295
0.0012
na
na
na
na
na
na
na
na
na
na
na
na
-2.9135
0.6859
-4.2477
0.0003
0.8521
0.7261
1.1735
0.2531
1.2156
0.3009
4.0399
0.0005
E
SE
t
P
6.2838
4.9509
1.2692
0.2176
12.5360
6.5845
1.9039
0.0701
-3.0709
0.8729
-3.5180
0.0019
na
na
na
na
0.9809
0.4729
2.0742
0.0500
61
Model 2 was a good reconstruction of Ct, although the reconstruction demonstrated
some over and under estimation of Ct outside of the observed data 95% confidence
intervals (Figure 5.5). The best reconstructive fit (i.e. least departure) occurred over the
winters of 2003/04 to 2009/10, the third population cycle (Figure 5.5). There was very
little departure between the reconstructions of models 2 and 5 (Figure 5.5).
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
08
/0
9
09
/1
0
0
Winter
Figure 5.5 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and the second ranked model 5 () using the NAO (Tables 5.1 and 5.2).
Vertical bars=95% confidence intervals.
62
Figure 5.6 shows the reconstructed influence of NAOt-1 on Ct, using the model 2
parameter estimates. The influence is on the slope of the coyote numerical response,
with an increase in the slope with a negative NAO phase, and a corresponding decrease
in the slope with a positive NAO phase.
50
45
NAOt-1 = -3
40
NAOt-1 = 0
35
CCt
t
30
25
NAOt-1 = +3
20
15
10
5
0
0
1
2
3
Ht-1
Ht-1
Figure 5.6 Influence of NAOt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with model 2 parameter estimates (Table 5.2).
63
5.2.2 El Niño-Southern Oscillation (SOI)
There was no direct significant relationship between coyote density (Ct) and the SOI the
same year (SOIt) (P>0.05; R2=0.003), Ct and the SOI the previous year (SOIt-1) (P>0.05;
R2=0.005), nor hare density (Ht) and the SOI the year preceding the autumn of hare
density data collection (i.e. SOIt-1 relative to Ht) (P>0.05; R2=0.007) (Figure 5.7).
(a)
(b)
(c)
Figure 5.7 (a) Coyote density against SOI the same year; (b) coyote density against SOI the year before;
and (c) hare density against SOI the year preceding hare data collection. SOI=mean winter (October to
March) index. Data are for the period 1985/86–2009/10.
64
The AICc analysis of coyote density against hare density and the SOI demonstrated that
the model with the lowest AICc and highest Akaike weight (ω1=0.53) was model 1
(Table 5.3). Model 1 describes a simple linear relationship between coyote and hare
density without any effect of climate and is described in section 5.1 above.
The second ranked model was model 2 (Table 5.3). The overall regression was
significant (F=6.71; df=2,20; P=0.0059) with R2=0.40, and indicated a positive effect of
hare density on coyote density, and a negative effect of the interaction between hares
and SOI, although estimates for this parameter (ß3) and the intercept (ß0) were not
significant (Table 5.4). The AICc difference for model 2 was low (∆AICc=2.28;
Table 5.3) showing support for this model as an alternative to model 1, however the
Akaike weight for model 2 was also low (ω2=0.169) indicating a low level of relative
support. The regression equation for the fitted model 2 is:
Ct = 5.119 + 9.914Ht-1 – 0.121SOIt-1×Ht-1
The remaining models (models 3, 4, 5 and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3022
(Table 5.3).
65
Table 5.3 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of the El Niño-Southern Oscillation (SOIt-1). RSS=residual sum of squares; R2= coefficient of
determination; K=number of parameters; ωi=Akaike weight; na=not applicable. The model with the most
support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2057.948
0.38
3
110.6245
0
0.5285
2
Ct = a + cHt-1 + dSOIt-1×H t-1
1997.891
0.40
4
112.9023
2.2779
0.1692
3
Ct = f + bHt-1 + gSOI t-1
2056.145
0.38
4
113.5634
2.9389
0.1216
4
Ct = a + bHt-1h
2053.600
na
4
113.5349
2.9104
0.1233
5
Ct = a + cHt-1h + dSOI t-1I×Ht-1h
1991.700
na
5
116.1382
5.5137
0.0336
6
Ct = f + bHt-1h + gSOI t-1
2052.400
na
5
116.8286
6.2042
0.0238
Table 5.4 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and SOIt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for SOIt-1; ß3=regression coefficient for interaction between SOIt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.4723
3.1506
1.7400
0.0971
5.1190
3.2134
1.59
0.1268
5.4093
3.2612
1.66
0.1129
9.4389
2.6107
3.6200
0.0016
9.9141
2.7062
3.66
0.0015
9.4926
2.7046
3.51
0.002
na
na
na
na
na
na
na
na
-0.0314
0.2371
-0.13
0.8960
na
na
na
na
-0.1211
0.1562
-0.78
0.4472
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
4.3193
7.4310
0.5813
0.5670
6.4876
4.9875
1.3008
0.2068
4.3447
7.5164
0.5780
0.5691
11.0879
9.5690
1.1587
0.2590
7.7223
7.2004
1.0725
0.2951
11.0260
9.7220
1.1341
0.2689
na
na
na
na
na
na
na
na
-0.0261
0.2447
-0.1067
0.9160
na
na
na
na
-0.1247
0.1352
-0.9223
0.3664
na
na
na
na
0.8521
0.7261
1.1735
0.2531
1.2701
0.9957
1.2756
0.2154
0.8611
0.7499
1.1483
0.2632
66
The model 1 reconstruction of Ct showed marked departure over the first two population
cycles (Figure 5.8). Markedly less departure is noted over the third population cycle,
i.e. from the winters 2002/03 onwards, with most estimates falling inside the observed
data 95% confidence intervals. There was very little departure between the
reconstructions of models 1 and 2, with only minor departure between these at high
coyote densities (Figure 5.8).
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
08
/0
9
09
/1
0
0
Winter
Figure 5.8 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 2 () using the SOI (Tables 5.3 and 5.4).
Vertical bars=95% confidence intervals.
67
Figure 5.9 shows the reconstructed influence of SOIt-1 on Ct, using the model 2
parameter estimates. The influence is on the slope of the coyote numerical response,
with a slight increase in the slope with a negative (La Niña) phase, and a corresponding
slight decrease in the slope with a positive (El Niño) phase.
45
40
35
SOIt-1 = -10
30
Ct
Ct
25
SOIt-1 = 0
20
SOIt-1 = +10
15
10
5
0
0
1
2
3
Ht-1Ht-1
Figure 5.9 Influence of SOIt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates (Table 5.4).
68
5.2.3 Pacific/North American (PNA)
There was no direct significant relationship between coyote density (Ct) and the PNA
the same year (PNAt) (P>0.05; R2=0.000), Ct and the PNA the previous year (PNAt-1)
(P>0.05; R2=0.068), nor hare density (Ht) and the PNA the year preceding the autumn
of hare density data collection (i.e. PNAt-1 relative to Ht) (P>0.05; R2=0.015)
(Figure 5.10).
(a)
(b)
(c)
Figure 5.10 (a) Coyote density against PNA the same year; (b) coyote density against PNA the year
before; and (c) hare density against PNA the year preceding hare data collection. PNA=mean winter
(October to March) index. Data are for the period 1985/86–2009/10.
69
The AICc analysis of coyote density against hare density and the PNA demonstrated
that the model with the lowest AICc and highest Akaike weight (ω1=0.54) was model 1
(Table 5.5). Model 1 describes a simple linear relationship between coyote and hare
density without any effect of climate and is described in section 5.1 above.
The second ranked model was model 2 (Table 5.5). The overall regression was
significant (F=6.53; df=2,20; P=0.0066) with R2=0.39. The model indicated a positive
effect of hare density on coyote density, and a positive effect of the interaction between
hares and PNA, although the estimates for this parameter (ß3) and the intercept (ß0)
were not significant (Table 5.6). The AICc difference for model 2 was low
(∆AICc=2.53;Table 5.6) showing support for this model as an alternative to model 1
given the data, however the Akaike weight for model 2 was very low (ω2=0.152)
showing a low level of relative support. The regression equation for the fitted
model 2 is:
Ct = 5.339 + 9.450Ht-1 + 2.474PNAt-1×Ht-1
The remaining models (models 3, 4, 5 and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3107
(Table 5.5).
70
Table 5.5 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of the Pacific/North American (PNAt-1). RSS=residual sum of squares; R2= coefficient of
determination; K=number of parameters; ωi=Akaike weight; na=not applicable. The model with the most
support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2057.948
0.38
3
110.6245
0
0.5377
2
Ct = a + cH t-1 + dPNAt-1×H t-1
2020.162
0.39
4
113.1573
2.5328
0.1515
3
Ct = f + bH t-1 + gPNA t-1
2046.368
0.39
4
113.4538
2.8293
0.1307
4
Ct = a + bHt-1h
2053.600
na
4
113.5349
2.9104
0.1255
5
Ct = a + cH t-1h + dPNA t-1×Ht-1h
2018.400
na
5
116.4444
5.8200
0.0293
6
Ct = f + bH t-1h + gPNA t-1
2044.300
na
5
116.7377
6.1132
0.0253
Table 5.6 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and PNAt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for PNAt-1; ß3=regression coefficient for interaction between PNAt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.4723
3.1506
1.7400
0.0971
5.3389
3.2061
1.67
0.1115
6.0668
3.6882
1.65
0.1150
9.4389
2.6107
3.6200
0.0016
9.4503
2.6506
3.57
0.0019
9.1249
2.8262
3.23
0.0042
na
na
na
na
na
na
na
na
-1.9089
5.6682
-0.34
0.7401
na
na
na
na
2.4744
4.0456
0.61
0.5477
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
4.3193
7.431
0.5813
0.5670
6.0559
5.5815
1.0850
0.2897
5.222
7.8221
0.6676
0.5113
11.0879
9.569
1.1587
0.2590
8.3796
7.4015
1.1321
0.2698
10.3166
9.7316
1.0601
0.3006
na
na
na
na
na
na
na
na
-1.7469
5.9204
-0.2951
0.7707
na
na
na
na
2.5921
4.2861
0.6048
0.5515
na
na
na
na
0.8521
0.7261
1.1735
0.2531
1.1109
0.8113
1.3693
0.1847
0.8885
0.7916
1.1224
0.2738
71
As described previously, the model 1 reconstruction of Ct showed marked departure
over the first two coyote population cycles, but markedly less departure over the third
(Figure 5.11). There was very little departure between the reconstructions of models 1
and 2 with only minor departure between these at higher coyote densities (Figure 5.11).
60
Coyote density (Ct)
50
40
30
20
10
86
/8
7
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
08
/0
9
0
Winter
Figure 5.11 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 2 () using the PNA (Tables 5.5 and 5.6).
Vertical bars=95% confidence intervals.
72
Figure 5.12 shows the reconstructed influence of PNAt-1 on Ct, using parameters
estimated by model 2. The influence is on the slope of the coyote numerical response,
with a slight increase in the slope with a positive PNA phase, and a corresponding slight
decrease in the slope with a negative PNA phase.
45
40
35
PNAt-1 = 0.5
30
Ct
Ct
25
PNAt-1 = 0
20
PNAt-1 = -0.5
15
10
5
0
0
1
2
3
t-1
Ht-1
H
Figure 5.12 Influence of PNAt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates (Table 5.6).
73
5.2.4 North Pacific Index (NPI)
There was no direct significant relationship between coyote density (Ct) and the NPI the
same year (NPIt) (P>0.05; R2=0.036), Ct and the NPI the previous year (NPIt-1) (P>0.05;
R2=0.000), nor hare density (Ht) and the NPI the year preceding the autumn of hare
density data collection (i.e. NPIt-1 relative to Ht) (P>0.05; R2=0.033) (Figure 5.13).
(a)
(b)
(c)
Figure 5.13 (a) Coyote density against NPI the same year; (b) coyote density against NPI the year before;
and (c) hare density against NPI the year preceding hare data collection. NPI=winter (November to
March) index. Data are for the period 1985/86–2009/10.
74
The AICc analysis of coyote density against hare density and the NPI demonstrated that
the model with the lowest AICc and highest Akaike weight (ω2=0.38) was model 2
(Table 5.7). Model 2 had a significant and positive effect of hare density (ß1), but a nonsignificant effect of NPI and hare density (ß3) (Table 5.8). The intercept (ß0) was not
significantly different from zero (Table 5.8). The overall regression was highly
significant (F=8.72; df=2,20; P<0.002) with R2= 0.47. The regression equation for the
fitted model 2 is:
Ct = 4.8492 + 23.1131Ht-1 – 1.4080NPIt-1×Ht-1
The second ranked model was model 1 (Table 5.7) and is described in section 5.1
above. The AICc difference for model 1 was very low (∆AICc=0.33) showing support
for this model as an alternative to model 2. The Akaike weight for model 1 was
ω1=0.32 (Table 5.7).
The remaining models (models 2, 3, 4, and 6) had the lowest support from the AICc
analysis. They had consistently low Akaike weights (ωi), the sum of which was
∑ ωi=0.30 (Table 5.7).
