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Hunting in neighbouring areas influences the dynamics of an unmanaged population of red deer

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Thesis

Hunting in neighbouring areas influences the dynamics of an unmanaged population of red deer

Abstract and Figures

Actions for managing ungulate populations are widespread and motivated by various reasons. Although their effects are monitored, long-term effect such as those affecting population dynamics, are not commonly evaluated. In this study, I focus on a red deer (Cervus elaphus) population living in the North Block of the Isle of Rum Scotland, which was intentionally released from cullying in 1974 whereas neighbouring populations were continuously harvested. I describe the last 40 years of the population dynamics for females and males, assess the effects of density, weather and age structure on the population, and discuss the effects that culling surrounding populations has had on this unmanaged population. I used deterministic matrix models considering two temporal scales of analysis (one 40 years matrix and eight 5 years matrices) for reporting vital rates, asymptotic growth rates and elasticities, and density dependent matrix models to identify the most influential factors for the population dynamics in both sexes. I found that the female population have had a slight increase during these 40 years (λ=1.0068) with small oscillations on elasticities, whereas males have been decreasing in number (λ=0.7928) and elasticities have changed abruptly for adult survival (from 0.83 to 0.06) and senior age survival (from 0.0123 to 0.8625). One of the most influencing factors on the dynamics was female density, changing the carrying capacity of females (1% reductions of its effect in survival and fecundity increased K in 1.057 and 1.393 units, respectively) and males (1% reductions in survival increased K in 2.237 units). Harvesting neighbouring areas could be influencing emigrations of adult males from this population, making it smaller and older, while females increase in number maintaining the carrying capacity. The “leakage” of males could be threatening this population as it is decreasing the genetic diversity and therefore increasing its extinction risk. I recommend modifying the harvesting strategy in order to decrease migrations from the North Block population. Management must include this population and should emulate natural pressures that modify dynamics in ungulates, like predation, in order to maintain this population with a minimum bias of human intervention.
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Hunting in neighbouring areas
influences the dynamics of an
unmanaged population of red deer
Nicolás Fuentes-Allende
September 2015
A thesis submitted for the partial fulfillment of the requirements for the degree
of Master of Science at Imperial College London
Formatted in the journal style of Ecological Applications.
Submitted for the MSc in Ecology, Evolution and Conservation
1
DECLARATION
Data from weather and the red deer inhabiting the North Block of the Isle of Rum were
provided by my supervisor (Professor Tim Coulson) and they belong to the Isle of Rum Red
Deer Project” (http://rumdeer.biology.ed.ac.uk/). I organized and cleaned these databases for
my own research purposes as well as I performed all the data analyses. All the analyses that I
did are described in the Methodology section. Professor Tim Coulson supervised me i)
orienting the general objective of my project and ii) assisting me in model construction when
it was necessary.
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HUNTING IN NEIGHBOURING AREAS INFLUENCES THE DYNAMICS OF AN
UNMANAGED POPULATION OF RED DEER
Abstract
Actions for managing ungulate populations are widespread and motivated by various reasons.
Although their effects are monitored, long-term effect such as those affecting population
dynamics, are not commonly evaluated. In this study, I focus on a red deer (Cervus elaphus)
population living in the North Block of the Isle of Rum Scotland, which was intentionally
released from cullying in 1974 whereas neighbouring populations were continuously
harvested. I describe the last 40 years of the population dynamics for females and males,
assess the effects of density, weather and age structure on the population, and discuss the
effects that culling surrounding populations has had on this unmanaged population. I used
deterministic matrix models considering two temporal scales of analysis (one 40 years matrix
and eight 5 years matrices) for reporting vital rates, asymptotic growth rates and elasticities,
and density dependent matrix models to identify the most influential factors for the
population dynamics in both sexes. I found that the female population have had a slight
increase during these 40 years (λ=1.0068) with small oscillations on elasticities, whereas
males have been decreasing in number (λ=0.7928) and elasticities have changed abruptly for
adult survival (from 0.83 to 0.06) and senior age survival (from 0.0123 to 0.8625). One of the
most influencing factors on the dynamics was female density, changing the carrying capacity
of females (1% reductions of its effect in survival and fecundity increased K in 1.057 and
1.393 units, respectively) and males (1% reductions in survival increased K in 2.237 units).
Harvesting neighbouring areas could be influencing emigrations of adult males from this
population, making it smaller and older, while females increase in number maintaining the
carrying capacity. The “leakage” of males could be threatening this population as it is
decreasing the genetic diversity and therefore increasing its extinction risk. I recommend
modifying the harvesting strategy in order to decrease migrations from the North Block
population. Management must include this population and should emulate natural pressures
that modify dynamics in ungulates, like predation, in order to maintain this population with a
minimum bias of human intervention.
