Ecological Modelling 265 (2013) 140–148
Contents lists available at SciVerse ScienceDirect
Ecological Modelling
journal homepage: www.elsevier.com/locate/ecolmodel
Sharing the bounty—Adjusting harvest to predator return in the
Scandinavian human–wolf–bear–moose system
Niclas Jonzén a , Håkan Sand b,∗ , Petter Wabakken c , Jon E. Swenson d,e , Jonas Kindberg f ,
Olof Liberg b , Guillaume Chapron b
a
Department of Biology, Ecology Building, Lund University, SE-22362 Lund, Sweden
Grimsö Wildlife Research Station, Department of Ecology, Swedish University of Agricultural Sciences, SE-73091 Riddarhyttan, Sweden
c
Hedmark University College, Department of Applied Ecology & Agricultural Sciences, N-2480 Koppang, Norway
d
Norwegian University of Life Sciences, Department of Ecology & Natural Resource Management, Box 5003, NO-1432-Aas, Norway
e
Norwegian Institute for Nature Research, Box 5685 Sluppen, NO-7485 Trondheim, Norway
f
Wildlife, Fish, and Environmental Studies, Swedish University of Agricultural Sciences, SE-901 83 Umeå, Sweden
b
a r t i c l e
i n f o
Article history:
Received 1 August 2012
Received in revised form 25 May 2013
Accepted 27 May 2013
Keywords:
Large carnivores
Demography
Management
Predator–prey
Hunting
Structured models
Ungulates
a b s t r a c t
The increase and range extension of wolves (Canis lupus L.) and brown bears (Ursus arctos L.) in Scandinavia
inevitably impacts moose (Alces alces L.) populations and, as a consequence, the size and composition
of the hunter harvest must be adjusted. We used a sex- and age-structured moose population model to
delineate optimal harvest strategies under predation and to compare the resulting harvest composition
with the strategy commonly implemented in practice. We examined how much moose density or adult
sex ratio needs to change to fully compensate for losses to predation. We found a harvest allocation
pattern in commonly used practical management across calves, bulls and cows that indicated a trade-off
strategy between maximising the number of shot moose, the yield biomass and the number of shot prime
bulls. This strategy performed quite well with respect to all yield measures and yielded an age structure
most similar to the strategies maximising harvest biomass and prime bulls. Unless predation pressure
was very high, the harvest loss could be completely compensated for by allowing a higher moose density.
In other situations the current hunting strategy was not possible to implement and the moose density
needed to sustain predation even without hunting increases dramatically. An alternative option to balance
the predation loss was to accept a more female-biased sex ratio in the winter population. Hence, it may be
possible to keep 50% calves in the harvest and still obtain the same total harvest if the proportion of bulls
in the harvest is increased to compensate for predation. The increase of large carnivores competing with
moose hunting creates conflicts and will inevitably reduce harvest yield unless hunting strategies change.
We show how increased moose density and redistribution of the harvest towards bulls can mitigate this
conflict and we provide a web-based tool, where stakeholders can compare the long-term effects of
alternative management decisions and eventually adjust their hunting strategy accordingly.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
All organisms experience variability in terms of spatial and temporal fluctuations in their abiotic and biotic environment, which is
reflected through individual vital rates, i.e. survival and fecundity.
Understanding the demographic and population dynamic consequences of external variability, be it abiotic, biotic processes or
human impact, is important for a range of ecological applications, including monitoring, conservation, pest control, fisheries
and wildlife management (e.g. Lande et al., 2003).
∗ Corresponding author.
E-mail address: [email protected] (H. Sand).
0304-3800/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.ecolmodel.2013.05.017
Some of the best-studied populations are found among ungulates species that are harvested for meat and trophies (e.g.
Clutton-Brock et al., 1982; Gaillard et al., 1998; McCullough, 1979).
In most ungulates, vital rates vary among age and sex classes
(Gaillard et al., 1998; Sæther, 1997) and any harvesting strategy
aiming for optimality in any sense (e.g. maximising the number of
animals harvested) must take age- and sex-specific variation into
account (Caughley, 1977). The optimal allocation of harvest across
stages will depend on the management goals. For instance, it is a
general finding that maximising the yield in terms of the number of
harvested individuals involves a high proportion of juveniles in the
harvest (Sæther et al., 2001), whereas the adult proportion must be
increased if the yield biomass is to be maximised (Sylvèn, 1995).