75
Table 5.7 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of the North Pacific Index (NPIt-1). RSS=residual sum of squares; R2= coefficient of determination;
K=number of parameters; ωi=Akaike weight; na=not applicable The model with the most support is shown
in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2057.94835
0.38
3
110.6245
0.331734
0.319
2
Ct = a + cHt-1 + dNPI t-1×Ht-1
1783.59567
0.47
4
110.2927
0
0.376
3
Ct = f + bHt-1 + gNPI t-1
1988.33393
0.40
4
112.7921
2.499311
0.108
4
Ct = a + bHt-1h
2053.6
na
4
113.5349
3.242149
0.074
5
Ct = a + cHt-1h + dNPI t-1×Ht-1h
1730.9
na
5
112.9102
2.617423
0.102
6
Ct = f + bHt-1h + gNPI t-1
1981.6
na
5
116.0212
5.728474
0.021
Table 5.8 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and NPIt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for NPIt-1; ß3=regression coefficient for interaction between NPIt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.4723
3.1506
1.7400
0.0971
4.8492
3.0265
1.60
0.1248
12.9356
9.4667
1.37
0.1870
4.3193
7.4310
0.5813
0.5670
8.1638
3.3032
2.4715
0.0217
9.4389
2.6107
3.6200
0.0016
23.1131
8.1843
2.82
0.0105
9.9844
2.7091
3.69
0.0015
11.0879
9.5690
1.1587
0.2590
14.1431
11.0310
1.2821
0.2131
na
na
na
na
na
na
na
na
-0.9034
1.0796
-0.84
0.4126
na
na
na
na
na
na
na
na
na
na
na
na
-1.4080
0.8028
-1.75
0.0947
na
na
na
na
na
na
na
na
-1.0229
0.7913
-1.2927
0.2095
na
na
na
na
na
na
na
na
na
na
na
na
0.8521
0.7261
1.1735
0.2531
1.8153
0.9697
1.8720
0.0746
E
SE
t
P
11.5748
11.7152
0.9880
0.3339
12.1298
10.1046
1.2004
0.2427
-0.9210
1.1082
-0.8311
0.4149
na
na
na
na
0.8240
0.6833
1.2059
0.2407
76
The model 2 reconstructed data showed marked departure from observed data over the
first two population cycles with estimates largely falling outside the observed data 95%
confidence intervals for those winters (Figure 5.14). There was some departure between
the reconstructions of models 2 and 1 over the first two population cycles with deviation
largely shown at cycle peaks (Figure 5.14).
60
Coyote density (Ct)
50
40
30
20
10
87
/8
88 8
/8
89 9
/9
90 0
/9
91 1
/9
92 2
/9
93 3
/9
94 4
/9
95 5
/9
96 6
/9
97 7
/9
98 8
/9
99 9
/0
00 0
/0
01 1
/0
02 2
/0
03 3
/0
04 4
/0
05 5
/0
06 6
/0
07 7
/0
08 8
/0
09 9
/1
0
0
Winter
Figure 5.14 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and the second ranked model 1 () using the NPI (Tables 5.7 and 5.8).
Vertical bars=95% confidence intervals.
77
Figure 5.15 shows the reconstructed influence of NPIt-1 on Ct using the model 2
parameter estimates. The influence is on the slope of the coyote numerical response,
with an increase in the slope with a lower NPI index, and a corresponding decrease in
the slope with an increased NPI index.
50
45
NPIt-1 = 5
40
35
Ct
30
NPIt-1 = 8
25
20
15
NPIt-1 = 13
10
5
0
1
2
3
4
Ht-1
Figure 5.15 Influence of NPIt-1 on coyote numerical response (Ct) to snowshoe hare density (Ht-1),
reconstructed with the model 2 parameter estimates (Table 5.8).
78
5.3 Coyote numerical response and local climate variables
5.3.1 Extreme maximum winter temperature
There was a significant negative relationship between coyote density (Ct) and mean
extreme maximum winter temperature (EmaxTEM) the same year (F=5.31; df=1,18;
P=0.033; R2=0.23) and the previous year (F=20.91; df=1,19; P=0.0002; R2=0.52)
(Figure 5.16(a) and (b)). The relationship between hare density (Ht) and EmaxTEM the
year preceding the autumn of hare density data collection (i.e. EmaxTEMt-1 relative
to Ht) was not significant (P>0.05; R2=0.10) (Figure 5.16(c)).
(a)
(b)
(c)
Figure 5.16 (a) Coyote density against mean extreme maximum winter temperature (EmaxTEM) the
same year; (b) coyote density against EmaxTEM the year before; and (c) hare density against EmaxTEM
the year preceding hare data collection. EmaxTEM=mean (October to March) extreme maximum winter
temperature (°C) recorded at Burwash Landing. Data are for the period 1985/86–2006/07. Solid lines
show significant fitted regressions.
79
The AICc analysis of coyote density against hare density and mean extreme maximum
winter temperature (EmaxTEM) demonstrated that the model with the lowest AICc and
highest Akaike weight (ω2=0.58) was model 2 (Table 5.9). Model 2 had a highly
significant and positive effect of hare density (ß1), and a highly significant negative
effect of EmaxTEM and hare density (ß3) (Table 5.10). The intercept (ß0) was
significantly different from zero (Table 5.10). The overall regression was highly
significant (F=14.55; df=2,18; P=0.0002) with R2=0.62. The regression equation for the
fitted model 2 is:
Ct = 8.605 + 20.817Ht-1 – 3.195EmaxTEMt-1×Ht-1
The second ranked model was model 3 (Table 5.9). The overall regression was
significant (F=12.29; df=2,18; P=0.0004) with R2=0.58, and indicated a positive effect
of hare density on coyote density, and a negative effect of EmaxTEM. The AICc
difference for model 3 was low (∆AICc=2.12;Table 5.9) showing support for this model
as an alternative to model 2 given the data, however the Akaike weight was low
(ω3=0.20) indicating a low level of relative support. Model 3 parameters ß0 and ß2 were
significant, but the coefficient for hare density (ß1) was not (Table 5.10). The regression
equation for the fitted model 3 is:
Ct = 30.674 + 4.330Ht-1 – 3.677EmaxTEMt-1
The remaining models (models 1, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.22
(Table 5.9).
80
Table 5.9 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of mean extreme maximum winter temperature (°C) for the months October-March (EmaxTEMt-1).
RSS=residual sum of squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike
weight; na=not applicable. The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
7.28
0.0152
2
Ct = a + cHt-1 + dEmaxTEMt-1×Ht-1
1244.0439
0.62
4
96.2136
0
0.5803
3
Ct = f + bHt-1 + gEmaxTEMt-1
1376.0930
0.58
4
98.3321
2.12
0.2012
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
10.26
0.0034
5
Ct = a + cHt-1h + dEmaxTEMt-1×Ht-1h
1187.2000
na
5
98.73144
2.52
0.1648
6
Ct = f + bHt-1h + gEmaxTEMt-1
1375.9000
na
5
101.8292
5.62
0.0350
Table 5.10 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and mean extreme maximum temperature (EmaxTEMt-1). ß0=intercept;
ß1=regression coefficient for Ht-1; ß2=regression coefficient for EmaxTEMt-1; ß3=regression
coefficient for interaction between EmaxTEMt-1 and Ht-1; ß4=power curve exponent;
E=estimate; SE=standard error; na=not applicable. The model with the most support is
shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
8.6048
2.8820
2.99
0.0079
30.6735
8.9099
3.44
0.0029
9.2878
2.7577
3.37
0.0032
20.8170
4.0579
5.13
<0.0001
4.3298
2.8736
1.51
0.1492
na
na
na
na
na
na
na
na
-3.6764
1.2492
-2.94
0.0087
na
na
na
na
-3.1946
0.9424
-3.39
0.0033
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
7.2345
4.2554
1.7001
0.1046
30.2506
11.1634
2.7098
0.0135
12.204
11.8921
1.0262
0.3170
27.2468
8.3566
3.2605
0.0039
4.8806
8.655
0.5639
0.5791
na
na
na
na
na
na
na
na
-3.6669
1.2923
-2.8375
0.0102
na
na
na
na
-3.8936
1.29
-3.0183
0.0068
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.6087
0.3836
1.5868
0.1282
0.8896
1.4812
0.6006
0.5549
81
5.3.2 Extreme minimum winter temperature
There was no direct significant relationship between coyote density (Ct) and mean
extreme minimum winter temperature the same year (EminTEMt) (P>0.05; R2=0.002),
but there was a significant, albeit weak, relationship between Ct and EminTEM the
previous year (EminTEM t-1) (F=4.61; df=1,19; P=0.044; R2=0.20) (Figure 5.17(a) and
(b)). There was no significant relationship between hare density (Ht) and EminTEM the
year preceding the autumn of hare density data collection (i.e. EminTEM t-1 relative
to Ht) (P>0.05; R2=0.040) (Figure 5.17(c)).
(a)
(b)
(c)
Figure 5.17 (a) Coyote density against mean extreme minimim winter temperature (EminTEM) the same
year; (b) coyote density against EminTEM the year before; and (c) hare density against EminTEM the
year preceding hare data collection. EminTEM=mean winter (October to March) extreme minimum
temperatures (°C) recorded at Burwash Landing. Data are for the period 1985/86–2006/07. Solid line
shows significant fitted regression.
82
The AICc analysis of coyote density against hare density and mean extreme minimum
winter temperature (EminTEM) demonstrated that the model with the lowest AICc and
highest Akaike weight (ω1=0.48) was model 1 (Table 5.11). Model 1 had a significant
and positive effect of hare density (ß1), but the intercept (ß0) was not significantly
different from zero (Table 5.12). The overall regression was significant (F=11.34;
df=1,19; P=0.0032) with R2=0.37. The regression equation for the fitted model 1 is:
Ct = 5.892 + 9.288Ht-1
Note that the parameter estimates for model 1 in the local climate analyses are different
to model 1 for the large-scale climate analyses, as the range of data is slightly different
(i.e. from 1985–2007 as opposed to 1985–2009), due to the lack of available quality
controlled local climate data after 2007 (refer section 4.3.5).
The second ranked model was model 3 (Table 5.11). The overall regression was
significant (F=6.32; df=2,18; P=0.0083) with R2=0.41. Model 3 indicated a positive
effect of hare density on coyote density, and a negative effect of EminTEM. The AICc
difference for model 3 was low (∆AICc<2;Table 5.11) showing support for this model
as an alternative to model 1 given the data, however the Akaike weight was low
(ω3=0.11) indicating very low model probability. The only parameter estimate that was
significant was ß1 (the effect of hares) while the parameter estimate for the intercept (ß0)
was unrealistic (Table 5.12). The regression equation for the fitted model 3 is:
Ct = –26.967 + 7.854Ht-1 – 0.951EminTEMt-1
The remaining models (models 2, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3177
(Table 5.11).
83
Table 5.11 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of mean extreme minimum temperature (°C) for the months October-March inclusive (EminTEMt-1).
RSS=residual sum of squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike
weight; na=not applicable. The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0
0.4810
2
Ct = a + cHt-1 + dEminTEM t-1×Ht-1
1993.3271
0.39
4
106.1138
2.6204
0.1297
3
Ct = f + bHt-1 + gEminTEM t-1
1911.6608
0.41
4
105.2353
1.7419
0.2013
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
2.9794
0.1084
5
Ct = a + cHt-1h + dEminTEM t-1×Ht-1h
1878.4000
na
5
108.3667
4.8733
0.0421
6
Ct = f + bHt-1h + gEminTEM t-1
1899.1000
na
5
108.5969
5.1035
0.0375
Table 5.12 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and mean extreme minimum temperature (EminTEMt-1). ß0=intercept;
ß1=regression coefficient for Ht-1; ß2=regression coefficient for EminTEMt-1; ß3=regression
coefficient for interaction between EminTEMt-1 and Ht-1; ß4=power curve exponent;
E=estimate; SE=standard error; na=not applicable. The model with the most support is
shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
6.4961
3.6309
1.79
0.0904
-26.9665
30.2935
-0.89
0.3851
9.2878
2.7577
3.37
0.0032
-9.6192
29.8233
-0.32
0.7508
7.8538
3.0420
2.58
0.0188
na
na
na
na
na
na
na
na
-0.9505
0.8707
-1.09
0.2894
na
na
na
na
-0.4928
0.7739
-0.64
0.5323
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
-2.0125
22.2908
-0.0903
0.9290
-29.6418
33.1324
-0.8946
0.3816
12.204
11.8921
1.0262
0.3170
-25.9616
40.893
-0.6349
0.5327
11.1915
13.3498
0.8383
0.4118
na
na
na
na
na
na
na
na
-0.9581
0.8933
-1.0725
0.2962
na
na
na
na
-1.2336
0.9863
-1.2507
0.2255
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.3569
0.5377
0.6638
0.5144
0.6909
0.8949
0.7720
0.4491
84
5.3.3 Precipitation
There was no direct significant relationship between coyote density (Ct) and total winter
precipitation the same year (PRECt) (P>0.05; R2=0.190), Ct and PREC the previous year
(PREC t-1) (P>0.05; R2=0.007), nor hare density (Ht) and PREC the year preceding the
autumn of hare density data collection (i.e. PREC t-1 relative to Ht) (P>0.05; R2=0.006)
(Figure 5.18).
(a)
(b)
(c)
Figure 5.18 (a) Coyote density against total winter precipitation (PREC) the same year; (b) coyote density
against PREC the year before; and (c) hare density against PREC the year preceding hare data collection.
PREC=total winter (October to March) precipitation (mm) recorded at Burwash Landing. Data are for the
period 1985/86–2006/07.
85
The AICc analysis of coyote density against hare density and total winter precipitation
(PREC) demonstrated that the model with the lowest AICc and highest Akaike weight
(ω1=0.50) was model 1 (Table 5.13). Model 1 for this dataset is described in section
5.3.2 above.