3
Keywords
Cervus elaphus; density-dependent model; deterministic model; elasticity analysis; harvesting
strategies; Isle of Rum; long-term effects; male migrations; red deer.
Introduction
Actions for managing ungulate populations are widespread, and are motivated for a number
of reasons e.g. research (Clutton-Brock et al. 2002), protecting threatened populations (Cosse
and González 2013), maintaining them as a natural resource (Milner-Gulland et al. 2004),
minimizing negative effects on humans (Hubbard and Nielsen 2009) or the environment
(Russell et al. 2001) and for economic reasons (Conover 2002). Management actions are
usually motivated by an immediate need, and therefore their effectiveness is usually assessed
in the short-term. Nevertheless, they also have long-term effects that are not always clear in
the short-term, like those on population dynamics (Coulson et al. 2004; Bocci et al. 2012),
which must be monitored.
Maintaining long-term monitoring programmes for ungulates is difficult, because budget
constraints and objectives may change with time. However, the monitoring programmes that
exist in the wild have been useful for understanding population dynamics (e.g Soay sheep
Ovis aries, Coulson et al. 2001; red deer, Clutton-Brock et al. 1982; bighorn sheep Ovis
canadensis, Coltman et al. 2003; moose Alces alces, Vucetich and Peterson 2004; review
Clutton-Brock and Sheldon 2010), and therefore improving management strategies. These
programmes have also allowed us to understand the effects that natural factors have on
population dynamics, like those related to weather (Boyce et al. 2006; Gaillard et al. 2013),
and the population itself (e.g. density, Owen-Smith 2006; age structure Coulson et al. 2001).
Elasticity analyses (Caswell 2001) from matrix models of age-structured (Leslie 1945) and
stage-structure populations (Lefkovitch 1965) have been of significant importance and widely
used by scientists and wildlife managers to understand population dynamics (Benton and
Grant 1999). Nevertheless, the way of how matrix models are performed needs to improve.
Firstly, these studies have mainly focused on the female subgroup in populations,
4
disregarding that males also affect the dynamics (Mysterud et al. 2002). And secondly, they
have been mainly focused at local scale, disregarding that some management actions could
stimulate or discourage migrations between neighbouring populations (e.g. land-use changes,
Lande et al. 2014; supplemental feeding, Jones et al. 2014).
In this study I focus on a red deer population of the North Block of the Isle of Rum, Scotland.
This population was released from culling in 1974, but the neighbouring areas continue to be
harvested (Clutton-Brock et al. 1982). I i) describe the population dynamics of the female and
male subgroups considering 40 years of records (1974-2013), ii) fit the density-dependent
model proposed by Coulson (2012) to explain the effect of weather (temperature and
precipitation), population density and age structure on the dynamics of each sex, iii) discuss
the causes and the long-term effects that the absence of culling in this population, coupled
with the constant harvesting of the surrounding populations, have provoked in the North
Block population, and iv) propose management recommendations to protect this valuable
study site.
Methodology
The data
Red deer data were collected from 1974 to 2013 in the North Block of the Isle of Rum,
Scotland (57001' N, 06017' W; NM-402996). This area is part of a long-term individual-
based study focused on a red deer population that was released from culling in 1974 and since
1982 when the population reached carrying capacity has been limited by food availability
(Clutton-Brock et al. 1982; Coulson et al. 2000). Starting in 1971, all individuals born into
the population have been tagged, followed throughout life until death and had their pedigree
identified (Clutton-Brock et al. 1982). Censuses have been performed since January 1974.
Censuses are conducted by one observer who covers the study area walking a set route that is
repeated a median number of 40 times per year (Clutton-Brock et al. 1982). Measures of age,
sex, population size (total population, female population and male population), mortality and
births are accurate, with a recapture rate near 1.0 (Fan et al. 2003). Missing data are
5
negligible (Clutton-Brock et al. 1982). Full details of the data collection methodology are
available in Clutton-Brock et al. (1982).
Individuals were grouped into four age classes: yearlings (1 year old), juveniles (2 years old),
adults (3-8 years old) and seniors (>8 years old), being the last two classes the only that are
able to breed (Catchpole et al. 2004). Precipitation and mean temperature during winter
(January to April) and the Rut (September to November) (Catchpole et al. 2004) were
collected daily from a local weather station on the Island (Clutton-Brock et al. 1982).
Weather data from winter season was used for survival analyses and data from Rut season
was used for fecundity analyses. When a month had more than four days of missing data, or
group of months had more than seven days of missing data it was excluded for the analysis in
order to decrease errors in estimations. All statistical analyses and modelling were performed
in R (R Development Core Team 2008).
