Journal of Animal Ecology 2012, 81, 960–969
doi: 10.1111/j.1365-2656.2012.01980.x
Demographic response to perturbations: the role of
compensatory density dependence in a North American
duck under variable harvest regulations and changing
habitat
Guillaume Péron1*, Christopher A. Nicolai2 and David N. Koons3
1
Department of Wildland Resources, Utah State University, 5230 Old Main Hill, Logan, UT 84322, USA; 2U.S. Fish & Wildlife
Service, 1340 Financial Blvd., Suite 234, Reno, NV 89502, USA; and 3Department of Wildland Resources and the Ecology
Center, Utah State University, 5230 Old Main Hill, Logan, UT 84322, USA
Summary
1. Most wild animal populations are subjected to many perturbations, including environmental
forcing and anthropogenic mortality. How population size varies in response to these perturbations largely depends on life-history strategy and density regulation.
2. Using the mid-continent population of redhead Aythya americana (a North American diving
duck), we investigated the population response to two major perturbations, changes in breeding
habitat availability (number of ponds in the study landscape) and changes in harvest regulations
directed at managing mortality patterns (bag limit). We used three types of data collected at the
continental scale (capture–recovery, population surveys and age- and sex ratios in the harvest) and
combined them into integrated population models to assess the interaction between density dependence and the effect of perturbations.
3. We observed a two-way interaction between the effects on fecundity of pond number and population density. Hatch-year female survival was also density dependent. Matrix modelling showed
that population booms could occur after especially wet years. However, the effect of moderate
variation in pond number was generally offset by density dependence the following year.
4. Mortality patterns were insensitive to changes in harvest regulations and, in males at least,
insensitive to density dependence as well. We discuss potential mechanisms for compensation of
hunting mortality as well as possible confounding factors.
5. Our results illustrate the interplay of density dependence and environmental variation both
shaping population dynamics in a harvested species, which could be generalized to help guide the
dual management of habitat and harvest regulations.
Key-words: additivity, capture–mark–recapture, capture–recovery, compensation, disturbance,
integrated population models, Leslie matrix, sensitivity, Waterfowl Breeding Population and
Habitat Survey
Introduction
In nature, the environment is never stable. Climate fluctuates,
random catastrophes occur and human activities alter
environmental conditions. These perturbations influence the
population dynamics of wild animals, both spatially and
temporally (Stenseth et al. 1999; Benton & Beckerman 2005;
Koons et al. 2005; Dodd, Ozgul & Oli 2006; Grosbois et al.
2008; and references therein). While life-history strategy (e.g.
Gaillard et al. 1989) determines to a large extent the sensitivity of populations to a given type of perturbation (Beissinger
*Correspondence author. E-mail: [email protected]
& Westphal 1998; Pfister 1998; Stahl & Oli 2006), this needs
to be understood within the broader framework of density
regulation (Saether et al. 2005; Bonenfant et al. 2009). Compensatory density dependence is indeed a major mechanism
enabling populations to offset the effect of perturbations of
anthropogenic or environmental origin (Burnham & Anderson 1984; Sinclair & Pech 1996; McCann, Botsford &
Hasting 2003; Benton & Beckerman 2005; McGowan et al.
2011). In other words, when a perturbation reduces the
population size or local population density, the remaining
individuals, freed from the negative effects of density, may
perform better than if no perturbation had occurred, thereby
‘buffering’ environmental variation. On the other hand, the
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society
Perturbations and density dependence 961
absence of compensatory density dependence can have dramatic consequences on population size. For example, lesser
snow goose Chen caerulescens caerulescens populations are
currently in a phase of exponential growth, mostly because
density dependence in winter mortality was reduced because
of increased food availability, and regulation via densitydependent breeding success proved to be inefficient in this
long-lived species (Alisauskas et al. 2011). Another contrasting example is provided by least Bell’s vireo Vireo belli pusillus, which can locally decline at a rapid rate because brood
parasitism by invasive brown-headed cowbirds Molothrus
ater reduces offspring production (Kus 2002) without density
dependence in adult survival later compensating the losses in
this short-lived species. By contrast, density dependence can
also be part of the mechanism through which perturbations
impact population size. In particular, adverse conditions
generally reduce available resources, exacerbating competition between individuals. For example, Tule elk Cervus
canadensis nannodes from Point Reyes, California, only experience density dependence during the years of poor vegetation
productivity (Howell et al. 2002).
To sum up, the extent to which a population will respond
to environmental or anthropogenic forcing is driven by: (i)
which demographic parameter(s) the perturbations affect
and whether these parameters are important for the species’
life-history strategy; (ii) whether the population is below or
above carrying capacity each year; and (iii) which demographic parameter(s) are density regulated. Despite these
clear-cut predictions and an abundant theoretical literature,
large uncertainties still exist about the actual functioning of
most wild animal populations. The analysis of time series
of population counts remains the major tool biodemographers use to study population dynamics and choose
between competing hypotheses (Stenseth et al. 1999; Creel
& Creel 2009). More rarely is a fully mechanistic model
(i.e. describing, as a function of environmental conditions
and density, the demographic processes of fecundity, survival and transition between stages) designed, tested and
calibrated using field data (Coulson, Milner-Gulland &
Clutton-Brock 2000; Oli & Armitage 2004; Jenouvrier et al.
2009). As a result, in most populations, density dependence
and environmental forcing are known to exist to some
extent, but without quantification of all the pathways
through which density can offset (or not) the effect of perturbations.