The second ranked model was model 2 (Table 5.13). The overall regression was
significant (F=6.16; df=2,18; P=0.0092) with R2=0.41 and indicated a positive effect of
hares on coyote density, and a negative effect of the interaction between hares and
PREC, however neither of the parameter estimates ß1 and ß3 nor the intercept (ß0) were
significant (Table 5.14). The AICc difference for model 2 was low (∆AICc<2;
Table 5.13) showing support for this model as an alternative to model 1 given the data,
however the Akaike weight was low (ω2=0.19) indicating very low model probability.
The regression equation for the fitted model 2 is:
Ct = 6.025 + 17.007Ht-1 – 0.124PRECt-1×Ht-1
The remaining models (models 3, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3075
(Table 5.13).
86
Table 5.13 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of total precipitation (mm) for the months October-March inclusive (PRECt-1). RSS=residual sum of
squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike weight; na=not applicable.
The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0
0.5041
2
Ct = a + cHt-1 + dPREC×Ht-1
1932.4797
0.41
4
105.4628
1.9694
0.1883
3
Ct = f + bHt-1 + gPRECt-1
2004.9104
0.38
4
106.2355
2.7421
0.1280
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
2.9794
0.1137
5
Ct = a +cHt-1h + dPREC×Ht-1h
1894.5000
na
5
108.5459
5.0526
0.0403
6
Ct = f + bHt-1h + gPRECt-1
1978.3000
na
5
109.4549
5.9615
0.0256
Table 5.14 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and PRECt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for PRECt-1; ß3=regression coefficient for interaction between PRECt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
6.0250
3.4532
1.74
0.0981
9.8839
8.1015
1.22
0.2382
9.2878
2.7577
3.37
0.0032
17.0066
8.2520
2.06
0.0541
9.7564
2.9377
3.32
0.0038
na
na
na
na
na
na
na
na
-0.0754
0.1380
-0.55
0.5911
na
na
na
na
-0.1242
0.1252
-0.99
0.3341
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
2.4203
10.9767
0.2205
0.8277
7.2172
13.1194
0.5501
0.5883
12.204
11.8921
1.0262
0.3170
23.6957
18.879
1.2551
0.2239
14.9347
15.5435
0.9608
0.3481
na
na
na
na
na
na
na
na
-0.095
0.146
-0.6507
0.5227
na
na
na
na
-0.1554
0.1527
-1.0177
0.3210
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.6745
0.6316
1.0679
0.2983
0.6491
0.7282
0.8914
0.3833
87
5.3.4 Rain
There was no significant relationship between coyote density (Ct) and total winter rain
the same year (RAINt) (P>0.05; R2=0.016), Ct and RAIN the previous year
(RAINt-1) (P>0.05; R2=0.013), nor hare density (Ht) and RAIN the year preceding the
autumn of hare density data collection (i.e. RAINt-1 relative to Ht) (P>0.05; R2=0.04)
(Figure 5.19).
(a)
(b)
(c)
Figure 5.19 (a) Coyote density against total winter rain (RAIN) the same year; (b) coyote density against
RAIN the year before; and (c) hare density against RAIN the year preceding hare data collection.
RAIN=total winter (October to March) rain (mm) recorded at Burwash Landing. Data are for the period
1985/86–2006/07.
88
The AICc analysis of coyote density against hare density and total winter rain (RAIN)
demonstrated that the model with the lowest AICc and highest Akaike weight
(ω1=0.40) was model 1 (Table 5.15). Model 1 for this dataset is described in section
5.3.2 above.
The second ranked model was model 2 (Table 5.15). The overall regression was
significant (F=6.76; df=2,18; P=0.0065) with R2=0.43, and indicated a positive effect of
hares on coyote density and a positive effect of the interaction between hares and RAIN,
however this latter parameter estimate (ß3) was not significant (Table 5.16). The AICc
difference for model 2 was low (∆AICc<2; Table 5.15) showing support for this model
as an alternative to model 1 given the data, however the Akaike weight was low
(ω2=0.23) indicating low model probability. The regression equation for the fitted
model 2 is:
Ct = 5.418 + 7.690Ht-1 + 1.190RAINt-1×Ht-1
The remaining models (models 3, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3704
(Table 5.15).
89
Table 5.15 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of total rain (mm) for the months October-March inclusive (RAINt-1). RSS=residual sum of squares;
R2=coefficient of determination; K=number of parameters; ωi=Akaike weight; na=not applicable. The
model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0
0.4035
2
Ct = a + cHt-1 + dRAIN t-1×Ht-1
1859.2016
0.43
4
104.6510
1.1576
0.2262
3
Ct = f + bHt-1 + gRAINt-1
1880.4809
0.42
4
104.8900
1.3966
0.2007
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
2.9794
0.0910
5
Ct = a + cHt-1h + dRAIN t-1×Ht-1h
1841.7000
na
5
107.9524
4.4590
0.0434
6
Ct = f + bHt-1h + gRAINt-1
1878.4000
na
5
108.3667
4.8733
0.0353
Table 5.16 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and RAINt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for RAINt-1; ß3=regression coefficient for interaction between RAINt-1 and Ht-1;
ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The model
with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
5.4180
3.4036
1.59
0.1288
2.8955
4.1870
0.69
0.4980
9.2878
2.7577
3.37
0.0032
7.6897
2.9657
2.59
0.0184
9.8698
2.7623
3.57
0.0022
na
na
na
na
na
na
na
na
1.1518
0.9373
1.23
0.2350
na
na
na
na
1.1897
0.9036
1.32
0.2045
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
3.2649
7.3655
0.4433
0.6623
2.2502
7.2795
0.3091
0.7604
12.204
11.8921
1.0262
0.3170
10.3103
8.455
1.2194
0.2369
10.8979
9.5276
1.1438
0.2662
na
na
na
na
na
na
na
na
1.1347
0.9767
1.1618
0.2590
na
na
na
na
1.3493
1.0577
1.2757
0.2167
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.7757
0.5239
1.4806
0.1543
0.9056
0.7751
1.1684
0.2564
90
5.3.5 Snow
There was no direct significant relationship between coyote density (Ct) and total winter
snow the same year (SNOWt) (P>0.05; R2=0.17), Ct and SNOW the previous year
(SNOW t-1) (P>0.05; R2=0.001), nor hare density (Ht) and SNOW the year preceding
the autumn of hare density data collection (i.e. SNOW t-1 relative to Ht) (P>0.05;
R2=0.02) (Figure 5.20).
(a)
(b)
(c)
Figure 5.20 (a) Coyote density against total snow (SNOW) the same year; (b) coyote density against
SNOW the year before; and (c) hare density against SNOW the year preceding hare data collection.
SNOW=total winter (October to March) snow (cm) recorded at Burwash Landing. Data are for the period
1985/86–2006/07.
91
The AICc analysis of coyote density against hare density and total winter snow
(SNOW) demonstrated that the model with the lowest AICc and highest Akaike weight
(ω1=0.46) was model 1 (Table 5.17). Model 1 for this dataset is described in section
5.3.2 above.
The second ranked model was model 2 (Table 5.17). The overall regression was
significant (F=6.19; df=2,18; P=0.009) with R2=0.41, and indicated a positive effect of
hares on coyote density and a negative effect of the interaction between hares and
SNOW, however this latter parameter estimate (ß3) was not significant (Table 5.18).
The AICc difference for model 2 was low (∆AICc<2; Table 5.17) showing support for
this model as an alternative to model 1 given the data, however the Akaike weight was
low (ω2=0.17) indicating very low model probability. The regression equation for the
fitted model 2 is:
Ct = 5.85 + 16.534Ht-1 – 0.079SNOWt-1×Ht-1
The remaining models (models 3, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3596
(Table 5.17).
92
Table 5.17 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of total snow (cm) for the months October-March inclusive (SNOWt-1). RSS=residual sum of
squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike weight; na=not applicable.
The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0
0.4636
2
Ct = a + cHt-1 + dSNOW×Ht-1
1928.7148
0.41
4
105.4218
1.9284
0.1768
3
Ct = f + bHt-1 + gSNOWt-1
1929.9142
0.41
4
105.4349
1.9415
0.1756
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
2.9794
0.1045
5
Ct = a + cHt-1h + dSNOW×Ht-1h
1866.1000
na
5
108.2288
4.7354
0.0434
6
Ct= f + bHt-1h + gSNOW t-1
1899.9000
na
5
108.6057
5.1123
0.0360
Table 5.18 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and SNOWt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for SNOWt-1; ß3=regression coefficient for interaction between SNOWt-1 and
Ht-1; ß4=power curve exponent; E=estimate; SE=standard error; na=not applicable. The
model with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
5.8516
3.4475
1.70
0.1069
13.0159
7.8824
1.65
0.1160
9.2878
2.7577
3.37
0.0032
16.5341
7.6793
2.15
0.0451
10.2815
2.9288
3.51
0.0025
na
na
na
na
na
na
na
na
-0.0961
0.0956
-1.01
0.3282
na
na
na
na
-0.0790
0.0781
-1.01
0.3254
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
0.5801
13.1352
0.0442
0.9652
10.1611
12.7757
0.7953
0.4358
12.204
11.8921
1.0262
0.3170
26.3146
19.702
1.3356
0.1967
15.3027
14.2911
1.0708
0.2970
na
na
na
na
na
na
na
na
-0.1059
0.0991
-1.0686
0.2980
na
na
na
na
-0.1132
0.0963
-1.1755
0.2536
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.5917
0.5729
1.0328
0.3140
0.6682
0.6712
0.9955
0.3314
93
5.3.6 Mean minimum winter temperature
There was no significant relationship between coyote density (Ct) and mean minimum
winter temperature the same year (minTEMt) (P>0.005; R2=0.02) (Figure 5.21(a)).
There was, however, a significant negative relationship between Ct and minTEM the
previous year (minTEM t-1) (F=7.35; df=1,19; P=0.0138; R2=0.28) (Figure 5.21(b)). The
relationship between hare density (Ht) and minTEM the year preceding the autumn of
hare density data collection (i.e. minTEM t-1 relative to Ht) was not significant
(P>0.005; R2=0.07) (Figure 5.21(c)).
(a)
(b)
(c)
Figure 5.21 (a) Coyote density against mean minimum winter temperature (minTEM) the same year;
(b) coyote density against minTEM the year before; and (c) hare density against minTEM the year
preceding hare data collection. minTEM=mean winter (October to March) minimum temperature (°C)
recorded at Burwash Landing. Data are for the period 1985/86–2006/07. Solid line shows significant
fitted regression.
94
The AICc analysis of coyote density against hare density and mean minimum winter
temperature (minTEM) demonstrated that the model with the lowest AICc and highest
Akaike weight (ω1=0.43) was model 1 (Table 5.19). Model 1 for this dataset is
described in section 5.3.2 above.
The second ranked model was model 3 (Table 5.19). The overall regression was
significant (F=6.74; df=2,18; P=0.007) with R2=0.43, and indicated a positive effect of
hare density on coyote density, and a negative effect of minTEM (Table 5.20). The
AICc difference for model 3 was low (∆AICc<2; Table 5.19) showing support for this
model as an alternative to model 1 given the data, however the Akaike weight was low
(ω3 =0.24) indicating low model probability. The only parameter estimate that was
significant was ß1 (the effect of hares) (Table 5.20). The parameter estimate for the
intercept (ß0) was unrealistic (Table 5.20). The regression equation for the fitted model
3 is:
Ct = –24.447 + 6.991Ht-1 – 1.591minTEMt-1
The remaining models (models 2, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3314
(Table 5.19).
95
Table 5.19 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of mean minimum temperature (°C) for the months October-March inclusive (minTEMt-1).
RSS=residual sum of squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike
weight; na=not applicable. The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0
0.4307
2
Ct = a + cHt-1 + dminTEMt-1×Ht-1
1969.7027
0.39
4
105.8634
2.3700
0.1317
3
Ct = f + bH t-1 + gminTEMt-1
1861.7859
0.43
4
104.6801
1.1868
0.2379
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
2.9794
0.0971
5
Ct = a + cH t-1h + dminTEMt-1×Ht-1h
1806.4000
na
5
107.5459
4.0526
0.0568
6
Ct = f + bH t-1h + gminTEMt-1
1843.6000
na
5
107.9740
4.4806
0.0458
Table 5.20 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and mean minimum temperature (minTEMt-1). ß0=intercept; ß1=regression
coefficient for Ht-1; ß2=regression coefficient for minTEMt-1; ß3=regression coefficient for
interaction between minTEMt-1 and Ht-1; ß4=power curve exponent; E=estimate;
SE=standard error; na=not applicable. The model with the most support is shown in bold.
Model
1
2
3
4
5
6
ß0
ß1
ß2
ß3
ß4
E
SE
t
P
E
SE
t
P
E
SE
t
P
5.8915
3.4493
1.71
0.1039
6.8623
3.6934
1.86
0.0796
-24.4470
23.4739
-1.04
0.3115
9.2878
2.7577
3.37
0.0032
-9.2350
23.5714
-0.39
0.6998
6.9913
3.2286
2.17
0.0440
na
na
na
na
na
na
na
na
-1.5906
1.2178
-1.31
0.2080
na
na
na
na
-0.8151
1.0300
-0.79
0.4390
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
E
SE
t
P
E
SE
t
P
E
SE
t
P
3.8431
9.3894
0.4093
0.6867
-2.9032
26.1785
-0.1109
0.9128
-28.8675
29.807
-0.9685
0.3444
12.204
11.8921
1.0262
0.3170
-22.5984
37.7695
-0.5983
0.5563
11.7114
17.221
0.6801
0.5043
na
na
na
na
na
na
na
na
-1.6326
1.2546
-1.3013
0.2080
na
na
na
na
-2.038
1.3206
-1.5432
0.1384
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.2899
0.483
0.6002
0.5551
0.5721
0.9724
0.5883
0.5629
96
5.3.7 Mean winter temperature
There was no direct significant relationship between coyote density (Ct) and mean
winter temperature the same year (TEMt) (P>0.05; R2=0.06) (Figure 5.22(a)). There
was, however, a significant negative relationship between Ct and TEM the previous
year (TEM t-1) (F=10.53; df=1,19; P=0.004; R2=0.36) (Figure 5.22(b)). The relationship
between hare density (Ht) and TEM the year preceding the autumn of hare density data
collection (i.e. TEM t-1 relative to Ht) was not significant (P>0.05; R2=0.10)
(Figure 5.22(c)).