Description of population dynamics
Leslie matrices were used as projection matrices of an age stage-classified population (Leslie
1945) to describe the population dynamics of each sex from 1974 to 2013 considering two
temporal scales of analysis. One scale considered the 40 years of study as a whole and
showed the general tendency of the population dynamic during the study period. In the
second one I divided the 40 years into 8 periods of 5 years in order to assess if the general
tendency has remained stable throughout the time. I chose the 5-year frame as it was used in
other studies before (Gaillard et al. 1998). Projection intervals were equivalent to the deer
year, starting the 15th of May and ending the 14th of May the next year. Average survival (Sx)
and fecundity rate (Fx) were calculated using data from a pre-breeding pulse census (Caswell
2001). Survival rates of the individuals that stay in the age class for more than one unit of
time (Px) and that pass to the next age class (Gx) were calculated using the following formulas
(Crouse et al. 1987):


6
where x represents the age class and dx represents the units of time that an individual stays in
the age class x before passing to class x+1. The population size at time t+1 is calculated by
the multiplication of the projection matrix with the number of individuals in the population at
time t (Leslie 1945):

 
  
 
 
where A represents the projection matrix for the red deer population in the study area, nt the
number of individuals in each age class in the population at time t, and y, j, a and s represent
yearlings, juveniles, adults and seniors age classes respectively. I report vital rates,
asymptotic growth rate (λ) and elasticities of the population growth rate to matrix entries
(Caswell 2001) for both temporal scales of analysis.
Effects of age structure, population size and weather on vital rates
1. Density dependent Model
I built two deterministic density dependent models for age stage-classified populations, one
for the female population and other for the male population. Vital rates depended on age
structure, population size and weather (precipitation and mean temperature). The formula that
I used to estimate vital rates was based on a density dependent model described by Coulson
(2012):




where Nt represents the population size at time t, and a, b,x, c and d are the intercept and the
slopes for age class x, weather and density, describing the linearized association between the
explanatory variables and the expected vital rate.
7
2. Selection of parameters
Model parameters were estimated from generalized linear models (GLM) for each vital rate
(Catchpole et al. 2004), using a quasi-binomial distribution (logit link function) for fecundity
of females and survival of both sexes, and a Gaussian distribution (identity link function) for
the fecundity rate of males as it exceeds 1. Each one of the four GLMs incorporated no more
than one explanatory variable per category (age structure, population size and weather). Vital
rates, as well as age structure, density and weather were obtained from the 40 years of study
in the North Block of Rum.
I first built GLMs with one explanatory variable, comparing their Akaike information
criterion (AIC) values within the same category of variables (Catchpole et al. 2004). I
selected the explanatory variable that generated the model with the lowest AIC in each
category. Models with differences 2 units were considered as equivalents (Burnham and
Anderson 2004). When models were equivalent, I selected the one that explained the highest
proportion of deviance. Models with AIC values equivalent or bigger than the Null model
(vital rate ~ 1) were discarded for parameters estimation.
3. Model validation and elasticity analysis
I ran the female and male models 100 times, each starting from 1 individual in the yearling
class. I discarded from the analysis the 10 first years of predictions as the models need to
equilibrate first. To validate the quality of each model I visually assessed if the simulated K
and age structure at equilibrium (λ=1) were similar to the observed carrying capacity (female
+ males) and the age structures (from female and male populations) in the study area. The
observed carrying capacity and the age structure were considered as the average value
between 1982 (when the population reached the equilibrium) and 2013.
Finally, I assessed how changes to the parameters affects carrying capacity and elasticities at
equilibrium (λ=1). I increased and decreased the parameter values by 1% depending on
whether they had a direct or inverse effect on the vital rates, respectively (Caswell 2001). I
ran the model making only one change per iteration. Then I calculated the carrying capacity
and elasticities for each simulation and I compared them with the estimations from the
original model.
8
Results
The smallest and largest population size in the female population was 90 (1974) and 217
(1998) individuals, and in the male population was 42 (1974) and 121 (1998) individuals for
the 40 years of study (Figure 1). The oldest female and male individuals were 23 and 16 years
old, which died in 1991 and 1999 respectively.
40 years deterministic matrix
Vital rates of the female and male populations are shown in Table 1 (first row of each
section). Female population shows a slight increasing tendency which is near the equilibrium
(λ=1.0068) (Table 1, first row first section). On the other hand, the male population is
showing a decreasing tendency which is not close to the equilibrium (λ=0.7928) (Table 1,
first row second section). Although asymptotic growth rates are different for females and
males, elasticities are similar. Survival of adults staying in the age class (Pa) and seniors
staying in the age class (Ps) have the biggest elasticities, being 0.424 and 0.192 in females,
and 0.524 and 0.216 in males, respectively (Figure 2, first column of each graph).