Here, we studied the dynamics of the mid-continent population of redhead Aythya americana, a North American diving duck. This breeding population encompasses a high
proportion of the world population of the species and
includes the famed Prairie Pothole Region. Mid-continent
redheads could be affected by two major perturbations: (i)
changes in the availability of breeding habitat and (ii)
changes in the intensity of hunting. For redheads, availability
of breeding habitat is measured by the number of ponds
within the landscapes used by the mid-continent population.
Redheads are habitat specialists and require ponds for building floating nests, as well as foraging and rearing broods,
which makes them an ideal study species for our purpose.
Hunting intensity is measured through the proxy of hunting
regulations, and bag limit in particular, which is the most
influential variable upon which managers can act (Conroy,
Miller & Hines 2002). The issue of identifying the relative
influence of these two perturbations on population dynamics
has come to the forefront of waterfowl ecology and management in North America (Conroy, Miller & Hines 2002;
Runge et al. 2006; Mattsson et al. 2012), but empirical studies are lacking, especially on the topic of compensatory density dependence. Here, for the first time, we simultaneously
investigate the relative influence of variability in habitat
availability, harvest regulations and compensatory density
dependence on both survival and fecundity, and how these
shape the population dynamics of a harvested species.
Materials and methods
We used capture–recovery data (CR; information on the age and
time at which individually marked redheads were shot by hunters),
population surveys (aerial counts of the breeding population on
stratified transects of habitat), and age- and sex-ratio data (from the
plumage features of wings of redheads shot by a subsample of hunters). To combine these three types of data and extract information
about density dependence and response to perturbations, we used
integrated population models (IPM; Besbeas et al. 2002; Brooks,
King & Morgan 2004). This method makes it possible to analyse the
three data sets at once and simultaneously estimate survival,
fecundity and population size. Below we (i) present the data sets,
which are available to the scientific community in the form of online
data bases; (ii) describe our use of IPMs to address our objectives;
and (iii) describe our assessment of how trustworthy the estimates
from the IPMs were compared to more standard analyses of single
data sets.
CAPTURE–RECOVERY DATA
We attained redhead banding and recovery data over the period of
1960–2009 (50 years) from the GameBirds data base (Bird Banding
Lab, USGS Patuxent Wildlife Research Center). Data from mid-continent states and provinces were selected (Alberta, Saskatchewan,
Manitoba, Montana, North and South Dakota, Minnesota and
Iowa). The analysis was restricted to normal wild birds released in
the same 10-min block as the banding location. Moreover, we
removed birds of unknown sex or age, and ducklings marked with
plasticine bands. We used data for birds that were banded in July,
August or September, which is after most ducks have completed nesting but generally before the opening of the hunting season. Band
recoveries were restricted to birds shot and reported between September and January, and of which the date of death was reported to the
nearest 10 days or more precisely.
We partitioned the data by sex and age class, where hatch-year
(HY) birds are defined as those hatched in the calendar year they
were banded, including ‘locals’ that were banded before fledging (see
the section ‘IPMs: general structure and assumptions’ below for justification). After hatch year (AHY) birds are those that hatched in
years previous to that of banding. These data filters resulted in a total
of 21 340 banded and released AHY females, 19 966 AHY males,
20 920 HY females and 21 084 HY males, from which 1135 AHY
females, 1480 AHY males, 1731 HY females and 1851 HY males
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
962 G. Pe´ron et al.
were shot and reported (i.e. recovered). Hereafter, HY stands for
birds in their first year of life from banding to first breeding season
and AHY for all other (adult) birds.
Throughout we use the abbreviation HY to designate birds during
their first twelve months of life, before their first breeding season, and
AHY to designate all other (adult) birds. This is different from the
standard North American bander terminology, which recommend
the use of SY (second year) for all birds in their second calendar year,
HY being restricted to the few months between hatching and December 31 of the calendar year of hatching.
POPULATION SURVEYS
We attained redhead breeding population surveys over the same 50year period, 1960–2009, from the Waterfowl Breeding Population
and Habitat Survey data base (Division of Migratory Bird Management, U.S. Fish & Wildlife Service). The analysis was restricted to
the strata pertaining to the mid-continent population: 22, 26–49 and
75. A number of post hoc corrections needed to be brought to the
raw count data. First, aerial surveys miss some of the birds that are
visible to observers on the ground (Smith 1995). For each year and
strata, a visibility correction factor is computed and we applied it to
the strata-specific count data (these correction factors were treated as
constants in our model). Second, many birds (mostly drakes) are
recorded as single; following the guidelines based on the knowledge
that the adult sex ratio is male-biased in this population, we considered that these birds were unpaired males (the alternative that these
birds are the mates of hidden, nesting females is less likely because
few nests are initiated before the surveys occur; Sorenson 1991).
Thus, the population survey consisted of the count of all redheads
seen (pairs, singles and groups of more than two birds), corrected for
imperfect visibility and summed over strata.
5.
males and all AHY females were present on the breeding
grounds in May at the time of the surveys.
Population size N: the number of individuals in each sex- and
age-specific stage, at the time of the May surveys, and within
the boundaries of the survey transects.