Whereas the optimal harvesting of a single age-structured population without predation (e.g. Getz and Haight, 1989) and ungulate
N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
population dynamics with predation (e.g. Jedrzejewski et al., 2002;
Messier, 1994; Vucetich et al., 2002) are well studied, the optimal
allocation of harvest effort found in single-species models in the
presence of a predator is less so. The return of large carnivores, such
as the wolf (Canis lupus L.), to areas where they have previously been
extinct or occurred in very low numbers offers an opportunity to
study how wildlife management, including hunting of ungulates,
may be adapted to the presence of large carnivores. One example
is given by Scandinavia, where the wolf declined strongly in the
19th and 20th centuries, with less than 10 individuals remaining
in Norway and Sweden in the late 1960s (Haglund, 1968). Since
1983, except for 1986, wolves have reproduced annually and the
Scandinavian (Sweden, Norway) population was estimated to be
289–325 individuals with 31 reproducing pairs in 2011 (Wabakken
et al., 2001, 2011).
Wolves in Scandinavia mainly prey upon moose (Alces alces L.)
(Sand et al., 2005, 2008) and because moose hunting has both great
economic and recreational value in Scandinavia (Boman et al., 2011;
Mattsson, 1990), there is a potential conflict with humans regarding
competition for game. In a first attempt to shed some light on how
the presence of wolves affect moose harvesting strategies, Nilsen
et al. (2005) concluded that harvest quotas must be reduced, but the
general relationship between harvesting strategy and yield maximisation is not affected. Since the publication of that study, new
data have become available suggesting that some of their assumptions may be refined for the Scandinavian wolf-moose system. First,
data suggest that kill rates in winter are in fact affected by moose
density (Sand et al., 2012a); hence there is a functional response
(Fryxell and Lundberg, 1997). Second, Nilsen et al. (2005) restricted
the predation to calves, yearlings and females of the oldest age class,
and assumed the kill rate to be proportional to their availability in
the population. We now have age- and sex-specific data on moose
killed by wolves suggesting that prey selection differs from the prey
availability in the population (H. Sand, unpublished data). Third, kill
rates are higher and selection with respect to age and sex differs
during summer and winter (Sand et al., 2008, 2012b). In addition to
these refinements, we incorporate two more important aspects of
predator impact on the moose population in Scandinavian. First, the
size of wolf territories shows large variation (Mattisson et al., 2013)
and predation rate on local moose populations varies depending
on these sizes (small territories have higher predation rate than
large territories; Wikenros, 2011), which provides a mechanism for
the variation in predation pressure. Finally, there are now areas in
Scandinavia that experience a predation pressure from both wolves
and brown bears (Ursus arctos L.), which also prey upon moose
(Swenson et al., 2007; Rauset et al., 2012; Dahle et al., 2013), and
we therefore also included predation by brown bears in our model.
In this paper we revisit some of the management issues studied
by Nilsen et al. (2005) using a population model based on empirical
demographic data, including the age and sex distribution of moose
killed by wolves and bears. In a sex- and age-structured population model, we first examined the effects of alternative optimal
harvest strategies, in terms of maximising the yield biomass, the
number of animals shot or the number of prime bulls shot, on the
harvest and the population age structure. We compared the harvest composition (calves, bulls, cows) of each optimal strategy with
the moose harvest strategy commonly implemented in practice
(Lavsund et al., 2003; Nilsen and Solberg, 2006). The latter turned
out to be a compromise between the alternative optimal strategies and we therefore focused the remaining part of the paper on
the effect of predation by wolves and brown bears on moose harvest yield when implementing this hunting strategy. We examined
how much the moose density or adult sex ratio must change to
fully compensate for losses to predation. We also found the critical moose density that does not allow any harvest at all for a
given wolf territory size (i.e. wolf density). Finally we present a
141
Table 1
Parameter values used in the model. Demographic data are from Ericsson et al.
(2001).
Parameter
Value
Explanation
Winter survival
s0
s1–12
s13
s14
s15
s16+
0.95
0.95
0.95
0.9
0.85
0.6
Calf survival
Male and female survival
Female survival
Female survival
Female survival
Female survival
Fecundity
f2
f3
f4–5
f6–12
f13–14
0.1
0.8
1
1.3
1.1
Calves per female
Calves per female
Calves per female
Calves per female
Calves per female
Weight-at-age
See Table 1 in Nilsen et al. (2005)
web-based tool developed from this model that allows stakeholders, – typically those in a local moose management unit, – to apply
our results to their local situation and, eventually, adjust their hunting strategy accordingly.