5 years deterministic matrices
In the female population, the calculated λs, vital rates (Table 1, second to ninth rows first
section) and elasticities (Figure 2, second to ninth columns graph a) of the 5 years matrices
have been slightly oscillating near the calculated values from the 40 years matrix (Figure 2,
first column graph a). This indicates that the female population has kept a stable pattern
with only a small fluctuation throughout the time.
Males have shown a different pattern. Their λ values have never reached the equilibrium
(λ=1) and it started to fall since the period 1994-1998 (λ=0.7925), reaching its lowest value in
the period 2009-2013 (λ=0.6652) (Table 1, second to ninth rows, second section). Adult
survivals (Pa and Ga) and fecundity (Fa) have decreased during the same period (Table 1,
second to ninth rows, second section). Pa, which had the biggest elasticity during the first 5
years of analysis (1974-1978, elasticity =0.83), started to decrease in the period 1994-1998
(elasticity=0.3016), reaching its lowest value in the period 2009-2013 (elasticity=0.0599)
9
(Figure 2, grey bars graph b). On the other hand, the elasticity of Ps increased from 0.0123
(period 1974-1978) to 0.8625 (period 2009-2013) (Figure 2, black bars graph b).
Density dependent matrix
Due to missing data, precipitation in October, October-November and September-October-
November were excluded from the analysis.
1. Female population
The best model to explain survival has age class, female density and precipitation in January
as explanatory variables (AIC= 686.76; it explains the 41.11% of the data deviance) (Table 2
section e). The best model to explain fecundity has female density and temperature in
September-October as explanatory variables (AIC= 496.73; it explains the 14.47% of the data
deviance) (Table 2 section j). Estimation of parameters are shown in Table 4 (sections a
and b).
The simulated female population (Figure 3, graph a) has a carrying capacity of 244
individuals, which is 18 units below the observed carrying capacity of the total population in
the North Block of Rum (K262 individuals). Age structures are the same for the simulated
population at equilibrium (λ=1) and the female population in the North Block of Rum
(yearlings≈12.37%, juveniles≈10.32%, adults≈47.22% and seniors≈30.09%). Population
structure, carrying capacity and elasticities at equilibrium are reported in Table 5 (section
a).
The elasticity analysis shows that the most influencing parameters for the population
dynamics are the survival of adults (intercept in the survival model) and the density of
females (Table 5, section b). Although changing the effects of parameters in 1% has
negligible impacts on elasticities, they change the carrying capacity. Increasing the effect of
adult survival in 1% increases the carrying capacity in 2.637 units, and decreasing the effect
of the female density on the survival and fecundity rates increases K in 1.057 and 1.393 units
respectively (Table 5, section b).
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2. Male population
The best model to explain survival has age structure, female density and temperature in
January as explanatory variables (AIC= 831.39; it explains the 12.41% of the data deviance)
(Table 3, section e). The best model to explain fecundity only contained age class as
explanatory variable (AIC= -75.5; it explains the 35.43% of the data deviance) (Table 3
section j). Estimation of parameters are shown in Table 4 (sections c and d).
The simulated male population (Figure 3, graph b) has a carrying capacity of 222
individuals which is 40 units below the observed carrying capacity of the total population in
the North Block of Rum. Age structures are different for the simulated population at
equilibrium (yearlings≈27.71%, juveniles≈18.77%, adults≈45.72% and seniors7.8%) and the
observed values in the male population in the North Block of Rum (yearlings≈23.69%,
juveniles≈26.25%, adults≈35.10% and seniors≈14.96%). Population structure, carrying
capacity and elasticities at equilibrium are reported in Table 5 (section c).
The elasticity analysis shows that the most influencing parameters for the population
dynamics are the survival of adults (intercept in the survival model) and the density of
females (Table 5, section d). Although changing the effects of parameters in 1% has
negligible impacts on elasticities, they do produce a bigger change on the carrying capacity
than in the female model. Increasing the survival of adults in 1% increases the carrying
capacity in 4.912 units, and decreasing the effect of female density on the survival rate
increases K in 2.237 units (Table 5, section b).
Discussion
Quality of the density dependent model
The model proposed by Coulson (2012) consisting of age structure, density and weather fits
the deer population in the North Block of Rum quite well. Although the simulated carrying
capacity and age structure from both models were similar to the observed values in the study
area, the model fits better for females than males. Unfortunately, predicting the dynamics of
the male population is not easy as they have not followed a clear pattern across the time
11
(Table 1). The inclusion of migration (Clutton-Brock et al. 1982) in the model would likely
improve it.