Integrated population models can be fit to a wide range of data
but several assumptions were required. First, fecundity was measured as the total number, per female that was present on the breeding grounds, of offspring that reached the age at which they could be
submitted to banding. Thus, this mixed together several parameters
traditionally used in waterfowl productivity studies: breeding probability (probability for a present female to actually nest), nest success
(probability for a nest to hatch at least one egg), hatching success
(percent eggs hatching from successful nest), brood success (probability for a successful nest to fledge at least one duckling), fledging
success (percent ducklings fledged from successful brood), re-nesting
probability, as well as survival from fledging up to the date of banding operations. Second, the first-year survival of HY birds was
assumed independent of whether or not they had fledged before
banding (this assumption was supported by a preliminary analysis
indicating that HY survival was not statistically different between
pre- and postfledgling HY birds, though Hestbeck et al. 1989 found
a ratio of 0Æ84 between the survival of pre- and postfledgling HY
birds in mallards Anas platyrhynchos). Third, all birds within the
same age- and sex class were considered equivalent in terms of survival, recovery probability and fecundity. Fourth, immigration and
emigration fluxes in and out of the mid continental population were
neglected. This was supported, as a first approximation, by the large
fraction of the world population that is included in the mid-continent population, as well as by Johnson & Grier (1988) and Arnold
et al. (2002); these two studies highlight the high rate of betweenyear site fidelity.
AGE- AND SEX RATIOS IN THE HUNTERS’ BAGS
MODEL FITTING
We attained redhead age- and sex-ratio data over the period of 1964–
2009 (four missing years due to small sample size) from the USFWS.
The USFWS computes range-wide age- and sex ratios in the harvest
based on the plumage features of duck wings that a subsample of
hunters mail back to the service.
The philosophy underlying IPMs is to separately construct the likelihood of each data type and then find the maximum of the combined
(product) likelihood (Besbeas et al. 2002). Although this method has
been presented in detail elsewhere and is now widely in use, we detail
below our procedure for building the likelihood.
INTEGRATED POPULATION MODELS: GENERAL
Likelihood of the CR data
STRUCTURE AND ASSUMPTIONS
The models were parameterized using:
1.
2.
3.
4.
Survival probability S: the probability for a bird to survive for
1 year, starting October 1.
Seber’s recovery probability r: the probability for a dead bird to
have died from hunting and have been reported as such.
Fecundity F: the number of offspring (of both sexes) per female,
at the time of banding operations in late summer.
Presence on the breeding ground s: the proportion of 1-year-old
(HY) females that are on the breeding grounds during the May
survey. At the local scale, Arnold et al. (2002) estimated this proportion to be 0Æ71 ± SE 0Æ19 by comparing the detection probability of individually marked females of varying age. Here, we
estimated this proportion at the mid-continent scale. We
assumed that the remaining fraction of HY females (1)s) either
spent the breeding season in migratory stopover locations, or
arrived after the population surveys. We also assumed that all
We used the m-array formulation of Seber’s capture–recovery models, as described in, for example Brooks, Catchpole & Morgan (2000)
and Schaub et al. (2007). That is, we first computed for each pair of
years (i,j), the number mi,j of individuals banded in year i and
recovered in year j (j = 51 was used for ‘not recovered’). Then we
expressed the probability Pi,j of event ‘recovered in year j | banded in
year i’ as a function of the time-specific survival and recovery
probabilities. Next, the mi,j values were modelled as the realization of
a multinomial process with the total number of individuals banded in
year i as the number of trials and the probabilities (Pi,j)j 2 1:51 as cell
probabilities. The only modification we brought to the standard CR
model formulation was that the recovery probability of newly
marked AHY birds was modelled separately during the first year
after banding relative to following years, to accommodate a potential
transient effect because of, for example, some overlap between
hunting and banding operations. We modelled the effect of ‘first year
after banding’ on recovery probability as an additive component to
other considered effects.
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
Perturbations and density dependence 963
Likelihood of the survey data
We constructed a two-age class, sex-specific, prebirth-pulse Leslie
matrix model. The state process was thereby (Besbeas et al. 2002;
Brooks, King & Morgan 2004; Schaub et al. 2007):
2
3
Nf;HY
6N
7
6 f;AHY 7
6
7
4 Nm;HY 5
Nm;AHY tþ1
2
s 0:5 F S~f;HY 0:5 F S~f;HY
6
Sf;AHY
Sf;AHY
6
¼6
4 s 0:5 F S~m;HY 0:5 F S~m;HY
0
0
0
0
0
0
0
0
Sm;AHY Sm;AHY
32
Nf;HY
3
76N
7 6 f;AHY
76
5 4 Nm;HY
7
7
7
5
t
Nm;AHY
t
eqn 1
where the subscripts f, m and t stand for ‘female’, ‘male’ and ‘year t’,
respectively, and other notations are as above. Because survival was
estimated from October to October, but population size was surveyed
in May, the HY survival in the above equation corresponded to the
7-month period from October to May, which we accommodated by
7=12
using S~K;HY;t ¼ SK;HY;t , where k stands for either male or female.
Demographic stochasticity (not shown in eqn 1) was modelled
through a Poisson process for the HY compartments and a binomial
process for the AHY compartments (Besbeas et al. 2002; Brooks,
King & Morgan 2004; Schaub et al. 2007).
The observation process was assumed to induce a Gaussian noise
around the count (eqn 2).
Yt ¼ ðNm;HY;t þ Nm;AHY;t þ sNf;HY;t þ Nf;HY;t Þ þ dt
eqn 2
whereYt is the breeding population count in year t, dt is normally distributed with mean 0 and standard deviation proportional to the
count ht = h0ÆYt (Véran & Lebreton 2008), and h0 is a parameter to
estimate.