(a)
(b)
(c)
Figure 5.22 (a) Coyote density against mean winter temperature (TEM) the same year; (b) coyote density
against TEM the year before; and (c) hare density against TEM the year preceding hare data collection.
TEM=mean winter (October to March) temperature (°C) recorded at Burwash Landing. Data are for the
period 1985/86–2006/07. Solid line shows significant fitted regression.
97
The AICc analysis of coyote density against hare density and mean winter temperature
(TEM) demonstrated that the model with the lowest AICc and highest Akaike weight
(ω3=0.32) was model 3 (Table 5.21). The overall regression was significant (F=7.76;
df=2,18; P=0.0037) with R2=0.46. Despite the overall significance of the regression,
none of the parameter estimates were significant and in particular, the estimate for the
intercept (ß0) was not significantly different to zero (Table 5.22). The regression
equation for the fitted model 3 is:
Ct = –21.743 + 6.0747Ht-1 – 2.206TEMt-1
The second ranked model was model 1 (Table 5.21) and is described in section 5.3.2
above. The AICc difference for this model was very low (∆AICc=0.14; Table 5.21)
indicating support for this model as an alternative to model 3, however the Akaike
weight was low (ω1=0.30) indicating low model probability.
The remaining models (models 2, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.3768
(Table 5.21).
98
Table 5.21 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of mean temperature (°C) for the months October-March inclusive (TEMt-1). RSS=residual sum of
squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike weight; na=not applicable.
The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
0.1351
0.3011
2
Ct = a + cHt-1 + dTEMt-1×Ht-1
1874.2941
0.42
4
104.8208
1.4625
0.1550
3
Ct = f + bHt-1 + gTEMt-1
1748.2080
0.46
4
103.3583
0
0.3221
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
3.1145
0.0679
5
Ct = a + cHt-1h + dTEMt-1×Ht-1h
1661.9000
na
5
105.7951
2.4368
0.0953
6
Ct = f + bHt-1h + gTEMt-1
1740.6000
na
5
106.7667
3.4084
0.0586
Table 5.22 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and TEMt-1. ß0=intercept; ß1=regression coefficient for Ht-1; ß2=regression
coefficient for mean temperature (TEMt-1); ß3=regression coefficient for interaction
between TEMt-1 and Ht-1; ß4=power curve exponent; E=estimate; SE=standard error; na=not
applicable. The model with the most support is shown in bold.
Model
1
2
3
4
5
6
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
ß0
ß1
ß2
ß3
ß4
5.8915
3.4493
1.71
0.1039
7.4529
3.6189
2.06
0.0542
-21.7433
16.3252
-1.33
0.1995
3.8431
9.3894
0.4093
0.6867
1.0274
15.3866
0.0668
0.9474
-23.7901
20.0301
-1.1877
0.2489
9.2878
2.7577
3.37
0.0032
-14.6469
19.2678
-0.76
0.4570
6.0741
3.2161
1.89
0.0752
12.204
11.8921
1.0262
0.3170
-25.2559
28.2257
-0.8948
0.3815
9.0327
13.6798
0.6603
0.5166
na
na
na
na
na
na
na
na
-2.2058
1.2765
-1.73
0.1011
na
na
na
na
na
na
na
na
-2.1977
1.3128
-1.6741
0.1097
na
na
na
na
-1.4914
1.1886
-1.25
0.2256
na
na
na
na
na
na
na
na
-2.8454
1.4096
-2.0186
0.0571
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.3221
0.4059
0.7935
0.4368
0.6606
1.0934
0.6042
0.5525
99
5.3.8 Mean maximum winter temperature
There was no direct significant relationship between coyote density (Ct) and mean
maximum winter temperatue the same year (maxTEMt) (P>0.05; R2=0.10)
(Figure 5.23(a)). There was, however, a significant negative relationship between Ct and
maxTEM the previous year (maxTEM t-1) (F=13.40; df=1,19; P=0.002; R2=0.41)
(Figure 5.23(b)). The relationship between hare density (Ht) and maxTEM the year
preceding the autumn of hare density data collection (i.e. maxTEM t-1 relative to Ht) was
not significant (P>0.05; R2=0.13) (Figure 5.23(c)).
(a)
(b)
(c)
Figure 5.23 (a) Coyote density against mean maximum winter temperature (maxTEM) the same year;
(b) coyote density against maxTEM the year before; and (c) hare density against maxTEM the year
preceding hare data collection. maxTEM=mean winter (October to March) maximum temperature (°C)
recorded at Burwash Landing. Data are for the period 1985/86–2006/07. Solid line shows significant
fitted regression.
100
The AICc analysis of coyote density against hare density and mean maximum winter
temperature (maxTEM) demonstrated that the model with the lowest AICc and highest
Akaike weight (ω3=0.37) was model 3 (Table 5.23). The overall regression was
significant (F=8.89; df=2,18; P=0.0021) with R2=0.50, and indicated a positive effect of
hare density and a negative effect of maxTEM. Despite the overall significance of the
regression, none of the parameter estimates were significant and in particular, the
estimate for the intercept (ß0) was unrealistic (Table 5.24). The regression equation for
the fitted model 3 is:
Ct = –10.123 + 5.416Ht-1 – 2.690maxTEMt-1
The second ranked model was model 2 (Table 5.23). The AICc difference for this model
was low (∆AICc<2; Table 5.23) showing support for this model as an alternative to
model 3, however, the Akaike weight was low (ω2=0.21) indicating low model
probability.
The remaining models (models 1, 4, 5, and 6) had the lowest support from the AICc
analysis. The sum of the Akaike weights (ωi) for these models was ∑ ωi=0.4252
(Table 5.23).
101
Table 5.23 The goodness of fit of models of coyote numerical response (density, Ct) to hares (Ht-1) with the
effect of mean maximum temperature (°C) for the months October-March inclusive (maxTEMt-1).
RSS=residual sum of squares; R2=coefficient of determination; K=number of parameters; ωi=Akaike
weight; na=not applicable. The model with the most support is shown in bold.
Model
Formula
RSS
R2
K
AICc
∆AICc
ωi
1
Ct = a + bHt-1
2038.2316
0.37
3
103.4934
1.5056
0.1720
2
Ct = a + bHt-1 + dmaxTEM×H t-1
1726.5018
0.47
4
103.0959
1.1082
0.2098
3
Ct = f + bH t-1 + gmaxTEM t-1
1637.7557
0.50
4
101.9878
0
0.3651
4
Ct = a + bHt-1h
2027.7000
na
4
106.4728
4.4851
0.0388
5
Ct = a + bH t-1h + dmaxTEM×Ht-1h
1508.0000
na
5
103.7544
1.7666
0.1509
6
Ct = f + bH t-1h + gmaxTEM t-1
1637.6000
na
5
105.4858
3.4980
0.0635
Table 5.24 Parameter estimates for models of the numerical response of coyote density (Ct)
to hares (Ht-1) and mean maximum temperature (maxTEMt-1). ß0=intercept; ß1=regression
coefficient for Ht-1; ß2=regression coefficient for maxTEMt-1; ß3=regression coefficient for
interaction between maxTEMt-1 and Ht-1; ß4=power curve exponent; E=estimate;
SE=standard error; na=not applicable. The model with the most support is shown in bold.
Model
1
2
3
4
5
6
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
E
SE
t
P
ß0
ß1
ß2
ß3
ß4
5.8915
3.4493
1.71
0.1039
7.9872
3.4625
2.31
0.0332
-10.1233
8.2681
-1.22
0.2366
3.8431
9.3894
0.4093
0.6867
4.5222
8.8366
0.5118
0.6144
-10.3229
9.5887
-1.0766
0.2945
9.2878
2.7577
3.37
0.0032
-12.3104
12.2610
-1.00
0.3287
5.4163
3.1393
1.73
0.1016
12.204
11.8921
1.0262
0.3170
-16.6427
17.6321
-0.9439
0.3565
5.8156
9.0772
0.6407
0.5290
na
na
na
na
na
na
na
na
-2.6897
1.2820
-2.10
0.0503
na
na
na
na
na
na
na
na
-2.6805
1.3322
-2.0121
0.0579
na
na
na
na
-2.3244
1.2894
-1.80
0.0882
na
na
na
na
na
na
na
na
-3.624
1.4639
-2.4756
0.0224
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
na
0.7555
0.7745
0.9755
0.3410
0.3859
0.3584
1.0767
0.2944
0.9344
1.3206
0.7076
0.4874
102
5.3.9 Reconstructions of coyote density using local climate variables
Extreme maximum winter temperature
The reconstructions of coyote density using models 2 and 3 (the first and second ranked
models respectively) showed departure from the observed data, falling outside of the
95% confidence intervals, particularly over the second population cycle (1995–2000)
(Figure 5.24).
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
0
Winter
Figure 5.24 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 2 (○) and second ranked model 3 () using EmaxTEM (Table 5.10). Vertical
bars=95% confidence intervals.
103
Figure 5.25 shows the reconstructed influence of EmaxTEMt-1 on Ct, using the model 2
parameter estimates. The influence is on the slope of coyote numerical response, with
an increase in the slope with lower extreme maximum winter temperatures (i.e. colder),
and a corresponding decrease in the slope with higher extreme maximum winter
temperatures (i.e. warmer).
40
35
EMaxTt-1 = 2.3°C
30
Ct
25
20
EMaxTt-1 = 5.43°C
15
10
EMaxTt-1 = 6.5°C
5
EMaxTt-1 = 8.48°C
0
0
1
2
3
Ht-1
Figure 5.25 Influence of EmaxTEMt-1 on coyote numerical response (Ct) to snowshoe hare density
(Ht-1), reconstructed with the model 2 parameter estimates (Table 5.10). EMaxTEM values: unbroken
lines=highest, mean, and lowest overall; broken line=threshold extreme maximum winter temperature
(i.e. no change in slope).
104
Extreme minimum winter temperature
The model 1 reconstruction of coyote density showed marked departure from the
observed data over the first two population cycles with estimates falling outside the
95% confidence intervals (Figure 5.26). Less departure from the observed data is noted
over the third population cycle. The second ranked model 3 exhibited gross departure
from the observed data with large over and under estimations (Figure 5.26).
90
Coyote density (Ct)
70
50
30
10
-10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
-30
Winter
Figure 5.26 Observed data (solid line) and estimates (broken lines) of coyote density reconstructed from
the first ranked model 1 (○) and the second ranked model 3 () using EminTEM (Table 5.12). Vertical
bars=95% confidence intervals.
105
Precipitation, rain and snow
The AICc analyses of precipitation, rain, and snow each nominated model 1 and
model 2 as the first and second ranked models respectively. In each case similar
reconstructions of the observed data were shown between models 1 and 2, with minimal
departures between them (Figure 5.27). The reconstructions were not a good fit of the
observed data over the first two population cycles, but improved markedly for the third,
i.e. from the winter of 2002/03 onwards (Figure 5.27).
Minimum, mean and maximum winter temperatures
Reconstructions of coyote density using the first and second ranked models for mean
minimum winter temperature (models 1 and 3 respectively), mean winter temperature
(models 3 and 1 respectively), and mean maximum temperature (models 3 and 2
respectively) against the observed data were typically unremarkable (Figure 5.28). The
least departure from the observed data in each case was again seen in the third
population cycle (Figure 5.28).
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
Coyote density (Ct)
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
Coyote density (Ct)
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
Coyote density (Ct)
106
(a)
60
50
40
30
20
10
0
Winter
(b)
60
50
40
30
20
10
0
Winter
(c)
60
50
40
30
20
10
0
Winter
Figure 5.27 (a) Precipitation, (b) rain and (c) snow. Observed data (solid line) and estimates (broken
lines) of coyote density reconstructed from the first ranked model 1 (○) and second ranked model 2 ()
(Tables 5.14, 5.16, and 5.18). Vertical bars=95% confidence intervals.
107
(a)
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
0
Winter
(b)
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
0
Winter
(c)
60
Coyote density (Ct)
50
40
30
20
10
87
/8
8
88
/8
9
89
/9
0
90
/9
1
91
/9
2
92
/9
3
93
/9
4
94
/9
5
95
/9
6
96
/9
7
97
/9
8
98
/9
9
99
/0
0
00
/0
1
01
/0
2
02
/0
3
03
/0
4
04
/0
5
05
/0
6
06
/0
7
07
/0
8
0
Winter
Figure 5.28 (a) Minimum, (b) mean and (c) maximum winter temperatures. Observed data (solid line)
and estimates (broken lines) of coyote density reconstructed from the first ranked model (○), and second
ranked model (). For (a) mean minimum winter temperature ○=model 1 and =model 3; for (b) mean
winter temperature ○=model 3 and =model 1; and for (c) mean maximum winter temperature ○=model
3 and =model 2 (Tables 5.20, 5.22, and 5.24). Vertical bars=95% confidence intervals.
108
5.4 Summary of Akaike weight values (ωi) for each climate variable
The summary of the Akaike weights (relative likelihood) for each model given the data
(Table 5.25) shows support for linear relationships between the coyote numerical
response to hare density (model 1) and hare density and climate (models 2 and 3).