Population dynamics
1. Deterministic matrices
Adult survival is the vital rate with the highest elasticity in females, which is concordant with
findings from other studies on wild ungulate populations (e.g review, Gaillard et al. 1998;
west African giraffe Giraffa camelopardalis peralta, Suraud et al. 2012; mule deer
Odocoileus hemionus, Forrester and Wittmer 2013; roe deer Capreolus capreolus, Gaillard et
al. 2013; feral horses Equus caballus, Richard et al. 2014) and other long-lived animals (e.g.
loggerhead sea turtles Caretta caretta, Crouse et al. 1987; killer whales Orcinus orca, Brault
and Caswell 1993). In males, elasticities behave differently. As Coulson et al. (2004) reported
for the first 27 years of study, the elasticity of adult survival has decreased throughout the
years, but this trend has become stronger in the last 15 years (Figure 2). The drop in adult
survival has made senior survival become the vital rate with the biggest elasticity, which
coincides with the pronounced declining of λ (Table 1). This is concordant with the findings
of Owen-Smith and Mason (2005) who showed that the decrease in λ is associated with drops
in the elasticity of adult survival in African ungulates. Other examples where adult survival
did not have the biggest elasticity are found in endangered ungulates (Sierra Nevada bighorn
sheep Ovis canadensis sierra, Johnson et al. 2010), and populations under high hunting
pressure (wild boar Sus scrofa, Bieber and Ruf 2005; roe deer, Nilsen et al. 2009).
Changes in elasticities and the asymptotic growth rate in the male population of Rum means
it has become older and smaller across the time. This could be caused by the emigration of
adults (Clutton-Brock et al. 1982; Clutton-Brock et al. 2002) while seniors stay (senescence
effect, Loison et al. 1999). Similar patterns have been reported before, with prime-age
individuals (adults) being more mobile than seniors (moose in Sweden, Singh et al. 2012; red
deer in the Western Carpathian Mountains, Kropil et al. 2015).
2. Density dependent matrix
Female density is one of the most important factors affecting the population dynamics of red
deer in the study area, having a negative effect on the vital rates of males and females (Table
12
5; Owen-Smith 2006; Richard et al. 2014). Clutton-Brock et al. (1982) reported that female
density was even more influential for the population dynamics than the total population
(females + males), which was also confirmed in this study 30 years later (Table 2 and Table
3). Because the population reached its carrying capacity in the early 80s (Clutton-Brock et al.
1985) and has kept fluctuating around it until now (Coulson et al. 2004), the population has
been regulated by density-dependence. Although both sexes are controlled by the same
factor, they behave differently. Females stay in the North Block of the island, with depressed
density-dependent vital rates, and controlled by food and space-restriction, while adult males
migrate to less crowded areas (Clutton-Brock et al. 1982; Clutton-Brock and Albon 1989;
Clutton-Brock et al. 2002). Similar strategies to confront increases in density have been
reported in other populations, where males increase migration distances (e.g. red deer in
Norway, Loe et al. 2009; red deer in Italian Alps, Bocci et al. 2012), and females tolerate
bigger group sizes (elk deer Cervus canadensis in Canada, Wal et al. 2013) when density
increases. This behaviour could be explained by “the activity budget hypothesis” (Ruckstuhl
and Neuhaus 2000) which suggests that with increasing dimorphism in the body size, males
and females increasingly differ in the time spent in different activities (e.g. males walking
and females foraging, Ruckstuhl and Neuhaus 2002).
3. Causes and consequences
The Isle of Rum is owned by the Scottish Natural Heritage (SNH) who practices hunting in
the remainder of the island (Milner-Gulland et al. 2004) and keeps those populations below
their carrying capacity. Because there are no fences in the island, males have free access to
other areas on the island (Milner-Gulland et al. 2004). This situation could be indirectly
influencing the population dynamics of male and female populations in the North Block.
Adult males migrate to those areas where they are hunted (Clutton-Brock et al. 2002), leaving
the female population to increase in size without changing the carrying capacity. This
situation is confirmed 15 years later with my results, where the North Block population
continues fluctuating near its carrying capacity (K≈262), the female population shows a slight
increase throughout the years (λ =1.0068; from 40-years deterministic matrix) with no
variation in their elasticities (Figure 2, graph a), and the male population is getting smaller
(λ =0.7928; from 40-years deterministic matrix) and older (elasticity of senior survival
=0.8625; period 2009-2013).