Likelihood of the age- and sex-ratio data
Four likelihood terms were involved (female age ratio, male age ratio,
AHY sex ratio and HY sex ratio) and were built in a similar way. For
the female age ratio, we first computed the expected proportion of
HY individuals among females shot by hunters in year t (denoted
Af,t), as a function of survival, recovery, presence probability and
fecundity.
Af;t ¼
AGE*SEX*TIME (the four age- and sex-specific time series varied
independently with time), AGE*(SEX + TIME) (the same time variation applied to males and females of a given age class) and AGE*
SEX + TIME (the time variation in the different classes was parallel). In these three models, we used the same parameterization for
both survival and recovery probabilities. Because the data did not
allow the estimation of age-specific fecundity, the models always had
a TIME-only structure for fecundity and a constant presence probability for first-year females. We used the deviance information criterion (DIC; Spiegelhalter et al. 2002) to select the preferred model out
of the three considered and denote it ‘Model 1’ hereafter.
TEMPORAL COVARIATES
To examine density regulation within the mid-continent redhead
population, we used population counts Yt, standardized to a mean of
0 and a standard deviation of 1, as a covariate affecting survival,
fecundity, recovery probability or any combination of these parameters. Survival from October 1 of calendar year t to October 1 of year
t + 1 was regressed against population count in May of year t, and
the effect of population count on recovery probability was modelled
in similar fashion. The underlying assumption is that population size
in May is representative of population density on the wintering
grounds during the next winter. Fecundity in breeding season of year
t was regressed against population count in May of year t. We used
population counts rather than modelled population size Nt as the
explanatory variable because of constraints on computational time.
Because in our model, population count is a noisy measure of population size, doing this was expected to reduce the statistical power for
detecting density dependence (by dragging the absolute value of the
regression slope towards zero).
To examine the effect of habitat quality and its interaction with
density dependence, we used the counts of pond number that are conducted during the May surveys (presented in Appendix S1, Supporting information). Pond number Pt, standardized to a mean of 0 and a
standard deviation of 1, is an indicator of habitat availability (the
more ponds, the more nesting locations, food availability, brood habitat, etc.). Survival from October 1 of year t to October 1 of year
t + 1 was regressed against pond number in May of year t, but we
did not consider the effect of pond number on recovery probability.
Fecundity in breeding season of year t was regressed against pond
number in May of year t.
0:5Ft ðsNf;HY;t þ Nf;AHY;t Þ ð1 Sf;HY;t Þ rf;HY;t
0:5Ft ðsNf;HY;t þ Nf;AHY;t Þ ð1 Sf;HY;t Þ rf;HY;t þ ðNf;HY;t þ Nf;AHY;t Þ ð1 Sf;AHY;t Þ rf;AHY;t
Then, we modelled the number of HY female wings sent by hunters
in year t according to a binomial distribution with the total number
of female wings sent by hunters in year t as the number of trials, and
Af,t as the success probability. The other three likelihoods were built
following a similar method.
MODEL SELECTION FOR SEX, AGE AND TIME EFFECTS
We first ran a series of three models in which demographic parameters varied with time following a fully varying parameterization (one
parameter per year). These three models differed in how age, sex and
time effects interacted or added to each other. We considered models
eqn 3
To examine the effect of changes in hunting regulations, we
attained data about bag limit (the number of redheads a hunter is legally allowed to shoot on any given day during the hunting season;
Appendix S1, Supporting information), hunting season length and
hunting season opening date. These three regulations varied in a
dependent fashion both among them and among flyways (ecological
and administrative units relevant to hunting regulations). We used
only the Central Flyway regulation data because this flyway is the
one where many mid-continent redheads spend the winter (along the
Gulf of Mexico coasts) and because variation in the hunting regulations of this flyway was for the most part mirrored in other flyways
(Appendix S4, Supporting information). Preliminary analyses
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
964 G. Pe´ron et al.
indicated that only the effect of bag limit was detectable, so we only
included that variable in further analyses (see also Conroy, Miller &
Hines 2002). Survival from October 1 of year t to October 1 of year
t + 1 was regressed against bag limit of the hunting season that
spans over years t and t + 1, and the effect of bag limit on recovery
probability was modelled in similar fashion. We did not consider the
effect of bag limit on fecundity.
To examine the effect of winter harshness, we used the U.S. statespecific average monthly temperatures, attained from NOAA. For
each winter, we computed an average over the lower 48 states and
over December to February (presented in Appendix S1, Supporting
information) and standardized it to a mean of 0 and a standard deviation of 1. Survival from October 1 of year t to October 1 of year
t + 1 was regressed against average temperature during winter of
year t to t + 1, and the effect of winter temperature on recovery
probability was modelled in a similar fashion. We did not consider
the effect of winter temperature on fecundity, nor did we consider the
interaction between winter temperature and May pond number or
population counts.
MODELS WITH COVARIATES AND STOCHASTICITY
Departing from Model 1 (see Model selection for sex, age and time
effects), we converted all time effects into a mixture of fixed temporal
covariate effects (see the previous section) and temporal random
effects. The random effects were normally distributed on the link
functions scales and corresponded to the temporal variance in demographic parameters not explained by the effect of covariates. Model 2
was the model including all the covariates. Nonsignificant effects
were those for which the 95% credible interval on the corresponding
parameter included zero. After discarding the nonsignificant covariate effects in Model 2, our final model for making inference was
called Model 3.