2. Materials and methods
2.1. Population model
We formulated a sex- and age-structured model with 17 age
classes for females and 13 age classes for males. In the absence
of predation and hunting, the population dynamics is described
by a single Leslie matrix based on the survival and reproductive
parameters (see Table 1 for numerical values):
−−→
−
→
Nt+1 = M × Nt
where
0
0
fi
fi
si
0
0
0
0
si
0
si
0
0
0
0
0
0
0
0
0
0
0
si
0
0
0
0
si
0
0
0
0
0
0
0
si
0
0
0
0
0
0
0
0
0
0
fi
fi
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
M=
0
si
0
si
The matrix is divided into sex-specific blocks (indicated by horizontal and vertical lines) but there is no sex difference in natural
mortality and we let the winter survival of males and females of
age class i be si and their reproduction rates in late spring/early
summer be fi .
In early summer the moose population is subject to predation
by bears, which we modeled as follows:
−
→
→
−
→ −
Nt = Nt − B · kb
where B is the average bear density and kb is a vector indicating the
class specific number of moose killed by a bear.
Brown bear density in central Sweden ranges from 0 to >30 per
1000 km2 (Bellemain et al., 2005; Kindberg et al., 2009). In our
analyses we used a medium bear density of 15/1000 km2 . However, because only adult (≥4 yr) bears are known to kill moose
142
N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
(Rauset et al., 2012; Dahle et al., 2013) and this age group constitutes approximately 50% of the total bear population (Swenson
et al., 1994) we considered an adult bear density of 7.5 adult bears
per 1000 km2 .
We assumed the number of calves killed per adult bear to be 6.8
(Swenson et al., 2007). On average, each adult bear also kills a minimum of 0.5 moose per year including 30% 1-year-old moose and
70% adult cows per season (Dahle et al., 2013). However, some of
the moose mortality that was registered as due to unknown causes
may in fact have been caused by predation by brown bears. Therefore we used a per capita kill rate of 1.0 adult moose per adult bear
and year.
During June-September the moose population size is reduced
by predation from wolves, which we modeled as follows:
−
→
→
−
→ −
Nt = Nt − A · ks
−
→
where A is the average wolf density and ks is a vector indicating the
class specific number of moose killed by a wolf during summer.
Because the number of killed moose per wolf territory is independent of pack size (Sand et al., 2012a), but also of the size of the
territory (H. Sand, unpublished data), we varied predation rates
(per area) by changing the size of wolf territories A. Scandinavian
wolf territories vary in size between 300 and 2000 km2 , with an
average of 900 km2 (Mattisson et al., 2013). We set A = 1000 km2
as a baseline, but we also let A take the values of 500 and 1500 to
simulate the effect of variation in territory size, i.e. differences in
wolf density.
A wolf pack kills on average 66 moose during summer independently of the size of the territory (Sand et al., 2008). The distribution
of moose kills in summer is 90% calves and 10% 1-year olds, with
no difference between males and females (Sand et al., 2008). In this
model, we assumed that the size of the wolf population is under
management control and therefore we used a fixed wolf population size independently of moose density. Although some studies
(Swenson et al., 2007; Testa, 1998) have reported that female
moose that lost their calves due to predation in early summer may
receive a slightly higher production of calves the following year
compared to females that not lost their calves, one other study did
not support this type of compensatory reproduction (Veisetaune,
2003). Therefore we did not include a parameter for compensatory
reproduction in our model.
Summer predation is followed by the hunting season in October,
which we modeled as follows:
−
→
−
→
Nt = MH × Nt
where MH is a transition matrix whose elements on the diagonal
correspond to the class-specific probability of not being harvested,
which we estimated from the age class distribution of shot moose.
The number of harvested moose was used to calculate an annual
yield of meat in kg (see Table 1 in Nilsen et al., 2005).