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The current scenario in the North Block could be driving a decrease in the genetic diversity of
the population, and therefore increasing its extinction risk (Frankham 1995). The leakage”
of males to other area where they are shot means a leak of genes, which becomes unavailable
for next generations in the North Block, making this population more susceptible to
unfavourable environmental conditions (Frankham 1995). Clutton-Brock et al. (2002)
reported this leak of genes before in the North Block population, when they found that
individuals with good antlers development (hereditable trait) were more likely to emigrate,
which was making this trait uncommon in the local population.
Controlling male migrations
Deer populations in Rum should be exposed to the same management action in order to
decrease the emigration of males from the North Block. Recommendations for harvesting
strategies considering migrations has been proposed before for other red deer populations in
Europe (e.g. Sweden, Jarnemo 2008; Italy, Bocci et al. 2012; Slovakia, Kropil et al. 2015).
One option to decrease it is to ban hunting activities on the entire island, making all
populations fluctuate near the ecological carrying capacity. Unfortunately, this is not feasible
as hunting is an important activity that generates profits for the SNH (Milner-Gulland et al.
2004). Another option is to apply the same harvesting strategy in all deer estates that allows
males to increase in number in their populations. Previous experiments have shown that
harvesting females facilitates this because of a reduction in male mortality and emigration
rates (Clutton-Brock et al. 2002; Milner-Gulland et al. 2004).
The harvesting strategy should also include the North Block population in order to maintain
all estates at equilibrium (λ=1). Since one of the research aims in this area is to not interfere
with the natural cycles, the management action could emulate predation, as it is a natural
pressure that influences population dynamics in ungulates (e.g. roe deer, Nilsen et al. 2009;
moose, Gervasi et al. 2012; mule deer, Forrester and Wittmer 2013). Cromsigt et al. (2013)
proposed different hunting strategies to emulate the effect of predation on preys and
discussed their benefits. They based their work on the ecology of fear theory” (Brown et al.
1999), which explains the effects that predators have on preys. Actions like hunting only a
stable proportion of the population per year, mainly on females and calves, and with no
14
restriction of time and space (like a natural predator would do) could reduce the bias that the
current harvesting strategy has provoked on the North Block.
The study of the red deer in the North Block of Rum is recognized as one of the most
important long-term mammal studies around the world (Clutton-Brock and Sheldon 2010)
where the aim is to monitor and describe how populations behave under natural conditions
without human intervention (Clutton-Brock et al. 1982). Because hunting in the remainder of
the island influences male emigrations and causes genetic loss from this target population, it
needs to be controlled. I recommend to restructure the current harvesting strategy at Rum in
order to minimize emigrations from this important research area (Clutton-Brock et al. 2002).
This action should be implemented regardless that the results of adopting it could be only
seen in the long-term (Coulson et al. 2004).
Acknowledgments
I thank Professor Tim Coulson (University of Oxford) for guiding me across this invaluable
learning process, and Erik Sandvig for his helpful comments. I receive a postgraduate
scholarship from the Comisión Nacional de Investigación Científica y Tecnológica
(CONICYT, Chile) to support my coursework at Imperial College London.
15
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21
Figure 1. Size of a) the total population, b) the female population, and c) the male population
from 1974 to 2013. The black, grey, downward diagonal and dotted areas represent seniors,
adults, juveniles and yearlings respectively. Dotted lines indicate 5 years periods.
22
Figure 2. Elasticities of a) the female population and b) the male population from 1974 to
2013. First columns of each graph show elasticities for the 40 years matrix, and second to
ninth columns elasticities for 5 years matrices.
23
Figure 3. Simulated population dynamics for the a) female and b) male populations. The
black, grey, downward diagonal and dotted areas represent seniors, adults, juveniles and
yearlings respectively. The dashed line represents the observed carrying capacity in the North
Block population.
24
Table 1. Lambda value and vital rates of the female and male populations from 1974 to 2013.
First rows of each section show rates for the 40 years matrix, and second to ninth rows rates
for 5 years matrices.