BAYESIAN INFERENCE
We fit all models in a Bayesian estimation framework using
WinBUGS (Spiegelhalter et al. 2003). The likelihood components
are assumed independent because banded birds and birds used in
age- and sex-ratio computations represent a very small subset of the
birds present on the surveyed strata. The product likelihood of the
data sets was combined with prior probability distributions to obtain
the joint posterior distribution of the parameters. For two of the
model parameters (s and F), normal prior distributions were built
using the results of two studies conducted in Manitoba. These studies
estimated first-year female breeding propensity to be 0Æ71 ±
sampling SE 0Æ19 (Arnold et al. 2002) and fecundity to be 4Æ2 30day-old ducklings per breeding female ± sampling SE 0Æ4 (Yerkes
2000). The latter estimate was considered abnormally high (partly
because productivity was especially high during the study and partly
because only females that built a nest were considered; see also
Stoudt 1971). As such, we multiplied the sampling error by ten to
obtain a ‘flatter’, less informative prior.
We used uninformative prior distributions for the remaining
parameters: normal prior distributions of mean 0 and variance 1000
for the slopes of the regressions, uniform prior distributions between 0
and 1 for h0, truncated positive normal prior distributions with mean
2000 and variance 10 000 for the initial population sizes, and uniform
[0,2] prior distributions for the hyperparameters describing the normal
distribution of the temporal random effects in demographic parameters. The latter distribution was chosen based on preliminary analyses
indicating that these hyperparameters’ values were all below 1.
We generated two chains of length 200 000, discarding the first
100 000 as burn-in. Convergence of the chains was assessed using the
Gelman–Rubin criterion described in Brooks & Gelman (1998),
which was below 1Æ3 for all model parameters. The R package r2winbugs (Sturtz, Ligges & Gelman 2005) was used to call WinBUGS and
export results into the R environment (R Development Core Team
2010). A practical note is that the fitting of the various models
exceeded 2 months of computer time overall.
PERFORMANCE ASSESSMENT OF THE IPMS
A major caveat regarding IPMs is that if one of the data types is
biased then, via the sampling covariance, the bias can propagate to
estimate that would not have been affected if the different data types
had been analysed separately. However, in the latter ad hoc
approach, some estimates are sometimes used as inputs for the computation of other ones, which can cause even greater risk of cascading
error and bias. For example, this is the case for the computation of
fecundity from age-ratio data, which requires that age specificity in
the vulnerability to hunting is accounted for through the use of agespecific recovery probability estimates (obtained from CR data). To
address that issue within the IPM framework, we compared the estimated parameter values from three data configurations: (i) using the
three types of data, (ii) discarding age- and sex-ratio data and (iii)
using CR data only. We examined (i) whether 95% CI intersected,
(ii) whether a potential bias in age-ratio data induced a bias in fecundity estimates that cascaded to survival estimates by forcing the compliance with population survey data. Lastly, (iii) we measured the
reduction in sampling variance (precision of the estimates; e.g. Péron
et al. 2010) in the IPM compared to the ad hoc approach.
Results
MODEL SELECTION FOR SEX, AGE AND TIME EFFECTS
The DIC-based model selection indicated that the model with
a full age, sex and time interaction performed best, given the
data [model AGE*SEX*TIME: DIC = 8179Æ5; vs. DIC of
8344Æ5 and 8530Æ8 for, respectively, model AGE*(SEX +
TIME) and model AGE*SEX + TIME]. Parameter estimates for this fully time-dependent population model (Model
1) are presented in Appendix S2 (Supporting information).
MODELS WITH COVARIATES AND STOCHASTICITY
The results from Model 2 (full covariate effect) are presented
in Appendix S3 (Supporting information). Based on these
results, we excluded: (i) the effect of pond number and average winter temperature on survival (all age and sex classes),
and the effect of population size on male survival; (ii) the
effect of average winter temperature on recovery (all age and
sex classes), and the effect of population size on male recovery; (iii) the effect of bag limit on survival probability (all age
and sex classes). The effect of bag limit was however significant for some bag limit · sex · age combinations (Appendix S3, parts A–f, Supporting information). All significant
effects were nevertheless positive (indicating a better survival
during years with higher bag limit). In addition, they were
not consistent, neither between levels of harvest regulations
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
Perturbations and density dependence 965
(increasing bag limit did not have an increasing impact), nor
between age and sex classes (all classes exhibited different
responses to bag limit). Therefore, we considered all bag-limit
effects on survival to be spurious and possibly linked to temporal covariance between bag limit and environmental conditions (see Discussion: ‘Perturbations by changes in mortality
patterns and possible confounding effects’).
Estimates of demographic parameters at average population size and pond number are presented in Table 1. In the
final Model 3, fecundity increased with pond number, but
this effect was offset when population size was high (as indicated by the interaction term in Table 2; see also Appendix S4, Supporting information). Female survival decreased
with population size (significant in HY birds only; Table 3).
Population size also affected female recovery probability
(interacting with age; Table 4). Recovery probability
increased with bag limit in all sex and age classes (Table 4),
suggesting a linkage between harvest regulations and the
band recovery process, but not the survival process.