Of the large-scale climate indices the NAO had the highest relative support with model
2, which incorporates the interactive effect of hares and the NAO (ω2=0.78). Of the
local climate variables mean extreme maximum winter temperature had the highest
relative support, again with model 2 (ω2=0.58). Model 1 which excludes the effect of
climate was favoured in the model selection process for seven candidate sets although
with relatively low support in each case.
Table 5.25 Summary of Akaike weights for each model for large-scale and local climate variables.
The model with the most support from the candidate set for each variable (row) is shown in bold.
ωi
Local climate variables
Large-scale climate
variables
Models
1
2
3
4
5
6
North Atlantic Oscillation
0.0001
0.7826
0.0046
0.0000
0.2118
0.0009
El Niño-Southern Oscillation
(Southern Oscillation Index)
0.5285
0.1692
0.1216
0.1233
0.0336
0.0238
Pacific/North American
0.5377
0.1515
0.1307
0.1255
0.0293
0.0253
North Pacific Index
0.3186
0.3761
0.1078
0.0744
0.1016
0.0214
Extreme maximum winter
temperature
0.0152
0.5803
0.2012
0.0034
0.1648
0.0350
Extreme minimum winter
temperature
0.4810
0.1297
0.2013
0.1084
0.0421
0.0375
Precipitation
0.5041
0.1883
0.1280
0.1137
0.0403
0.0256
Rain
0.4035
0.2262
0.2007
0.0910
0.434
0.0353
Snow
0.4636
0.1768
0.1756
0.1045
0.0434
0.0360
Minimum winter temperature
0.4307
0.1317
0.2379
0.0971
0.0568
0.0458
Winter temperature
0.3011
0.1550
0.3221
0.0679
0.0953
0.0586
Maximum winter temperature
0.1720
0.2098
0.3651
0.0388
0.1509
0.0635
109
CHAPTER 6: RESULTS—RELATIVE SUPPORT FOR EACH CLIMATE
VARIABLE BY MODEL
This chapter assesses relative support for each climate variable on a model-by-model
basis. The previous chapter assessed relative support for each model on a climate
variable-by-climate variable basis.
6.1 Model 2 (Ct = a + bHt-1 + dWt-1×Ht-1)
For large-scale climate indices, the NAO had an Akaike weight of ωNAO=0.99 and
R2=0.76. The remaining large-scale indices each had very low Akaike weights
(∑ ωi=0.00014) and large AICc differences (∆AICc > 18) showing virtually no
empirical support for them given the data (Table 6.1). For local climate variables,
EmaxTEM had an Akaike weight of ωEmaxTEM=0.91 and R2=0.62. The remaining local
variables had very low Akaike weights (∑ ωi=0.087) and ∆AICc > 6 showing little
empirical support for them given the data (Table 6.1).
Local
n=21
Large-scale
n=23
Table 6.1 The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
interactive effect of each climate variable (Wt-1) for model 2 ranked by Akaike weight. RSS=residual
sum of squares; R2=coefficient of determination; K (number of parameters)=4; ωi=Akaike weight.
Model 2 formula: Ct = a + bHt-1 + dWt-1×Ht-1. The climate variable with the most support for each
set is shown in bold.
Climate
variable (Wt-1)
RSS
R2
AICc
∆AICc
ωi
Rank
NAO
794.9132
0.76
91.70521
0
0.9999
1
NPI
1783.5957
0.47
110.2927
18.59
0.0001
2
SOI
1997.8908
0.40
112.9023
21.20
0.0000
3
PNA
2020.1624
0.39
113.1573
21.45
0.0000
4
EMaxTEM
1244.0439
0.62
96.2136
0
0.9131
1
maxTEM
1726.5018
0.47
103.0959
6.88
0.0292
2
RAIN
1859.2016
0.43
104.6510
8.44
0.0134
3
TEM
1874.2941
0.42
104.8208
8.61
0.0123
4
SNOW
1928.7148
0.41
105.4218
9.21
0.0091
5
PREC
1932.4797
0.41
105.4628
9.25
0.0090
6
minTEM
1969.7027
0.39
105.8634
9.65
0.0073
7
EMinTEM
1993.3271
0.39
106.1138
9.90
0.0065
8
110
6.2 Model 3 (Ct = f + bHt-1 + gWt-1)
For large-scale climate indices, the NAO had an Akaike weight of ωNAO=0.99 and
R2=0.63. The remaining large-scale indices each had very low Akaike weights
(∑ ωi=0.01) and large AICc differences (∆AICc > 10) showing virtually no empirical
support for them given the data (Table 6.2).
For local climate variables, EmaxTEM had an Akaike weight of ωEmaxTEM=0.71 and
R2=0.58. The AICc difference between EmaxTEM and the second ranked variable,
mean maximum winter temperature (maxTEM) was low (∆AICc=3.66) but so too was
the Akaike weight (ωmaxTEM=0.11). The remaining local variables had low Akaike
weights (∑ ωi=0.18) and ∆AICc > 5 showing low empirical support for them given the
data (Table 6.2).
Local
n=21
Large-scale
n=23
Table 6.2 The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with the
additive effect of each climate variable (Wt-1) for model 3 ranked by Akaike weight. RSS=residual sum
of squares; R2=coefficient of determination; K (number of parameters)=4; ωi=Akaike weight.
Model 3 formula: Ct = f + bHt-1 + gWt-1. The climate variable with the most support for each set is
shown in bold.
Climate
variable (Wt-1)
RSS
R2
AICc
∆AICc
ωi
Rank
NAO
1243.5382
0.63
101.9973
0
0.9893
1
NPI
1988.3339
0.40
112.7921
10.79
0.0045
2
PNA
2046.3683
0.39
113.4538
11.46
0.0032
3
SOI
2056.1453
0.38
113.5634
11.57
0.0030
4
EMaxTEM
1376.0930
0.58
98.3321
0
0.7138
1
maxTEM
1637.7557
0.50
101.9878
3.66
0.1148
2
TEM
1748.2080
0.46
103.3583
5.03
0.0578
3
minTEM
1861.7859
0.43
104.6801
6.35
0.0299
4
RAIN
1880.4809
0.42
104.8900
6.56
0.0269
5
EMinTEM
1911.6608
0.41
105.2353
6.90
0.0226
6
SNOW
1929.9142
0.41
105.4349
7.10
0.0205
7
PREC
2004.9104
0.38
106.2355
7.90
0.0137
8
111
6.3 Model 5 (Ct = a + cHt-1h + dWt-1×Ht-1h)
For large-scale climate indices, the NAO had an Akaike weight of ωNAO=0.99. The
remaining large-scale indices each had very low Akaike weights (∑ ωi=0.0001), and
large AICc differences (∆AICc > 18) showing virtually no empirical support for them
given the data (Table 6.3).
For local climate variables, EmaxTEM had an Akaike weight of ωEmaxTEM=0.86. The
remaining local variables had very low Akaike weights (∑ ωi=0.14) and ∆AICc > 5
showing little empirical support for them given the data (Table 6.3).
Local
n=21
Large-scale
n=23
Table 6.3 The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with
the interactive effect of each climate variable (Wt-1) for model 5 ranked by Akaike weight.
RSS=residual sum of squares; K (number of parameters)=5; ωi=Akaike weight.
Model 5 formula: Ct = a + cHt-1h + dWt-1×Ht-1h. The climate variable with the most support
for each set is shown in bold.
Climate
variable (Wt-1)
RSS
AICc
∆AICc
ωi
Rank
NAO
771.3000
94.31883
0
0.9999
1
NPI
1730.9000
112.9102
18.59
0.0001
2
SOI
1991.7000
116.1382
21.82
0.0000
3
PNA
2018.4000
116.4444
22.13
0.0000
4
EMaxTEM
1187.2000
98.73144
0
0.8645
1
maxTEM
1508.0000
103.7544
5.02
0.0702
2
TEM
1661.9000
105.7951
7.06
0.0253
3
minTEM
1806.4000
107.5459
8.81
0.0105
4
RAIN
1841.7000
107.9524
9.22
0.0086
5
SNOW
1866.1000
108.2288
9.50
0.0075
6
EMinTEM
1878.4000
108.3667
9.64
0.0070
7
PREC
1894.5000
108.5459
9.81
0.0064
8
112
6.4 Model 6 (Ct = f + bHt-1h + gWt-1)
For large-scale climate indices, the NAO had an Akaike weight of ωNAO=0.99. The
remaining large-scale indices each had very low Akaike weights (∑ ωi=0.011) and large
AICc differences (∆AICc > 10) showing very little empirical support for them given the
data (Table 6.4).
For local climate variables, EmaxTEM had an Akaike weight of ωEmaxTEM=0.70. The
AICc difference between EmaxTEM and the second ranked variable maxTEM was low
(∆AICc=3.66) but so too was the Akaike weight (ωmaxTEM=0.11). The remaining local
variables had low AICc differences between them (∆AICc ≤ 7.63) but also had very low
Akaike weights (∑ ωi=0.19) showing low support for them given the data (Table 6.4).
Local
n=21
Large-scale
n=23
Table 6.4 The goodness of fit of coyote numerical response (density, Ct) to hares (Ht-1) with
the additive effect of each climate variable (Wt-1) for model 6 ranked by Akaike weight.
RSS=residual sum of squares; K (number of parameters)=5; ωi=Akaike weight. Model 6
formula: Ct = f + bHt-1h + gWt-1. The climate variable with the most support for each set is
shown in bold.
Climate
variable (Wt-1)
RSS
AICc
∆AICc
ωi
Rank
NAO
1243.4000
105.3020
0
0.9890
1
NPI
1981.6000
116.0212
10.72
0.0047
2
PNA
2044.3000
116.7377
11.44
0.0033
3
SOI
2052.4000
116.8286
11.53
0.0031
4
EMaxTEM
1375.9000
101.8292
0
0.7045
1
maxTEM
1637.6000
105.4858
3.66
0.1132
2
TEM
1740.6000
106.7667
4.94
0.0597
3
minTEM
1843.6000
107.9740
6.14
0.0326
4
RAIN
1878.4000
108.3667
6.54
0.0268
5
EMinTEM
1899.1000
108.5969
6.77
0.0239
6
SNOW
1899.9000
108.6057
6.78
0.0238
7
PREC
1978.3000
109.4549
7.63
0.0156
8
113
6.5 Summary of Akaike weight values (ωi) by model
AICc analyses conducted on a model-by-model basis for models that incorporated a
climate parameter (models 2, 3, 5 and 6) consistently showed the NAO as having the
most support (ωNAO>0.9) of the large-scale climate indices (Table 6.5). Mean extreme
maximum winter temperature (EmaxTEM) consistently had the most support
(ωEmaxTEM>0.7) of the local climate variables (Table 6.6).
6.6 Relationships between the NAO and the local climate variables
Of further interest was the potential influence of the NAO on local climate variables,
given the strong support for the effect of the NAO on the coyote numerical response
(Table 5.25 and Table 6.5). Least-squares regression analyses estimated relationships
between the NAO and each local climate variable averaged (temperature variables) or
totaled (for precipitation, rain and snow) for the months coinciding with the NAO
winter index (December to March inclusive). These analyses did not find any significant
relationship (P<0.05) between the NAO and any of the local climate variables
(Appendix 3).
114
Table 6.5 Summary of Akaike weights (ωi) for each large-scale climate variable by
model. The climate variable with the most support for each model is shown in bold.
ωi
Large-scale climate variable
Model
Formula
NAO
NPI
PNA
SOI
2
Ct = a + cHt-1 + dWt-1×Ht-1
0.9999
0.0001
0.0000
0.0000
3
Ct = f + bHt-1 + gWt-1
0.9893
0.0045
0.0032
0.0030
5
Ct = a + cHt-1h + dWt-1×Ht-1h
0.9999
0.0001
0.0000
0.0000
6
Ct = f + bHt-1h + gWt-1
0.9890
0.0047
0.0033
0.0031
Table 6.6 Summary of Akaike weights (ωi) for each local climate variable by model. The climate variable
with the most support for each model is shown in bold.
ωi
Model
Formula
EmaxTEM
maxTEM
TEM
EminTEM
MinTEM
Rain
Prec
Snow
Local climate variable
2
Ct = a + cHt-1 + dWt-1×Ht-1
0.9131
0.0292
0.0123
0.0065
0.0073
0.0134
0.0090
0.0091
3
Ct = f + bHt-1 + gWt-1
0.7138
0.1148
0.0578
0.0226
0.0299
0.0269
0.0137
0.0205
5
Ct = a + cHt-1h + dWt-1×Ht-1h
0.8645
0.0702
0.0253
0.0070
0.0105
0.0086
0.0064
0.0075
6
Ct = f + bHt-1h + gWt-1
0.7045
0.1132
0.0597
0.0239
0.0326
0.0268
0.0156
0.0238
115
CHAPTER 7: DISCUSSION
The results of this study show clear evidence of a numerical response relationship
between coyote density and snowshoe hare density that is influenced by climate.
Model 2 incorporating the NAO received the strongest level of support (Tables 5.1, 5.2
and 5.25) while an intermediate level of support was given to model 2 that incorporated
extreme maximum local winter temperature (Tables 5.9, 5.10 and 5.25). The results
indicate that cooler winter temperatures have a positive effect on the coyote numerical
response (Figures 5.6 and 5.25). Further, the results show that these climate variables do
not affect coyotes or snowshoe hares separately in the Yukon, but influence their
interaction which is apparent in the coyote population density the following winter.