Hunting is followed by wolf winter predation during 243 days
(1 October–May 31), which we modelled as follows:
−
→
→
−
→ −
Nt = Nt − F · kw
Based on recent analyses (Sand et al., 2012a) we assumed a
functional response type II:
F =c·
aX
b+X
where F is the number of killed moose per wolf pack, X is the moose
population density per km2 , i.e. the total number of moose available
in a wolf territory of size A, and a (=48) and b (=1.21) are respectively
the maximum kill rate and half saturation point estimated by fitting a Michaelis-Menten equation (using the non linear regression
function in SPSS) to data on kill rates and moose density presented
in Sand et al., 2012a. Parameter c (=2.43) accounts for the fact that
kill rates are measured per 100 days, but winter predation lasts
for 243 days. The age distribution of wolf-killed moose found in
−
→
empirical studies in winter kw is approximately 74% calves, 5.5% 1year old males, 6.3% 1-year old females, 1.8% 2–10 year old males,
4.9% 2–10 year old females, and 7.3% >10 year old females (H. Sand,
unpublished data). Even though wolf packs mainly target calves, the
total moose population density is assumed to affect the functional
response (Sand et al., 2012a).
Finally, our model also included compensatory mortality (which
there is evidence for, see Sand et al., 2012b) as follows:
−−→
−
→
· Nt
Nt+1 = (1 + ˛)
is a vector indicating the proportion of moose that died
where ˛
from predation but would still have died from natural mortality.
We let the degree of compensation be 17% in calves, 6% in 1 year
olds and 8% in cows older than 10 years (Sand et al., 2012b).
2.2. Hunting strategies in theory and practice
In Scandinavia, moose management is a typical multi-criteria
decision problem (Sylvèn, 1995), such that there are several
conflicting goals. Moose hunting generates both economic and
recreational values (Boman et al., 2011; Storaas et al., 2001). However, high moose density can have negative effects by causing
browsing damages to forestry and increasing the risk of moosevehicle accidents (Hörnberg, 2001; Seiler, 2004). Although moose
population density varies geographically (Hörnberg, 2001; Sand
et al., 2012a), moose are generally managed with the trade-off
to maximise harvest yield while minimising damages to forestry.
Thus, the objective in most management units is to balance the
population at some critical level accepted by both landowners and
hunters (Lavsund et al., 2003). Using a winter density of one moose
per km2 as default, we were interested in finding the optimal harvest fraction of calves (hcalf ), bulls (hbull ) and cows (hcow ), such that
the yield per area was maximised. We considered three alternative
optimal strategies maximising one of the following: (i) the number
of moose shot per area (number/km2 ), (ii) the yield biomass per
area (kg/km2 ), and (iii) the number of prime bulls (≥5 years) shot
per area (number/km2 ). For each of these goals we calculate the
three yield measures, as well as the optimal distribution of harvest
between calves, bulls and cows. These proportions were compared
with the hunting strategy that has been implemented in many
areas, where approximately 50% of the shot animals are calves, 25%
bulls and 25% cows (Lavsund et al., 2003; Nilsen and Solberg, 2006;
Wikenros, 2011). This strategy is a compromise among different
goals and the strategy we implemented when evaluating the role
of predation for moose hunting. The main reason for presenting
the proportion of calves, bulls and cows in the harvest, rather than
the harvest fraction of the population, is to make the results easier
to communicate to wildlife managers. Even if the harvest fractions
are the control variables that are adjusted to reach a given management goal, in practice Scandinavian moose managers are adjusting
the proportion of a given hunting quota or bag limit that should
be animals of a given age (calves, adults) and sex (adult males,
females).
One way to compensate for harvest loss due to predation is to
allow for a higher moose density or a more female-biased winter
population by harvesting a higher proportion of adult males. We
examined how to compensate for harvest loss in a 1000 km2 wolf
territory by keeping the moose population at low (0.5 moose/km2 ),
average (1.0 moose/km2 ), and high (1.5 moose/km2 ) densities. For
each moose density, we let the model search for the combination of
harvest fractions that fully compensated for predation and plotted
the resulting adult sex ratio.
N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
143
Fig. 1. The proportion of the number of shot moose, calves, bulls and cows, when maximising yield in terms of (a) the number shot, (b) biomass, (c) the number of prime
bulls, compared to (d) the actual distribution found in data.
Starting from the target winter density (after winter predation
but before natural mortality), the model was iterated 50 generations, which removed transient dynamics, and in year 50 we
evaluated population density, sex ratio and yield for all combinations of harvest fractions, where hcalf , hbull and hcow were varied in
steps of 0.005. We accepted all solutions where the winter density
was within 5% of the target density and the adult winter sex ratio
was even.