PERFORMANCE ASSESSMENT OF THE IPMS
In all but one case, the 95% CI of parameters estimates from
the three considered data configurations broadly intersected
(presented and discussed in Appendix S4, Supporting information). There was no apparent ‘cascading bias’ (Appendix S4, Supporting information). We observed, on average
over the ten parameters used to describe survival in Model 3,
a decrease in the SD of the posterior distribution when using
Table 1. Back-transformed (identity scale) parameter estimates
under average conditions of population size and pond number, from
Model 3. For fecundity, ‘offspring per female’ stands for the number
of duckling of both sexes surviving up to the banding operations in
July–September, per female present on the breeding ground in May.
‘Presence of HY females’ stands for the probability for a hatch-year
female to reach the breeding grounds before the May survey
immediately preceding their first birthday, conditional on survival.
For recovery, these values correspond to years with a bag limit of
zero (see Table 4). Average population count on the survey area was
7649 individuals and average pond number was 27 618
Mean
SD
Table 2. Parameter estimates for the fecundity submodel (number of
offspring of both sexes per female; F) in Model 3. All effects are on
the log scale. Nonsignificant effects (95% credible interval
encompassing 0) are indicated in italic font. Pond number and
population counts were standardized, so that the intercepts
correspond to the actual estimated value of demographic parameters
at the average conditions of pond number of population counts
Intercept
Population count
Pond number
Interaction of population
count and pond number
Time random effect
Mean
SD
95% Credible
interval
0Æ400
)0Æ063
0Æ477
)0Æ157
0Æ094
0Æ068
0Æ053
0Æ063
0Æ217; 0Æ575
)0Æ194; 0Æ061
0Æ39; 0Æ589
)0Æ262; )0Æ024
0Æ188
0Æ051
0Æ11; 0Æ306
Table 3. Parameter estimates for the survival submodel (S) in Model
3. All effects are on the logit scale. Nonsignificant effects (95%
credible interval encompassing 0) are indicated in italic font.
Population counts were standardized. Sex- and age-specific
intercepts are omitted for conciseness but are presented (after
transformation into the identity scale) in Table 1
Mean
SD
Density dependence (effect of population count)
AHY females
)0Æ065
0Æ074
HY females
)0Æ227
0Æ098
Time random effects
AHY males
0Æ033
0Æ018
AHY females
0Æ056
0Æ034
HY males
0Æ098
0Æ067
HY females
0Æ049
0Æ033
95% Credible
interval
)0Æ233; 0Æ06
)0Æ407; )0Æ031
0Æ008; 0Æ076
0Æ014; 0Æ139
0Æ016; 0Æ262
0Æ006; 0Æ126
AHY, after hatch year; HY, hatch-year.
IPMs: )18% when comparing configuration A to C (Appendix S4, Supporting information), )5% when comparing B–C
and )7% when comparing A–B. These results indicated that
utilizing all of the available data in an IPM framework
increased precision in our estimates without inducing
significant bias.
95% Credible
interval
Discussion
Fecundity
Offspring per female (F)
Presence of HY females (s)
Survival probability (S)
AHY males
AHY females
HY males
HY females
Recovery probability (r)
AHY males
AHY females
HY males
HY females
1Æ499
0Æ522
0Æ141
0Æ099
1Æ242; 1Æ776
0Æ404; 0Æ763
0Æ707
0Æ648
0Æ447
0Æ466
0Æ009
0Æ012
0Æ023
0Æ024
0Æ690; 0Æ725
0Æ624; 0Æ669
0Æ401; 0Æ492
0Æ419; 0Æ511
0Æ036
0Æ021
0Æ048
0Æ036
0Æ002
0Æ002
0Æ005
0Æ002
0Æ031; 0Æ041
0Æ017; 0Æ026
0Æ039; 0Æ058
0Æ031; 0Æ041
AHY, after hatch year; HY, hatch-year.
By combining three types of data that are usually analysed
separately, we could document simultaneously the variation
in survival and fecundity of the mid-continent redhead population, in relation to changes in pond number (habitat availability), population size (density dependence) and harvest
regulations (bag limit).
PERTURBATIONS BY CHANGES IN HABITAT
AVAILABILITY AND MODEL PREDICTIONS
We found that availability of ponds affected only fecundity. Our data and analysis nevertheless did not allow us
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
966 G. Pe´ron et al.
partly occurred via competition between females (crowding
effects operating at local scales), but we cannot exclude
regulation via variation in the use of suboptimal habitats
(mechanisms operating at the landscape or larger scale).
We also found some evidence for density dependence in
female survival, but this was not related to the availability
of May ponds.
Using the deterministic part of the matrix population
model described in eqn 1, we estimated yearly female population growth rate (Caswell 2000). A large part of the pond
number · population count space resulted in a declining
population (Fig. 1a), suggesting that, especially when population count was above its temporal average (positive value
of standardized population count in Fig. 1), the population
was above carrying capacity. This result was congruent with
the observed trend in population size over the period 1960–
1990 (small-scale oscillations around a long-term stable
trend, suggesting a population at carrying capacity), as well
as with the more ample variation in population size observed
since 1990 (possibly linked to the lasting effect of a series of
wet years in the late 1990s and then again in the mid-2000s).
Years with high pond numbers (standardized value above 1
in Fig. 1) were likely to produce ‘population booms’, such as
recorded in 1999 (1998 being the year with highest number of
pond). Overall, density regulation was strongest in wet years
(standardized pond number above 0 in Fig. 1a), but mostly
because drought years (standardized pond number below )1
in Fig. 1a) were always years of decline independently of
population size. We note that such conclusions are limited by
the absence in the data set of the combination ‘low pond
number – high population size’. Our results nevertheless set
the stage for developing more intricate population models
and further investigating the implication of compensatory
density dependence for population dynamics in redheads and
other species. In particular, field crews distinguish ‘singles’,
‘groups’ and ‘pairs’, the latter being assumed to represent the
breeding segment of the population, while others could be
nonbreeders; this structure of the population survey data
could be used to estimate temporal variation in parameter s
and provide deeper insight into the redhead reproductive
strategy.