The results firstly extend the positive relationship between coyote and snowshoe hare
densities previously reported for Canadian boreal forest coyote populations (Keith et al.,
1977; Todd et al., 1981; O'Donoghue et al., 1997; Patterson and Messier, 2001).
Secondly, the results provide a greater level of support for the hypothesis that coyote
density is related to both snowshoe hare density and climate the previous year
(Table 5.25) rather than the hypothesis that the coyote numerical response is related to
snowshoe hare density alone. The coefficient of determination (R2) for the numerical
response increased from 0.38 (model 1, Figure 5.3, Table 5.1) to 0.76 (model 2, Table
5.1) and 0.62 (model 2, Table 5.9) with the inclusion of the interactive effect of the
NAO and extreme maximum winter temperature respectively. The linear numerical
responses had greater support (higher Akaike weights) than the curved numerical
responses. However, the linear relationship is likely the straight part of a curve, which
would be more obvious with very high hare densities.
7.1 The influence of climate on the coyote numerical response
The following hypothesis is proposed to explain how the NAO may be affecting the
coyote numerical response (i.e. influencing the slope of the relationship, model 2). An
underlying assumption of this hypothesis is that the mechanistic (population size
estimate) approach applied in this study is analogous to a demographic (reproduction,
116
survival, fecundity) approach, in the sense of Hone and Sibly (2002) (Figure 2.3
herein).
It has already been established that the NAO exerts a dominant influence on wintertime
temperatures and precipitation across much of the northern hemisphere, including
Canada (Hurrell, 1995b; Hurrell et al., 2003; Hurrell and Deser, 2009) (section 3.1.4).
The negative NAO phase equates to colder temperatures in north-western Canada
(Stenseth et al., 1999; Mysterud et al., 2003; Stenseth et al., 2004a; Stenseth et al.,
2004b) and at Kluane very cold winter temperatures can act to limit snowfall (Krebs et
al., 2001b). By contrast, warmer (milder) winters in high latitude regions may increase
the level of snowfall (Beniston et al., 2003; Räisänen, 2008).
A variety of studies have demonstrated: (i) that coyote hunting efficiency and success is
reduced in, and coyotes tend to move out of, areas of deep, soft snow; and (ii) that
coyote population dynamics (reproduction, recruitment, fecundity, and migration
patterns) are directly linked to food. These topics were explored in sections 1.6.3, 2.5
and 3.1.3. If the amount of winter snowfall is limited by cold temperatures due to a
negative NAO phase at year t-1, then coyote functional response (hunting efficiency and
success and, thus, ability to access food and convert that food into more predators) is
increased over the course of that winter. Therefore, it is proposed that following
favourable winters, fecundity of the coyote population (number of young born annually)
and juvenile survival is increased, which would be reflected in coyote density (number
of tracks detected) at year t (Figure 5.6).
Conversely, if snow conditions at year t-1 were not conducive to efficient and effective
hunting (i.e. increased snow depth in milder winters due to a positive NAO phase),
coyote density could be influenced in two ways. Firstly, coyotes may move to more
suitable habitats that have less ground snow cover, as has been shown in other studies
(Gese et al., 1996a; Gese et al., 1996b; O'Donoghue et al., 1998a; Tremblay et al.,
1998; Crête et al., 2001; Crête and Larivière, 2003; Thibault and Ouellet, 2005).
Secondly, the added energetic costs of hunting, and reduced hunting ability and success
could result in lowered body condition and survival, lower pregnancy rates, and lower
reproductive success as has also been shown in other studies (Clark, 1972; Bekoff,
1978; Todd et al., 1981; Todd and Keith, 1983; Crête and Larivière, 2003; Thibault and
117
Ouellet, 2005). In both instances, the fecundity of the population would be reduced,
which would again be reflected in coyote density (number of tracks detected) at
year t (Figure 5.6).
The significant albeit weak negative relationships between coyote density at year t and
all winter temperature variables at year t-1 support this hypothesis (Figures 5.16(b),
5.17(b), 5.21(b), 5.22(b) and 5.23(b)). However, only one model that incorporated a
local temperature variable (model 2 with the interactive effect of extreme maximum
winter temperature) was shown a plausible level of support by the AICc analyses
(Tables 5.9 and 5.25). The mechanism underlying the relationship between the coyote
numerical response and the extreme maximum winter temperature variable is difficult to
explain. It was expected that extreme warmer winter temperatures greater than 0°C
would positively influence coyote numerical response. However, it was found that
warmer winter temperatures and extreme winter temperatures greater than 6.5°C had a
negative effect on coyote numerical response (Figures 5.16(a) and (b) and 5.25). As has
been discussed, milder winters at Kluane can increase snowfall and maintain the snow’s
soft properties. Paradoxically, extreme warmer winter temperatures can in fact cause a
hardening of the snow surface through thaw-refreeze, thereby potentially improving
coyote hunting efficiency and success on snowshoe hares. It is this process that Stenseth
et al. (2004b) describe as central to the functional response dynamics (killing rate
success) of Canada lynx. This anomaly is explored further in section 7.5 below.
7.2 The influence of climate on snowshoe hares
As previously discussed, little work has been done to investigate the potential influence
of climate on snowshoe hare population dynamics (sections 3.1.2 and 3.1.3). Two
studies have implied that snow depth can have a negative influence on snowshoe hare
population dynamics, namely via its effects on hare survival (Watt, 1973) and
reproduction (Sinclair et al., 1993). However, in these instances the evidence remains
either anecdotal (in the case of Watt, 1973) or requires further research (in the case of
Sinclair et al., 1993). In this study, there was no evidence of a direct relationship
between hare density (at time t) or any of the climate variables (at time t-1) evaluated
(Figures 5.16(c) to 5.23(c) inclusive).
118
Watt (1973) proposed that variation in snowfall depth was the main contributing factor
of year-to-year survival of juvenile hares from Lake Alexander, Minnesota USA
(central North America). Namely, increased snowfall as a result of lower winter
temperatures (at time t-1) negatively affected the offspring (at time t) of the females
subjected to the snowfall. Whilst Watt’s (1973) findings were not supported by
statistical analysis or biological explanation, it appears that the dynamics of the
Minnesota snowshoe hare population could have been strongly influenced by
temperature and snow through its effect on juvenile mortality. This is in contrast to
studies on the early survival of juvenile snowshoe hares at Kluane, where the main
proximate cause of juvenile mortality is predation, largely by red squirrels and arctic
ground squirrels (Spermophilus parryii) (O'Donoghue, 1994). Indeed for Kluane
populations predation remains the main cause of mortality, accounting for greater than
90% of deaths across all age classes (O'Donoghue, 1994; Boonstra et al., 1998; Hodges
et al., 2001). Hence, while it appears that climate may be acting directly on the
dynamics of the Minnesota hare population, it is predation which directly influences the
dynamics of the Kluane population.
The hypothesis by Sinclair et al. (1993) that climate variability caused by solar activity
(sunspot numbers at time t-2) influences Kluane snowshoe hare reproductive output
(at time t) requires further study. Sinclair et al. (1993) proposed that their findings be
further tested by obtaining more climate data, however further exploration of their
hypothesis has yet to be pursued. Krebs and Berteaux (2006) later proposed two
possible causal mechanisms to explain the relationship between sunspot numbers and
hare reproductive output. Namely, sunspot activity influenced snow depth, and the snow
depth could, in turn, influence: (i) hare food supplies leading to reduced nutrition; or
(ii) predator hunting behaviour leading to increased stress levels. To date, there is little
evidence that Kluane hare populations are limited by food supply at any time (Krebs et
al., 2001a). There is, however, evidence to suggest that hare reproductive output can be
adversely influenced by predator-induced chronic stress, namely caused by high
predation risk and failed attacks (Boonstra et al., 1998). Failed attacks by coyotes and
lynx are more likely during periods of increased snow depth (O'Donoghue et al., 1998a;
O'Donoghue et al., 1998b). Therefore, it appears that if climate is acting to influence
snowshoe hare population dynamics in the Yukon, that influence is indirect and via their
predators.
119
7.3 Comparisons to other predator–prey studies with the NAO
For terrestrial systems, the NAO has been shown to influence a broad range of
biological processes across a number of taxonomic groups including plants, amphibians,
birds, and mammals (Ottersen et al., 2001; Mysterud et al., 2003). The mechanisms by
which the NAO is suggested to affect processes include its influence on temperature,
precipitation, snow characteristics, vegetation growth, seed production, and seasonal
weather conditions (Mysterud et al., 2003). The effect of the NAO on population
dynamics of ungulates in north-western Europe has been a topic of particular interest.
There have been many studies undertaken over the past decade that show strong
relationships between the NAO and ungulate abundance, body condition, growth, over
winter survival, breeding success, fecundity, and sex ratios (for examples see Mysterud
et al., 2003). These biological variables have been found to be influenced negatively by
variation in climate (winter severity, rainfall and snow depth) and strongly correlated
with the NAO winter index (Ottersen et al., 2001; Stenseth et al., 2002; Mysterud et al.,
2003).
In contrast, the number of studies evaluating the influence of the NAO (and other largescale climate phenomena) on terrestrial carnivores and predator-prey interactions have
been markedly less. Long-term studies on carnivore populations are rare and there are
relatively few studies of temporal changes in terrestrial predator demography (Mysterud
et al., 2003). This may be a legacy of the challenges such field studies inherently pose,
particularly those involving highly mobile and cryptic predators. The incorporation of a
climate parameter into models of predator numerical response undertaken in this study
is novel, and there are, therefore, few published studies available to which the current
study can be compared directly.
There are several studies that have identified possible mechanistic links between the
NAO and terrestrial mammalian carnivores: that of Stenseth et al. (1999; 2004a; 2004b)
on Canada lynx; and that of Post and Stenseth (1998) and Post et al. (1999) on grey
wolves (introduced in sections 1.2.2 and 3.1.4). These studies did not directly measure
the influence of climate on predator numerical response, but did find strong
relationships between the predation dynamics (functional response) of these predators
and climatic variability as a result of the NAO. For lynx, the mechanisms involved in
120
these studies have been shown to be direct and relate to predator hunting efficiency,
success, and behaviour as a result of snow conditions (Stenseth et al., 1999; 2004a;
2004b). For wolves, the mechanisms were indirect via the influence of climate on the
vulnerability of prey populations (Post and Stenseth, 1998; Post et al., 1999; Mysterud
et al., 2003).
For Canada lynx it was proposed that the NAO affected hunting behaviour and success
through its influence on temperature and snow properties, and this in turn influenced
lynx population dynamics (Stenseth et al., 2004a; 2004b). The lynx killing rate of hares
(functional response) was found to be reduced when the frequency of winter warm
spells was reduced (Stenseth et al., 2004b). It was proposed that the colder temperatures
maintained deep, soft snow which adversely influenced the ability of lynx to catch
snowshoe hares (Stenseth et al., 2004a). Although an explicit comparison between the
influence of climate on the functional response of lynx and numerical response of
coyotes is difficult to make, the results presented in this study support the hypothesis
that coyote population dynamics are negatively influenced by warmer winters
(Figures 5.6 and 5.25) which is converse to the lynx study. Support for direct negative
relationships between coyote density and temperature the previous winter is
intermediate to weak (determined by R2 values), but is none the less significant
(Figures 5.16(b), 5.17(b) and 5.21(b) to 5.23(b) inclusive).
Stenseth et al. (2004b) report that the correlation between the winter NAO index and
local winter temperatures has differential signs between east and west Canada. That is,
during a negative NAO phase eastern Canada (Atlantic region) will experience warmer
winter temperatures, whereas cooler winter temperatures will be occurring in western
Canada (Continental and Pacific regions) with converse conditions prevailing during a
positive NAO phase (Figures 3.1 and 3.2) (Stenseth et al., 2004b). The study of
Stenseth et al. (2004b) implies that lynx population dynamics are adversely influenced
by colder winter temperatures, which for western Canada equates to a negative NAO
phase. This is contradictory with what has been found for coyotes in this study
(Figure 5.6). The best-fit model 2 that includes the effect of the NAO (Tables 5.1 and
5.25) shows that a negative NAO phase has a positive effect on coyote population
dynamics (Figure 5.6).
121
With respect to the study of Stenseth et al. (2004b) it is pertinent to note that a specific
NAO index was not directly incorporated into their candidate set of functional response
models. In addition, the coefficient for the snow sinking depth variable used was not
statistically significant in their best model. This may have been a consequence of the
fact that the snow variable used was obtained over the course of a 10 year period (1987–
1996) during which time there were eight consecutive years of a positive NAO phase
(Figure 4.7 herein). Furthermore, Stenseth et al (2004b) did not quantify the threshold
temperatures at which adverse snow sinking depth is maintained, or rather did not
quantify a threshold temperature at which lynx killing rate is reduced. This makes
explicit comparison between studies difficult. Here it has been shown that a mean
extreme maximum winter temperature above 6.5°C has a negative influence on coyote
density (Figure 5.25).
For grey wolves living on Isle Royale, Michigan USA, it seems increased winter snow
related to the NAO is advantageous. Wolf hunting success was significantly increased
during winters of deep snow as a result of the increased vulnerability of their prey
species (moose) (Post and Stenseth, 1998; Post et al., 1999). Variation in wolf pack size
(and, hence, wolf numerical response) was strongly correlated with the NAO, which in
turn, was negatively correlated with snow depth (Post et al., 1999). During years of
increased snow depth wolf pack size increased and a greater number of moose were able
to be killed per day. Wolf mortality was found to decline following years of increased
snow depth (Post et al., 1999). A similar functional response has been found for coyote
populations in Nova Scotia, Canada (Patterson et al., 1998). Coyote predation on whitetailed deer was found to increase sharply, and continue to increase disproportionately
relative to the availability of snowshoe hares, as deer became increasingly vulnerable
with increased snow depth (Patterson et al., 1998). At Kluane the diet of coyotes in
terms of both percentage of kills and percentage biomass of kills, remains dominated by
snowshoe hares. It is increasingly supplemented with small mammals (squirrels and
voles) as snowshoe hare density declines (O'Donoghue et al., 1998b).