Period λ
GyGjPaGaPsFaFs
1974-2013 1.0068 0.8841 0.9446 0.7957 0.1222 0.8113 0.1506 0.1688
1974-1978 1.0748 0.9080 0.9620 0.8150 0.1431 0.8458 0.1923 0.2419
1979-1983 0.9894 0.8706 0.9429 0.7903 0.1169 0.7965 0.1353 0.1683
1984-1988 1.0037 0.8421 0.9885 0.7992 0.1257 0.7833 0.1609 0.1518
1989-1993 0.9998 0.8864 0.9213 0.7980 0.1245 0.7584 0.1675 0.1542
1994-1998 1.0501 0.8759 0.9619 0.8007 0.1272 0.8210 0.1965 0.2341
1999-2003 0.9965 0.9423 0.9388 0.7917 0.1183 0.7748 0.1440 0.1608
2004-2008 0.9919 0.8644 0.9524 0.7918 0.1183 0.8163 0.1429 0.1429
2009-2013 0.9587 0.8938 0.8876 0.7865 0.1133 0.8085 0.0893 0.1460
1974-2013 0.7928 0.6710 0.7140 0.6999 0.0560 0.6405 0.0318 0.2446
1974-1978 0.7511 0.5784 0.7273 0.7135 0.0626 0.2381 0.0199 0.2500
1979-1983 0.7876 0.5616 0.7273 0.7504 0.0846 0.4365 0.0330 0.0976
1984-1988 0.8531 0.5455 0.7703 0.7727 0.1013 0.5978 0.0569 0.2075
1989-1993 0.8548 0.8254 0.8197 0.7434 0.0799 0.6225 0.0414 0.2297
1994-1998 0.7925 0.7563 0.7260 0.6576 0.0392 0.7134 0.0266 0.2577
1999-2003 0.7002 0.6744 0.7091 0.6295 0.0307 0.5382 0.0291 0.2292
2004-2008 0.7008 0.6810 0.6000 0.5269 0.0115 0.6672 0.0096 0.5806
2009-2013 0.6652 0.7700 0.6154 0.5025 0.0089 0.6506 0.0000 0.2500
Female population
Male population
25
Table 2. Selection of parameters for the density dependent matrix of the female population.
Sections a) to e) show the survival rate in function of the null model, age structure,
population size, weather and the best parameters respectively. Sections f) to j) show the
fecundity rate in function of the null model, age structure, population size, weather and the
best parameters respectively. Stars represent the best parameter to include in the final model,
and two stars represent the best model for each vital rate. ΔAIC is the difference between the
AIC of the model and the lowest AIC in that category.
Vital rate in function of df Estimate
Explained
deviance [%]
AIC ∆AIC
a) Null model 159 418.34 0.00 848.74
b) Age class 156 281.46 32.72 717.86 *
Total population 158 -0.0060 394.64 5.67 827.05 1.20 *
Female population 158 -0.0077 393.45 5.95 825.85 0.00 *
Male population 158 -0.0035 414.13 1.01 846.53 20.68
Rain in January 158 -0.0015 402.78 3.72 835.19 0.00 *
Rain in February 158 -0.0006 415.57 0.66 847.98 12.79
Rain in March 158 -0.0006 416.19 0.51 848.59 13.40
Rain in April 158 -0.0007 416.94 0.33 849.35 14.16
Rain in Mar-Apr 158 -0.0006 415.07 0.78 847.47 12.28
Rain in Feb-Mar-Apr 158 -0.0005 412.89 1.30 845.30 10.11
Rain in Jan-Feb-Mar 158 -0.0006 407.45 2.60 839.86 4.67
Rain in Jan-Feb-Mar-Apr 158 -0.0006 406.53 2.82 838.93 3.74
Temperature in January 158 -0.0823 410.65 1.84 843.05 7.86
Temperature in February 158 -0.0737 412.81 1.32 845.22 10.03
Temperature in March 158 -0.0998 409.30 2.16 841.71 6.52
Temperature in April 158 -0.0434 416.53 0.43 848.93 13.74
Temperature in Mar-Apr 158 -0.1114 410.83 1.80 843.24 8.05
Temperature in Feb-Mar-Apr 158 -0.1297 409.26 2.17 841.67 6.48
Temperature in Jan-Feb-Mar 158 -0.1316 406.99 2.71 839.39 4.20
Temperature in Jan-Feb-Mar-Apr 158 -0.1488 407.12 2.68 839.53 4.34
Age class + Total population + Rain in Jan 154 250.13 40.21 690.53 3.77
Age class + Female population + Rain in Jan 154 246.36 41.11 686.76 0.00 **
f) Null model 79 217.77 0.00 524.25
g) Age class 78 214.74 1.39 523.22
Total population 78 -0.0044 205.15 5.80 513.63 18.28
Female population 78 -0.0079 186.87 14.19 495.35 0.00 *
Male population 78 0.0002 217.76 0.00 526.24 30.89
Rain in September 78 -0.0007 213.60 1.91 522.08 7.34
Rain in November 78 -0.0002 217.56 0.10 526.04 8.28
Rain in Sep-Oct 78 -0.0002 217.77 0.00 524.25 6.49
Temperature in September 78 -0.1484 209.28 3.90 517.76 0.00 *
Temperature in October 78 -0.0449 215.96 0.83 524.44 6.68
Temperature in November 78 -0.0142 217.54 0.11 526.02 8.26
Temperature in Sep-Oct 78 -0.1423 210.72 3.24 519.20 1.44 *
Temperature in Oct-Nov 78 -0.0450 216.62 0.53 525.10 7.34
Temperature in Sep-Oct-Nov 78 -0.1029 214.07 1.70 522.55 4.79
Female population + T° in Sep 77 186.86 14.19 497.34 1.99
Female population + T° in Sep-Oct 77 186.26 14.47 496.73 1.38 **
Female population 78 186.87 14.19 495.35 0.00
e)
d)
c)
h)
Fecundity rate
i)
j)
Survival rate
26
Table 3. Selection of parameters for the density dependent matrix of the male population.