Table 4. Parameter estimates for the recovery probability submodel
(r) in Model 3. All effects are on the logit scale. Nonsignificant effects
(95% credible interval encompassing 0) are indicated in italic font.
Population counts were standardized. Sex- and age-specific
intercepts for bag limit of zero are presented (after transformation
into the identity scale) in Table 1
Mean
95% Credible
interval
SD
Effect of bag limit 1, shared or not with canvasback (similar species;
Aythya valisineria)
AHY males
0Æ564
0Æ107
0Æ351; 0Æ768
AHY females
0Æ667
0Æ128
0Æ407; 0Æ929
HY males
0Æ791
0Æ124
0Æ549; 1Æ041
HY females
1Æ151
0Æ097
0Æ944; 1Æ322
Effect of bag limit 2, shared or not with canvasback
AHY males
1Æ128
0Æ094
0Æ932; 1Æ323
AHY females
1Æ226
0Æ158
0Æ894; 1Æ489
HY males
1Æ165
0Æ131
0Æ925; 1Æ431
HY females
1Æ411
0Æ122
1Æ14; 1Æ629
Effect of bag limit >2
AHY males
1Æ118
0Æ159
0Æ751; 1Æ404
AHY females
1Æ237
0Æ220
0Æ822; 1Æ677
HY males
1Æ677
0Æ182
1Æ349; 2Æ003
HY females
1Æ563
0Æ213
1Æ158; 1Æ954
Density dependence (effect of population count)
AHY females
)0Æ057
0Æ076
)0Æ202; 0Æ117
HY females
)0Æ277
0Æ077
)0Æ432; )0Æ134
Time random effects
AHY males
0Æ038
0Æ017
0Æ013; 0Æ078
AHY females
0Æ052
0Æ021
0Æ023; 0Æ105
HY males
0Æ096
0Æ039
0Æ046; 0Æ197
HY females
0Æ088
0Æ027
0Æ05; 0Æ152
AHY, after hatch year; HY, hatch-year.
to decipher if the relationship was attributed to a direct
effect of pond number (or other habitat attributes that covary with pond number) on breeding success per se or on
breeding propensity. The interaction of the effect of pond
number with the effect of population size on fecundity
(Table 2) indicated that the positive influence of pond
number could be offset in years of high population size.
This suggests that density dependence in fecundity at least
1·2
1
0·8
–2
0·6
2
–1
0
o
nc
1
Pond
n
0
–1
umb
er
Ɵo
ula
1
–2
2
p
Po
t
un
(c)
0·4
0·3
0·2
0·1
2
–2
t
un
–1
o
nc
1
0
Pond
n
0
–1
umb
er
1
–2
2
p
Po
Ɵo
ula
SensiƟvity to populaƟon count
(b)
SensiƟvity to pond number
PopulaƟon growth rate
(a)
0
–0·05
–0·1
–0·15
–0·2
–0·25
2
–2
–1
1
0
Pond
n
0
–1
umb
er
n
Ɵo
ula
1
–2
2
nt
u
co
p
Po
Fig. 1. Female-only, prebreeding census, deterministic matrix population model based on the results of the integrated population model for
mid-continent redheads. (a) Population growth rate. (b) Sensitivity of population growth rate to change in pond number. (c) Sensitivity of population growth rate to change in population count (density dependence). Population size and pond number have been standardized (mean of zero
and standard deviation of one). Prediction standard errors are omitted for clarity.
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
Perturbations and density dependence 967
PERTURBATIONS BY CHANGES IN MORTALITY
PATTERNS AND POSSIBLE CONFOUNDING EFFECTS
Harvest regulations such as bag limit constitute a proxy for
the realized hunting pressure, and they constitute the variable
upon which managers can act (Johnson & Moore 1996;
Conroy, Miller & Hines 2002). However, numerous other
factors, from hunter numbers and behaviour, to epidemic
disease outbreaks and variation in landscape features also
play a role in shaping the actual proportion of deaths that is
attributable to hunting (partial controllability; Nichols et al.
2007). Our result that bag limit did not correlate with survival
in the expected negative direction, but was positively correlated with recovery probability as predicted, nevertheless
suggests that under past hunting regulations, a large part of
the variation in hunting-related mortality was compensated
by decreases in others sources of mortality (Burnham &
Anderson 1984; G. Péron, unpublished analysis). However,
our analysis did not account for a probable effect of bag limit
on hunters’ reporting behaviour. Indeed, in years with low
redhead bag limit but higher limits for other duck species,
hunters may inadvertently shoot redheads and be reluctant
to report the bands found on these birds. Thereby, the
observed effect of bag limit on recovery probability might at
least partly stem from an effect of bag limit on reporting rate
rather than on hunting pressure.