These studies on coyotes, lynx and wolves all serve to highlight the effects of the NAO
on predator numerical and functional responses. The numerical and functional responses
of predators are inherently related. If hunting of preferred prey is efficient and
successful (functional response) a predator will be better placed biologically to survive
122
and reproduce (numerical response) (Sinclair et al., 2006). Thus, an avenue for future
research would be to evaluate the influence of climate on the coyote’s functional
response, as has been done for the Canada lynx described above (Stenseth et al., 1999;
Stenseth et al., 2004b). Another area of further research that would be of great interest
would be to compare the results of this study with similar studies for Canada lynx and
populations of eastern Canadian coyotes. A comparative study on the influence of
climate on the lynx numerical response may help explain the discordant findings
(relative to the influence of the NAO) between this study and that of Stenseth et al.
(2004b). Furthermore, a comparative study on eastern Canadian coyotes may determine
whether or not coyote population dynamics (abundances) are similarly structured
geographically according to the NAO defined climatic zones across Canada, as has been
found for the Canada lynx (Stenseth et al., 1999; Stenseth et al., 2004a).
7.4 The relationship between the NAO and local climate variables
Some studies have found direct correlations between the NAO and local or regional
climate variables, namely temperature, precipitation, and snow (Post and Stenseth,
1998; Mysterud et al., 2000; Syed et al., 2006; Sepp, 2009). In this study, however, no
such relationships were found (section 6.6; Appendix 3). The relationships between
local weather patterns and large-scale indices are not always straightforward, and are
subject to a number of determining factors (Mysterud et al., 2000; Stenseth et al., 2003).
These include spatial (geographical) variation between an explicit local variable and the
value or range of values of the large-scale index in question. An example of this can be
seen in the study of Mysterud et al. (2000) who found relationships between the NAO
and snow depth to be dependent on several spatial factors including altitude and degrees
of latitude and longitude. A further factor is variation in the relationship over time (the
relationship exists, then it does not, then it exists again: termed non-stationarity). Nonstationarity has been found, for example, with the relationship between the NAO and
temperature in the Barents Sea (Stenseth et al., 2003). The values of a large-scale index
that combines temporal and spatial features of multiple weather components is unlikely,
therefore, to directly correlate with any single local climate variable (Stenseth et al.,
2003; Stenseth and Mysterud, 2005).
123
7.5 Why was there little support for models with local climate variables?
In the Yukon Territory coyotes are considered on the edge of their range and are limited
to the southern region, and locally according to elevation, by snow depths (Liz Hofer,
Kluane senior field technician and coyote and lynx track surveyor, and Mark
O’Donoghue, personal communications). Therefore, it was expected there would be
stronger support for models that incorporated local climate variables (Tables 5.25, 6.1 to
6.4 inclusive and 6.6), and in particular snow depth. Models that incorporated the snow
depth variable, however, were not shown any level of plausible support in the AICc
analyses (Tables 5.17, 5.18 and 6.6). Support was expected for the extreme maximum
winter temperature variable, and, indeed, this variable was shown strong relative
support by the model-by-model AICc analyses (Table 6.6), but as has already been
discussed, the direction of the relationship (negative) was unexpected (Table 5.10;
Figures 5.16(a) and (b) and 5.25).
These circumstances support the proposition that overall, the local climate variables
used failed to capture the climatic conditions that influence coyote numerical response
(Table 5.25). There are two possible explanations for this. Firstly, this finding is not
uncommon in ecological studies that use individual measures of local climate, namely
because it is typically the interaction between multiple variables (such as temperature,
snow and extremes of these) that influence ecological processes (Stenseth et al., 2003;
Hallett et al., 2004; Stenseth and Mysterud, 2005). Indeed, in this study, the winter
NAO index has been much better able to capture the ‘blend’ of climate variables at play
(Table 5.25). This finding is supported by the overwhelming level of relative support
given to this climate index in the model-by-model AICc analyses (Table 6.5),
corroborating the assertion of Hallett et al. (2004) that the NAO can be a better
descriptor of ecological processes than local climate.
The second explanation is more complex and arises out of the provenance of the local
climate data used (refer section 4.3.5) and the issue of spatial scale. There are no climate
data available for Kluane. The local climate data used in this study (and that of Krebs et
al., 2001b for the KEMP) were obtained from a weather station at Burwash Landing
located some 60 km north-west from the study site (Figure 4.1). These data are the
closest and most reliable available for the immediate region. The climate data from
124
Burwash Landing and Whitehorse (located 210 km east of the study site; Figure 4.1)
were highly correlated (Appendix 1) indicating a level of spatial homogeneity in climate
conditions. Hence, the extent to which the lack of Kluane climate data poses a limitation
on studies that aim to evaluate the effect of climate on Kluane ecosystem processes (this
one included) is unclear. The local region can display considerable variation in
temperature, precipitation, and snow across and within years and along its own
topographic and altitudinal gradients (Krebs et al., 2001b). At Kluane such variations in
climate can be amplified, with the study site often showing marked differences in winter
conditions within short distances (less than 1000 metres), and also high variability in the
timing of winter weather events from year to year (Krebs et al., 2001b). For example, in
a given year at Kluane the majority of winter snow may fall early (in December), late
(in February), or may fall continuously over the winter months. The snow depth will be
dependent on elevation throughout the site, which ranges from approximately 760 m to
over 1170 m above sea level. Because of the mountain topography of the region, no
weather station will be typical of all the conditions within the study area (Krebs et al.,
2001b). Hence, the local climate data evaluated may not be at the immediate local scale
required to capture the mechanisms underlying changes in coyote density.
7.6 What are the extra effects on coyote density not explained by the
effects of snowshoe hare density and climate?
Despite the strong support for an effect of the NAO and intermediate support for
extreme maximum winter temperatures on coyote density hypothesised by model 2,
these relationships could still only account for 76% (Table 5.1; Figure 5.5) and 62%
(Table 5.9; Figure 5.24) of the variation in coyote density respectively. Therefore,
further effects on coyote density are likely to be operating which are not captured by
model 2, and these effects might help to describe some of the differences between the
reconstructed and observed coyote densities (Figures 5.5 and 5.24). Some of these
potential effects are explored below.
125
7.6.1 Population demography and social structure
In their study of Soay sheep (Ovis aries), Coulson et al. (2001) demonstrated
unambiguously how the demography of a population influenced its overall response to
climate variation. Animals of different age and sex classes expend different amounts of
energy at different times of the year and this is dependent on their behaviour,
reproductive effort, growth, and maintenance. Coulson et al. (2001) showed how these
differences, in turn, can lead to variation in the way respective demographic classes
respond to climatic variability. Hence, similar winter conditions, whether adverse or
favourable, can result in different dynamics (rates of survival, mortality) in populations
of the same size (Coulson et al., 2001). By incorporating demographic heterogeneities
in a complex age-structured mechanistic population model, Coulson et al. (2001) were
able to account for 92% of the variation between predicted and observed
population size.
There is no explicit evidence to date that shows different age classes of coyotes have
differing probabilities of survival given particular winter conditions, as has been
demonstrated for some high latitude ungulates (Clutton-Brock and Coulson, 2002). It
has been demonstrated, however, that the age structure and social organisation of coyote
populations can be influenced by prey availability (Bekoff, 1978; Todd et al., 1981;
Todd and Keith, 1983), and that the age and social structure of a population can be
dependent on the stage of the prey’s population cycle (phase-dependency, discussed
below) (O'Donoghue et al., 1998a; O'Donoghue et al., 1998b; Stenseth et al., 1998).
Both age structure (affecting foraging and hunting experience and efficiency) and social
organisation (affecting hierarchical dominance and population dynamics) can
significantly influence coyote predation dynamics (functional response) (Bekoff, 1978;
Todd and Keith, 1983; Windberg, 1995; Patterson and Messier, 2001; Crête and
Larivière, 2003; Pitt et al., 2003; Thibault and Ouellet, 2005). As with many other canid
species, the social organisation of coyote populations can lead to strong densitydependence.
126
7.6.2 Density and phase dependencies
The density-dependent paradigm (complementary to the mechanistic paradigm)
describes the changes in the proportion of a population’s per capita birth and death rates
as the population increases (Krebs, 1995; Sinclair et al., 2006). That is, the paradigm
assumes these rates are related to population density (Krebs, 1995). The underlying
causes for the changes in these rates are termed density-dependent factors, and include
resource (food) availability, intra and interspecific competition and predation (Sibly and
Hone, 2002; Sinclair et al., 2006). There are several examples of predator studies that
have demonstrated that the subject population’s density or population growth rate is
influenced by density-dependence (Krebs, 1995; Forchhammer et al., 1998; Dennis and
Otten, 2000; Sibly and Hone, 2002; Hone and Clutton-Brock, 2007).
The inclusion of a density-dependent term in a priori models that attempt to describe
population dynamic processes has been strongly advocated (Brook and Bradshaw, 2006;
Hone et al., 2007). It may be particularly useful in studies on populations of highly
social mammals such as canids, where internal social factors such as density-dependent
breeding constraints imparted on subordinate females, dominant female infanticide, and
rapid compensatory reproduction and/or immigration in response to mortality, can
strongly influence population growth (Connolly, 1978; Windberg, 1995; Fleming et al.,
2001). As an example, density-dependence in the Kluane coyote population may
account for over estimation of coyote density at cyclic peaks (Figure 5.24).
Phase-dependence can describe how a predator population changes its response and
behaviour, demographic structure, and/or pattern of density dependence relative to
particular stages of predator and/or prey population cycles (Stenseth et al., 1998). Both
coyote and lynx demonstrate marked variation in their reproductive output, killing rate
of hares (functional response), territoriality, and intraspecific interactions at different
phases of the hare population cycle (O'Donoghue et al., 1998a; O'Donoghue et al.,
1998b). For example, reduction in coyote output in years of low hare density can cause
a shift upwards in the mean age of coyotes, with the distribution reversed at higher hare
densities (Stenseth et al., 1998). Individuals surviving into the low phase of the hare
cycle switch to alternative prey (voles and squirrels) and use different hunting tactics
(O'Donoghue et al., 1998a; O'Donoghue et al., 1998b). This behaviour could persist
127
into the subsequent early increase phase of the hare cycle (Stenseth et al., 1998).
Stenseth et al. (1998) showed that the dynamic patterns (population structure) of lynx
are both density and phase dependent. Thus, both density and phase dependence may
explain some of the variation in coyote population density not explained by the best
model in this study.
7.6.3 Alternative prey
The availability of alternative prey may also influence coyote density and may account
for some of the unexplained variation. Model parameter estimates for the intercept
(ß0; origin) obtained in the least-squares regression analyses were rarely significant.
This indicates there is no threshold density of hares required for a coyote population to
exist. Despite Kluane coyotes showing strong specialisation for snowshoe hares, a range
of alternative mammalian prey (squirrels, voles, and mice) are sought and are a
particularly important source of food during years of low snowshoe hare density
(O'Donoghue et al., 1998b; O'Donoghue et al., 2001). But these alternative prey sources
are not always readily available to coyotes: squirrels spend much time in winter in their
arboreal nests (O'Donoghue et al., 1998a), and the capture success of voles and mice
that live under the snow during winter can be reduced if the snow is too deep and has a
hard surface (Gese et al., 1996b). Alternative prey might, therefore, account for the
under estimation of coyote density in the model reconstructions (Figures 5.5 and 5.24).
7.6.4 Interspecific competition with other predators
Interspecific competition is an interaction between species where individuals of one
species suffer a reduction in fecundity, growth, or survivorship as a result of
interference or exploitation of a shared resource by individuals of another species
(Tilman, 2007; Krebs, 2009). Interference competition occurs directly between
individuals by, for example, aggression when individuals interfere with foraging,
survival, reproduction of others, or by directly preventing their physical establishment
in a portion of habitat. Exploitative competition between species occurs indirectly
through a common limiting resource. For example the use of the resource depletes the
amount available to others, or there is competition for space (Sinclair et al., 2006;
Krebs, 2009). Interspecific competition can have a profound influence on a population’s
dynamics (abundance) and, in particular, has been found to be a strong limiting factor in
128
carnivore populations (Fedriani et al., 2000; Creel, 2001; Tannerfeldt et al., 2002;
Mezquida et al., 2006; Gehrt and Prange, 2007; Tilman, 2007).
Studies examining intraguild interference competition involving coyotes have shown
coyote populations to be both limited themselves by competing predators (Fuller and
Keith, 1981; Berger and Gese, 2007; Merkle et al., 2009), and causing limitation to
other predator populations (Dekker, 1983; Voigt and Earle, 1983; White and Garrott,
1999; Fedriani et al., 2000; Gehrt and Prange, 2007). At Kluane there is no direct
evidence of interference competition between coyotes and lynx or other predators
(O'Donoghue et al., 1998a) although this has not been tested formally. Interference
competition and predation between wolves and coyotes causing limitation on coyote
distribution and abundance is well documented (Fuller and Keith, 1981; Berger and
Gese, 2007; Merkle et al., 2009), but again, has not been evaluated formally at Kluane.