3. Results
Our model showed that, in the absence of hunting or predation,
the moose population had an annual growth rate of about 24%. The
adult winter sex ratio was even (49% bulls) and the proportion of
prime bulls (≥5 years old) was approximately 12%.
3.1. Harvest in absence of carnivores
In accordance with previous work (Sylvèn, 1995; Nilsen et al.,
2005), the optimal harvest strategy to maximise the harvest yield
in terms of the number of shot animals is to target mainly calves
(Fig. 1a). The strategies maximising the yield biomass or the number of prime bulls were almost identical (Fig. 1b and c) and are
achieved by taking out mainly adult moose. The typical harvest allocation pattern across calves, bulls and cows presently in practice
indicated a trade-off among these goals (Fig. 1d), and we found that
Fig. 2. Moose harvest yield expressed as (a) number of shot animals/km2 , (b) kg/km2 , or (c) number of shot prime bulls/km2 for 4 different hunting strategies. 1: maximising
yield number, 2: maximizing yield biomass, 3: maximizing the number of prime bulls shot, and 4: the actual hunting strategy used in Sweden (i.e. the actual distribution of
harvest in Fig. 1d). The moose density in winter was set to 1 moose per km2 .
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N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
Fig. 3. The stable age distribution of Swedish moose in the winter population for
(a) males and (b) females for different hunting strategies (see Fig. 1).
it performed quite well with respect to all yield measures (Fig. 2).
The different harvest strategies had a strong effect on the population age structure, especially on the younger age classes, where the
harvest strategy used in practice yielded an age structure more similar to the strategies maximizing harvest biomass and prime bulls
(Fig. 3).
3.2. Harvest in presence of carnivores present
Predation by wolves and bears inevitably decreased the harvest yield. In an average-sized wolf territory (A = 1000 km2 ) and at
a moose density of 1/km2 , the yield was reduced by 35%, 36%, and
24%, when expressed as the number of shot animals/km2 (Fig. 4a),
kg/km2 (Fig. 4b), or number of shot prime bulls/km2 (Fig. 4c). The
corresponding figures for brown bears at a medium bear density
(15/1000 km2 ) were 18%, 18%, and 9%. When the moose population
was reduced by both bears and wolves, the harvest loss was more
than additive, due to the restriction that the adult (≥1 yr old) sex
ratio should be even both in the winter population and in the harvest. Hence, in a 1000 km2 wolf territory where bears are present
at medium density, the harvest in terms of the number of moose
harvested had to be reduced by 57% to fully compensate for the
loss to wolf and bear predation. Due to the age selectivity in wolf
and bear predation, the surviving moose population is older and
the proportion of prime animals is higher compared to a harvested
moose population that is not predated upon (Fig. 4d and e). Note
however, that the demographic effect of predation was stronger in
bulls compared to cows. The reason was that, to reach the management goals (i.e. even adult sex ratio and stable population size) in
the presence of wolves and/or bears, hcow had to be reduced more
than hbull , which reduced the difference in female age structure and
average age between situations with and without predation.
Because a higher moose density could sustain a higher predation pressure, increasing moose density could be an option to
compensate for harvest loss due to predation (Fig. 5). Unless predation pressure was very high, e.g. in small (A = 500 km2 ) wolf
territories or in medium-sized wolf territories in combination with
high (30 per 1000 km2 ) bear densities, the harvest loss could be
completely compensated for by allowing a higher moose density
(Fig. 5). This can by understood by considering the type II functional response (Eq. (2)). When moose density increases, so does
the number of killed moose, but towards an asymptote. Hence, the
predation pressure decreases with increasing moose density. However, when predation pressure was very high in relation to moose
density, harvesting 50% calves, 25% bulls and 25% cows and still
maintain an even adult sex ratio and stable population size, was
not possible and the moose density needed to sustain this predation pressure even without hunting increased dramatically (Fig. 6).