Compensation for hunting mortality is often thought to
be linked to density dependence: in years with higher than
average hunting pressure, population density is artificially
lowered on the wintering grounds, enabling the individuals
that escape hunters to experience lower natural mortality
(Burnham & Anderson 1984). The lack of strong density
dependence in redhead survival (especially in males) suggests
that the lack of effect of bag limit on survival stems either
from an inability of bag limit regulation to effectively modify
hunting pressure, or from compensatory mechanisms other
than density dependence (e.g. individual heterogeneity in
vulnerability to hunting). However, note that our measurement of density dependence in survival was based on a measure of spring population size (before breeding) and may not
have been representative of population density during the
winter. A more precise alternative would have been to first
model the transition from spring to autumn, then estimate
the effect of autumn population size on survival from one
autumn to the next–this analysis was however computationally prohibitive.
With respect to our results, we can furthermore point to
several possible confounding factors. First, during all but
three consecutive years, bag limit was £2. This limited variation in bag limit potentially lent more importance to variation in factors other than hunting regulation. Second, the
decision for setting bag limits is in part based on the results of
the May survey. Thus, even if there is considerable variation
in population size that is not directly translated into variation
in bag limit, the fact that bag limit and population size covaried positively is of concern. In addition, the power to test the
effect of hunting closures (bag limit of zero) is compulsorily
low (low number of recoveries), which was enhanced by the
fact that all five closed seasons occurred at the beginning of
the study period, when the number of ‘available’ banded
birds was lower.
LINK WITH WATERFOWL LIFE HISTORY AND
MANAGEMENT
Within Anatidae, the Aythya life-history strategy is close to
the ‘bet-hedging strategy’ (Saether & Bakke 2000) of producing large number of offspring in occasional good years
(Yerkes 2000). In other words, females are thought to
capitalize on survival to experience at least one good year
with good reproductive output in their lifetime. Our results
tend to confirm this. First, the fecundity estimate was
relatively low under average conditions but varied with the
number of ponds and density. This suggested that redhead
females were adjusting their breeding effort to encountered
conditions, possibly by modulating their use of typical
nesting as opposed to parasitic egg laying (Sorenson 1991).
Second, the between-year variation in survival probability
was moderate (Table 3: back-transformed estimates of
temporal variation in survival indicate a temporal SD of less
than 5% of the intercept value of survival in all age classes).
This suggested the occurrence of environmental canalization
as observed in bet-hedging, long-lived species (Gaillard &
Yoccoz 2003; Nevoux et al. 2010). Given the large 95% CI
on the estimates of temporal variation in redhead survival
(Table 3), caution is however needed with such an interpretation. Bringing support to that theory, however, Sorenson
(1991) found that during a local drought (1988 breeding
season), the rate of parasitic egg laying by redhead females
increased more than twofold, and the rate of skipping reproduction increased more than threefold, with a corresponding
decrease in typical nesting behaviour. The less energetically
costly (as well as less predation risky) behaviours were
thereby predominant when breeding success prospects were
lowest, as expected within the bet-hedging life-history
strategy. Third, a high proportion (estimated 48%) of firstyear females apparently did not breed during their first year.
This is coherent with an overall pattern of a slower life history
(Koons et al. 2006 in lesser scaup Aythya affinis) than, for
example similarly sized mallard, in which most females
attempt to breed at 1 year of age and repetitively attempt to
re-nest after failure (Hoekman et al. 2002). HY redhead
females may exhibit a slower spring migration than AHY
females and thus arrive on the breeding grounds after the
May surveys (Naugle et al. 2000), thus the low s estimate, but
this interpretation needs confirmation.
It has been previously found in other North American
waterfowl that fecundity is an important driver of population
dynamics. In declining populations of pintails Anas acuta
and black brant Branta nigricans, survival is not the cause of
the decline (respectively, Rice et al. 2010 and Sedinger et al.
2007), leaving fecundity responsible (because at the large spatial scales of the mentioned studies emigration and immigration are negligible). Similarly, most temporal variation in
2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969
968 G. Pe´ron et al.
mid-continent mallard population growth rate is explained
by changes in offspring production (Hoekman et al. 2002).
In the mid-continent redhead population, population booms
driven by fecundity were possible in very wet years (Fig. 1).
However, smaller scale changes in pond numbers were largely compensated for by density dependence in fecundity,
suggesting that the population typically fluctuates around its
carrying capacity. Consequently, 10-year projections of the
population trajectory based on auto-regressive predictions of
pond number indicated a stable population size (result not
shown). Overall, our study illustrates the insights that can be
gained from a combined analysis of all demographic parameters in relation to environmental variables and density. Such
insights can help document life-history variation and bring
support to life-history theories (Gaillard et al. 1989; Pfister
1998; Saether et al. 2005) as well as be used to refine population models used in management schemes (McGowan et al.
2011). Our modelling approach seems especially useful for
guiding the dual management of harvest regulations and
landscape conservation policies for exploited species (Runge
et al. 2006; Mattsson et al. 2012).
Acknowledgements
G.P. was supported by a Quinney post-doctoral fellowship. We are grateful to
Todd W. Arnold and James D. Nichols for comments on an earlier version of
this article.
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Received 14 October 2011; accepted 10 February 2012
Handling Editor: Michael Wunder
Supporting information
Additional Supporting Information may be found in the online version of this article.
Appendix S1. Temporal covariates.
Appendix S2. Results from Model 1: fixed time effects.
Appendix S3. Results from Model 2: full covariate effects.
Appendix S4. Performance assessment of integrated population
models: comparison of parameter estimates obtained using varying
combinations of datasets.
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2012 The Authors. Journal of Animal Ecology 2012 British Ecological Society, Journal of Animal Ecology, 81, 960–969