Recent work evaluating the influence of the respective role of specialist predators in
shaping the lynx–snowshoe hare cycle suggests exploitative competition between
specialist predators of snowshoe hares may be occurring (Tyson et al., 2010). Kluane
snowshoe hares have three key predators: lynx, coyotes, and great-horned owls (Bubo
virginianus) (Hodges et al., 2001). By incorporating the additional effect of coyotes and
great-horned owls into a lynx–snowshoe hare predator-prey model that used Kluane
population census data, Tyson et al. (2010) were able to achieve a model solution that
closely matched observed snowshoe hare–predator cycles. Their simulation model was
able to accurately capture predator lags, and maximum and minimum snowshoe hare
and predator densities. The model demonstrated that lynx, coyotes, and great horned
owls each played a crucial role in the predation dynamics of the lynx–snowshoe hare
cycle. In particular, owls were found to impart an increasing predation impact on hares
at low hare densities, when competition between predators for this shared food resource
is greatest. Exploitative competition between coyotes and other snowshoe hare
predators might account for the difference between the estimated (reconstructed) and
observed coyote densities, particularly at the low stages of the population cycle
(Figures 5.5 and 5.24).
129
Other than the lynx–snowshoe hare population modelling of Tyson et al. (2010)
surprisingly little work has been undertaken (in terms of the longstanding interest in
Kluane boreal forest ecosystem processes) to elicit the influence of intraguild
competition between predators on respective predator population dynamics.
Incorporation of the effect of other important sympatric predators on coyote population
dynamics warrants further investigation in future studies.
7.6.5 Human harvest and disease
Further factors often not considered in predator response studies, but which may also
account for some of the unexplained variation (namely over estimation in model
reconstructions), are the potential impacts of disease and human harvest. Disease has
been implicated in the limitation of coyote populations (Nellis and Keith, 1976;
Connolly, 1978; Gier et al., 1978; Windberg, 1995), yet its effects on mortality rates
and morbidity are rarely measured. Canine parvovirus epizootic, hookworm, Lyme
disease, canine distemper and mange in particular are known for their potential to cause
significant juvenile losses in wild canine populations (Nellis and Keith, 1976;
Windberg, 1995; Macdonald and Sillero-Zubiri, 2004).
With respect to human harvest, there is no evidence of Kluane coyote populations being
subjected to dedicated human control. Despite this, all coyote mortalities recorded in the
study by O’Donoghue et al. (1997) were identified as human-caused. Indiscriminate
human harvest has been shown to affect canid population ecology, density, and social
dynamics (Bekoff, 1978; Corbett, 1995; Windberg, 1995; Patterson and Messier, 2001;
Macdonald and Sillero-Zubiri, 2004), which could, in turn, influence the outcome of
numerical response studies. For example, human removal of animals can result in
reduced competition, and thus increased survival amongst the remaining population or it
can release internal social constraints (number of breeding females) that would
otherwise limit population growth (Bekoff, 1978; Corbett, 1995; Windberg, 1995;
Conover, 2001).
130
7.7 Synopsis
The below model is presented as a schematic summary of this study (Figure 7.1). It
proposes that winter climate affects the Kluane coyote population via its direct influence
on the coyote functional response to hares. The coyote functional response is a measure
of the number of prey individuals can catch and eat and convert into new predators and
this, in turn, influences the population’s reproduction, survival, and fecundity rates and
movement patterns. The effects of these factors are shown in the coyote numerical
response (track count data) the following winter. Thus, this study proposed how the
NAO influenced the coyote numerical response via the functional response, with
positive effects dependent on a prevailing negative NAO phase. A negative NAO phase
can limit snowfall which can enhance coyote hunting efficiency and success. Factors
not captured by the best-fit numerical response model, but likely to be contributing to
variation in coyote density, include competition with other predators, alternative prey,
demographic and social structure of the population, phase and density dependence
factors, and mortality caused by humans or diseases (shown in the rectangular boxes).
Competition,
alternative prey
Little evidence
of influence of
climate on hares
Age & social structure,
phase & density dependence
Human harvest,
disease
Influence on
reproduction, survival,
fecundity, movement
Coyote functional
response to hares
Climate
Autumn
Hares t-1
Winter
Coyotes t-1
Effect shows up as
coyote density (tracks)
Autumn
Hares t
Winter
Coyotes t
Figure 7.1 Model of factors influencing the coyote numerical response. Solid arrow lines represent
factors described in this study; broken arrow lines represent other potential contributing factors.
131
7.8 Implications of the study
The findings of this study have a potential longer-term implication for Canadian boreal
forest dwelling coyotes and the surrounding community. A notable feature of the NAO
is its prevailing trend toward a more positive phase over the past several decades, with a
magnitude that is considered unprecedented in the observational record (Hurrell, 1995b;
Visbeck et al., 2001; Hurrell et al., 2003; IPCC, 2007). Some of the most pronounced
anomalies have occurred since the winter of 1989, a year in which a record positive
value of the NAO winter index was documented (Visbeck et al., 2001) (Figure 4.7
herein). Although it is considered this trend is likely to be the result of anthropogenic
greenhouse gas emissions (Visbeck et al., 2001; IPCC, 2007), scientific consensus as to
the actual mechanisms causing the shift is yet to be reached (Visbeck et al., 2001; IPCC,
2007; Trouet et al., 2009). In any event, the findings of the current study indicate that a
continued trend of a positive NAO phase could see an overall longer-term reduction in
the density of coyotes at Kluane (Figure 5.6).
Any reduction in coyote density at Kluane would not, at least initially, be expected to
significantly influence snowshoe hare population dynamics. Hare dynamics are
influenced by numerous mammalian and avian predators, and it is considered that any
predation pressure eliminated by the reduction or removal of any one species would
almost certainly be compensated for by the remaining predators (Krebs et al., 2001a).
A significant impact could be shown, however, should any other key hare predators also
respond adversely to an increased positive NAO phase. Experiments conducted by
Hodges et al. (2001) at Kluane demonstrated that snowshoe hare survival rate is
markedly increased, and the collapse in hare survival that normally occurs at the peak
and decline phases of the hare cycle is almost eliminated, by the exclusion of both
coyotes and lynx (Hodges et al., 2001; Krebs et al., 2001a). Hence, should lynx
populations respond to the NAO in a similar manner to coyotes, and the trend for a
positive NAO phase continues, the snowshoe hare population cycle could be radically
altered, which could, in turn, lead to cascading effects at higher and/or lower trophic
levels (Krebs et al., 2001a). As such, further exploration of the NAO–lynx relationship
identified by Stenseth et al. (1999; 2004a; 2004b) would be beneficial, particularly in
terms of identifying with more certainty which NAO phase has a negative effect on lynx
density.
132
7.9 Conclusions
This study extends a previous notable study (O’Donoghue et al., 1997) on the predation
dynamics of an important member of the Canidae family of carnivores. It has
demonstrated that climate, namely the NAO, has an influence on a terrestrial
mammalian predator-prey interaction, and as such, addresses a key gap in the current
state of knowledge. Some of the limitations inherent in relating climate variability to
population dynamics have been, however, highlighted by this study. Firstly, that local
climate variables which are often assumed to be good predictors of ecological
processes, do not always present as such. In this respect, this study illustrates how a
large-scale climate index can better help explain an ecological process than local
climate variables. Secondly, the cause-and-effect relationships of unexpected results are
often difficult to explain. This latter point exemplifies the difficulty encountered in
attempting to unravel the causal links between changes in a population’s density to
climate variation without the benefit of manipulative or observational experiments.
Nevertheless, the first rule of climate ecology, and, indeed, the information-theoretic
approach to model selection, is to state specific, detailed, mechanistic hypotheses based
on the best understanding of factors thought to be involved in the process of interest.
This thesis complies with this fundamental assumption.
Numerical response models can be readily applied, or modified and applied, to
alternative studies (Bayliss and Choquenot, 2002; Hone and Sibly, 2002). The method
applied to this study and its subsequent results, therefore, have a broader relevance and
application to other predator-prey systems. This may be particularly so for such systems
as those in the higher latitudes of the northern hemisphere that are currently
experiencing significant and rapid effects of global climate change and within which
predators play an important keystone role (Gilg et al., 2009).
The unique longstanding community-scale monitoring undertaken at Kluane, and the
resultant exemplary datasets for a large number of species across multiple trophic
levels, provides an excellent opportunity to study the long-term influence of climate on
a broad range of ecosystem processes. This study emphasises the usefulness of such
data sets in evaluating ecological hypotheses expressed as models that seek a more
explicit explanation of the extrinsic factors involved in predator-prey interactions.
133
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APPENDIX 1: Regression analysis of local climate variables: Burwash
Landing and Whitehorse, Yukon
Table A1 Correlation by least-squares regression analysis between each local climate variable for
Burwash Landing and Whitehorse, Yukon to allow for prediction of five missing Burwash Landing
values (section 4.3.5). Data are from Environment Canada (2010b) and are for the winter period
(October–March) for the years 1986/87 to 2006/07. Regression equation: Burwash = a + bWhitehorse;
df=degrees of freedom; R2=coefficient of determination.
Figure
A1
Variable
df
F-value
P-value
R2
Regression equation
a
Mean extreme maximum
temperature (°C)
1,112
456.88
<0.0001
0.80
EmaxTEMB = 0.599314 +
0.920129×EmaxTEMW
b
Mean extreme minimum
temperature (°C)
1,112
738.19
<0.0001
0.87
EminTEMB = -11.23297 +
0.84391×EminTEMW
c
Total precipitation (mm)
1,112
64.05
<0.0001
0.36
PRECB = 3.234884 +
0.37934×PRECW
d
Total rain (mm)
1,113
102.44
<0.0001
0.48
RAINB = 0.078448 +
0.175463×RAINW
e
Total snow (cm)
1,112
65.43
<0.0001
0.37
TSB = 4.858306 +
0.424151×TSW
f
Mean minimum
temperature (°C)
1,113
1067.83
<0.0001
0.90
MMinTB = -6.567389 +
1.032161×MMinMTW
g
Mean temperature (°C)
1,113
1308.56
<0.0001
0.92
MTB = -4.312744 +
1.034861×MTW
h
Mean maximum
temperature (°C)
1,113
1386.30
<0.0001
0.92
MMaxTB = -2.05667 +
1.04269×MMaxTW
(a)
(b)
Figure A1 Local climate variable correlations for Burwash Landing and Whitehorse. Data are means and
totals for winter months (October–March) for the years 1986/87 to 2006/07: (a) mean extreme maximum
temperature (°C); (b) mean extreme minimum temperature (°C). Solid lines show significant fitted
regressions. Figure A1 continued over.
147
(c)
(d)
(e)
(f)
(g)
(h)
Figure A1 cont. Local climate variable correlations for Burwash Landing and Whitehorse. Data are
means and totals for winter months (October–March) for the years 1986/87 to 2006/07: (c) Total winter
precipitation (mm); (d) total rain (mm); (e) total snow (cm); (f) mean minimum temperature (°C);
(g) mean temperature (°C); (h) mean maximum temperature (°C). Solid lines show significant fitted
regressions.
148
APPENDIX 2: Partial correlation coefficients and P-values for coyote track
counts and climate, correcting for coyote population estimate
Table A2 Pearson partial correlation coefficients; N=9; P>r under H0: Partial Rho=0.
Partial variable=coyote population estimate; variables=coyote track count and climate. Data
were for the period 1987–1996 (n=9). Bold indicates significant correlation.
Variables
Correlation coefficient (r)
P-value
Tracks; NAO
-0.60
0.11
Tracks; SOI
-0.28
0.51
Tracks; PNA
-0.06
0.90
Tracks; NPI
-0.71
0.05
Tracks; EmaxTEM
-0.79
0.02
Tracks; EminTEM
-0.08
0.85
Tracks; PREC
0.35
0.40
Tracks; RAIN
0.55
0.16
Tracks; SNOW
0.37
0.36
Tracks; minTEM
-0.09
0.83
Tracks; TEM
-0.27
0.51
Tracks; maxTEM
-0.46
0.25
149
APPENDIX 3: Regression analysis of the winter North Atlantic Oscillation
index and local climate variables
Table A3 Correlation by least-squares regression analysis between the winter NAO
index and each local climate variable for Burwash Landing, Yukon (section 6.6). NAO
data from Hurrell (1995a); local climate data from Environment Canada (2010b). All
data are for the period December–March for the years 1984/85 to 2006/07. Degrees of
freedom=1,21; R2=coefficient of determination.
Figure
A3
Variable
F-value
P-value
R2
a
Mean extreme maximum
temperature (°C)
0.61
0.44
0.03
b
Mean extreme minimum
temperature (°C)
0.93
0.35
0.04
c
Total precipitation (mm)
0.90
0.35
0.04
d
Total rain (mm)
2.47
0.13
0.11
e
Total snow (cm)
0.90
0.35
0.04
f
Mean minimum temperature (°C)
1.91
0.18
0.08
g
Mean temperature (°C)
1.41
0.25
0.06
h
Mean maximum temperature (°C)
0.85
0.37
0.04
(a)
(b)
Figure A3 North Atlantic Oscillation and local climate variable correlations for Burwash Landing,
Yukon. Local climate data are means and totals for the months December–March for the years 1984/85 to
2006/07: (a) mean extreme maximum temperature (°C); (b) mean extreme minimum temperature (°C).
Figure A3 continued over.
150
(c)
(d)
(e)
(f)
(g)
(h)
Figure A3 cont. North Atlantic Oscillation and local climate variable correlations for Burwash Landing,
Yukon. Local climate data are means and totals for the months December–March for the years 1984/85 to
2006/07: (c) Total winter precipitation (mm); (d) total rain (mm); (e) total snow (cm); (f) mean minimum
temperature (°C); (g) mean temperature (°C); (h) mean maximum temperature (°C).