The exact increase in moose density needed to fully compensate for
predation was, of course, dependent on the harvest strategy implemented. For the harvest strategy studied here, the moose density
Fig. 4. (a–c) Moose yield per km2 as a function of wolf territory size with bears (black lines with circles) and without bears (white bars). (d) The average age of cows (black
lines) and bulls (grey lines), and (e) the percentage of prime cows (black lines) and prime bulls (grey lines) for different combinations of wolf and bear predation. In all panels
the implemented harvest strategy is to let 50% of the shot animals be calves, 25% bulls and 25% cows.
N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
Fig. 5. Yield as number of moose harvested per km2 as a function of moose density for different predation pressures from wolves (a) and wolves + bears (b) when
harvesting 50% calves, 25% bulls and 25% cows. Yield without predation is shown
for comparison (white bars). A refers to the size of a wolf territory (in km2 ). Note
that when predation was very high in relation to moose density, no solutions were
found.
must be increased by 0.4 moose per km2 to fully compensate for
the harvest loss in an average-sized (1000 km2 ) wolf territory.
Yet another option to balance the predation loss is to accept
an adult sex ratio biased towards females in the winter population. The higher the moose density, the less biased the adult
sex ratio needed to be (Fig. 7). Hence, it may be possible to keep
50% calves in the harvest and still obtain the same total harvest
if the proportion of bulls in the harvest was increased from 25%
to 29% (moose density = 1.5 moose/km2 ) or to 31% (moose density = 1 moose/km2 ) to compensate for predation. However, for a
moose density of 0.5 moose/km2 , the proportion of bulls in the harvest must be increased to 36% and females decreased to 14%, and the
total harvest also had to be reduced by 21% to avoid overharvesting
with population decline as a result.
Fig. 6. Moose density needed for positive population growth when harvesting 50%
calves, 25% bulls and 25% cows. White bars: Wolves only. Line and circles: Wolves
and bears.
145
Fig. 7. The resulting proportion of bulls in the adult winter population (y-axis) at
different moose densities when harvesting 50% calves in a 1000 km2 wolf territory.
The proportion of cows and bulls in the harvest were adjusted to obtain the same
number of shot animals as in the absence of wolves. When the moose density was 0.5,
this was not possible, however, and the best solution resulted in a c. 21% reduction
of the yield per area. The pie charts show the distribution of harvest among calves,
bulls and cows for different moose densities. The arrows emphasize the location of
the pie charts (proportion of bulls in the adult winter population) along the y-axis.
4. Discussion
Using a sex- and age-structured population model, we have
shown that the moose harvest strategy presently implemented in
Scandinavia is a compromise between the optimal strategies maximising either the number of shot animals, meat or prime bulls,
and performs well with respect to the different yield measures.
This strategy is still possible to implement, but in the presence of
wolves and bears, the overall yield will decrease unless compensated for by either allowing the moose population to reach a higher
density or allowing for an adult female-biased sex ratio. The latter
can be achieved by increasing the harvested fraction of bulls and
decreasing the harvested fractions of calves and cows.
One adaptive strategy that hunters may adopt in theory, and
which seems to be used in practice (Wikenros, 2011), is to reduce
harvest for a few years after wolf colonisation of the local moose
management unit. The purpose of this reduction is either to avoid
a negative population growth and thus reduced moose density
and harvest, or alternatively to obtain an increase in moose density and thereby allow for a future harvest that may partly, or
totally, compensate for predation. Our model showed that to fully
compensate for the addition of an average wolf territory, moose
density had to be increased by approximately 0.4 moose per km2 .
It should be noted, however, that our model did not include density
dependence, but if moose density is increased enough, per capita
reproductive rates may decrease with density (Grøtan et al., 2009).
Furthermore, such high increase in moose density is not an available option in most areas, because it would result in increased
browsing damage to commercially valuable forests (Angelstam
et al., 2000; Hörnberg, 2001). In fact, the question of whether an
increase in moose density is an appropriate alternative to increases
in large carnivore populations belongs to the broader debate of
how costs and benefits of returning large carnivores affect users of
the landscape (hunters, landowners, ecotourism industries, and the
society) and which adjustment of land use is deemed acceptable.
It is well known that female-biased populations are often more
productive than male-biased populations (e.g. Caughley, 1977),
which also provides a solution to how to minimise the harvest loss
in predator–prey systems. However, this solution is built on the
assumption that the pregnancy rates are not negatively affected by
a skewed sex ratio. Whereas there are examples where strongly
biased harvests have had severe implications for population sustainability (Ginsberg and Milner-Gulland, 1994), this does not seem
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N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
Fig. 8. Screenshot of a web-based tool developed from our model and intended for a stakeholder audience. Although this tool uses the same model as the one presented in
this paper, all quantitative complexity is hidden and the user can concentrate on understanding how a moose population reacts to different predator densities and hunting
strategies. The tool is accessible at http://www.algforvaltning.se/moosemodel/.
to be the case in Scandinavian moose, as long as the adult proportion of males constitutes at least 25–30% of the adult population
(Sæther et al., 2003; Solberg et al., 2002). However, according to our
model, a harvest strategy aiming at maintaining a similar yield with
and without predators may result in an adult sex ratio with <25%
males, depending on the predation pressure applied. Although this
may not significantly affect the pregnancy rates and the number
of offspring produced, there are indications that such a strongly
female-biased sex ratio may affect the timing of the mating season
for a portion of females in the population (Milner et al., 2007). Some
females may be mated later in the season, i.e. during their second or
third ovulation cycle (Markgren, 1969), resulting in a later date of
parturition during the following spring (Sæther et al., 2003). Also, a
strongly female-biased adult sex ratio will result in lowered average male age and fewer prime males in the population. We do not
know to what extent this may result in directional selection, e.g. by
lowering the level of sexual selection and thereby favouring smaller
male body size (e.g. Mysterud et al., 2005; Tiilikainen et al., 2010),
but this deserves more detailed studies (Mysterud, 2011).
We have confirmed the conclusions by Nilsen et al. (2005) that
(1) the addition of wolves into this ecosystem will lead to a significant reduction in harvest yield and (2) that the general relationship
between harvest composition and yield is not affected by the addition of large predators, such as wolves and brown bears. This result
seemed to be robust, because we included additional parameters
(functional response, extent of wolf predation being compensatory)
and refined some of the data (age selective predation) used by
Nilsen et al. (2005). Our model also included observed variation
in wolf density, as measured in terms of variable territory sizes
observed in the wolf population, but also the addition of predation
by brown bears. The latter is important, because the expanding wolf
population in Scandinavia is beginning to overlap with medium
to high-density areas of the expanding brown bear population
(Kindberg et al., 2011). The total predation pressure from both
wolves and bears had a large impact on the harvest yield. In fact,
if small wolf territories occurred in combination with the presence
of brown bears (medium density), harvest yield was reduced by
approximately 0.25 moose/km2 , or with >50% at a moose density
of 1/km2 ; a situation that did not allow for full compensation by
adjusting the adult sex ratio.
In Scandinavia, the wolf population is currently growing in size
and density (Liberg et al., 2012; Wabakken et al., 2011). Continued wolf population growth may result in an increased density of
wolves and reduced territory size (Hayes and Harestad, 2000). The
brown bear population is also increasing, with increased densities
mainly at the expansion front of the population that now overlaps
with the expanding wolf population (Kindberg et al., 2011). A future
scenario is therefore increased predation pressure on moose by
both these large carnivores, which in turn will result in an intensified competition with hunters for exploiting the moose population.
Finding strategies that maximise yield in terms of number of animals, biomass, or number of prime bulls is a useful tool for directing
management strategies and increasing our understanding of the
human exploitation of this system. However, in most models of harvest optimisation, including ours, these maximisation strategies do
not include variation in hunting effort associated with the different strategies. In reality, maximisation of yield will likely result in
a largely increased hunting effort, e.g. the number of hunting days
needed per shot moose. This is because these optimal strategies
require that the main harvest is directed towards certain age and
sex categories of moose. As the harvest quota of these categories is
fulfilled, more and more time will be devoted to search for and find
the last portion of harvestable fraction of these categories and during this search many non-harvestable moose will be encountered
but not harvested. Thus, in practice the harvest strategy applied by
Scandinavian hunters could be considered as an optimal strategy
trading off yield and effort.
In practice, moose management is a typical case of multi-criteria
decision analysis, and previous attempts to put economic weights
on the number of moose shot, meat yield and number of prime
bulls shot suggest that a female-biased population (two females
per adult male) provides the maximal yield value (Sylvèn, 1995).
N. Jonzén et al. / Ecological Modelling 265 (2013) 140–148
We suggest the adoption of a comprehensive approach to the system of moose wildlife management and land use in Scandinavia,
where serious attempts are made to identify the conflicting goals,
alternative decisions and the expected costs and revenues of alternative outcomes. Such an endeavour transgresses the boundaries
of scientific disciplines and would require input from e.g. ecology,
economics, behavioural sciences and statistics.
It is often argued that quantitative inferences on ecological systems have poor applicability to the decision makers’
real-world questions – i.e. the typical “knowing – doing gap”
(Knight et al., 2008; McNie, 2007). We took the opportunity of
a recent decision (Prop., 2009/10:239) by the Swedish Government to reform moose management and developed a web-based
tool (Fig. 8 and see online supplement for details) available at
http://www.algforvaltning.se/moosemodel/, which would allow
stakeholders to get an increased qualitative understanding for the
long-term effects of alternative hunting strategies on demography, population size and yield. In this way we decrease the gap
between academic science and practical management, which is
important when applying ecological knowledge to real-world problems (Milner-Gulland et al., 2012).
Acknowledgements
N.J. was financially supported by the Swedish Research Council
(VR) and FORMAS. H.S., G.C., P.W., J.E.S., J.K. and O.L. were supported
by the Swedish Environmental Protection Agency, the Swedish
Association for Hunting and Wildlife Management, World Wildlife
Fund for Nature (Sweden), Swedish University of Agricultural
Sciences, the Directorate for Nature Management (Norway), Norwegian Research Council, Norwegian Institute for Nature Research,
Hedmark University College, County Governor of Hedmark, and
NORSKOG.
Appendix A. Supplementary data
Supplementary data associated with this article can be
found, in the online version, at http://dx.doi.org/10.1016/
j.ecolmodel.2013.05.017.
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Supplement to “Sharing the bounty” by Jonzén et al. Delivering quantitative results obtained from complex mathematical models is not a simple task. First, it is tempting for researchers to remain locked into pure academic thinking and to deliver results in a way that poorly addresses stakeholder concerns. Second, awareness of this risk may lead to over-­‐
simplifying research results and to delivering trivial findings with no real added value for the stakeholders. Finally, because stakeholders are unlikely to be (or be willing to become) familiar with the standard tools used by quantitative ecologists (e.g. scripting languages like R or Matlab), researchers who are willing to explain results in a dynamic and interactive way face the additional difficulty of selecting an appropriate technology. Our objective here was to present our results in a semi-­‐quantitative way; to propose an interactive tool that would go further than displaying the general patterns of our findings; but without allowing a user to enter their own data on moose population density, harvest and predation and use the model as a predictor of future moose population dynamics. We also wanted this tool to be intuitive to use and to be accessible to as many people as possible. After developing several prototypes, the solution we selected was a web-­‐based model that provides graphic controls to select hunting parameters and instantaneously displays the predicted moose population from the same model as the one described in this paper. The reasoning behind using a web-­‐based model was that a browser is the most widespread software and is installed by default on any modern computer. In addition, the programming language Objective-­‐J coupled with the Cappuccino framework makes it possible nowadays to develop desktop-­‐class applications that run within a web browser. A further advantage of being web-­‐based is that a user does not need to install anything and always runs the latest update of the tool. However, keeping the model web-­‐based raised the challenge of how to run model computations efficiently. Because we did not want to run a simplified version of the model and because there is no open-­‐source web programming language that offers fast matrix computations, we split the tool into two distinct parts: the graphical user interface, which runs within the browser, and the model part, which runs server-­‐side, both parts being linked by a PHP script. Having the model running on a dedicated server makes possible to use a low-­‐level programming language (in our case C) coupled with optimised mathematical libraries (GNU Scientific Library and BLAS). In practice, the user visits this website http://www.algforvaltning.se/moosemodel/ with a browser (Google Chrome, Firefox and Safari) and Javascript enabled. The user selects the size of the hunting area, the moose density, indices of predation pressure and a planned hunting strategy. Any parameter change triggers a simulation, which is sent to and runs on the server and then back to the browser. Displayed results include the population trends during 5 years, the expected yield the last year, and the asymptotic sex and age structure of the moose population (see Fig. 8). Because the population model is a compiled multi-­‐
threaded C code, each simulation takes less than 1/10 second and there is virtually no waiting time. This allowed us to avoid having a “run” button and to improve the user experience by allowing him/her to observe how a gradual change of parameters affects the moose population as the results are updated dynamically and continuously.