Sections a) to e) show the survival rate in function of the null model, age structure,
population size, weather and the best parameters respectively. Sections f) to i) show the
fecundity rate in function of the null model, age structure, population size and weather
respectively. Stars represent the best parameter to include in the final model, and two stars
represent the best model for each vital rate. ΔAIC is the difference between the AIC of the
model and the lowest AIC in that category.
Vital rate in function of df Estimate
Explained
deviance [%]
AIC ∆AIC
a) Null model 157 410.21 0.00 872.31
b) Age class 154 379.44 7.50 847.54 *
Total population 156 -0.0006 409.94 0.07 874.04 21.48
Female population 156 -0.0067 388.46 5.30 852.56 0.00 *
Male population 156 0.0044 404.26 1.45 868.36 15.80
Rain in January 156 -0.0010 402.74 1.82 866.84 6.26
Rain in February 156 -0.0003 409.57 0.16 873.67 13.09
Rain in March 156 0.0005 408.92 0.31 873.02 12.44
Rain in April 156 0.0014 403.27 1.69 867.36 6.78
Rain in Mar-Apr 156 0.0008 403.91 1.54 868.01 7.43
Rain in Feb-Mar-Apr 156 0.0003 408.87 0.33 872.97 12.39
Rain in Jan-Feb-Mar 156 -0.0002 408.65 0.38 872.75 12.17
Rain in Jan-Feb-Mar-Apr 156 -0.0001 410.09 0.03 874.19 13.61
Temperature in January 156 -0.1023 396.49 3.34 860.58 0.00 *
Temperature in February 156 -0.0735 404.16 1.47 868.26 7.68
Temperature in March 156 -0.0714 406.09 1.00 870.18 9.60
Temperature in April 156 -0.0401 408.80 0.34 872.90 12.32
Temperature in Mar-Apr 156 -0.0894 406.10 1.00 870.20 9.62
Temperature in Feb-Mar-Apr 156 -0.1118 403.82 1.56 867.92 7.34
Temperature in Jan-Feb-Mar 156 -0.1318 398.17 2.94 862.27 1.69 *
Temperature in Jan-Feb-Mar-Apr 156 -0.1492 398.70 2.81 862.79 2.21
Age class + Female population + T° in Jan 152 359.29 12.41 831.39 0.00 **
Age class + Female population + T° in Jan-Feb-Mar 152 361.48 11.88 833.57 2.18
f) Null model 77 36.00 0.00 -43.39
g) Age class 76 23.25 35.43 -75.50 **
Total population 76 0.0005 35.68 0.88 -42.08 0.65
Female population 76 0.0008 35.39 1.70 -42.73 0.00
Male population 76 -0.0001 35.99 0.01 -41.40 1.33
Rain in September 76 0.0000 36.00 0.00 -41.39 0.80
Rain in November 76 -0.0001 35.75 0.69 -41.92 0.26
Rain in Sep-Oct 76 0.0000 35.99 0.02 -41.40 0.79
Temperature in September 76 0.0016 36.00 0.01 -41.39 0.80
Temperature in October 76 0.0084 35.85 0.41 -41.71 0.48
Temperature in November 76 0.0107 35.75 0.70 -41.93 0.25
Temperature in Sep-Oct 76 0.0141 35.85 0.40 -41.70 0.49
Temperature in Oct-Nov 76 0.0187 35.63 1.02 -42.19 0.00
Temperature in Sep-Oct-Nov 76 0.0240 35.66 0.95 -42.13 0.06
h)
c)
d)
e)
i)
Survival rate
Fecundity rate
27
Table 4. Parameters for the female and male density dependent models. Sections show the
parameters for the a) survival and b) fecundity of females, and the c) survival and d)
fecundity of males. Stars indicate p < 0.05.
Param eter Es tima te
Standard
Error
t value Pr(>|t|)
(Interc ept) 4.04004 0.38184 10.580 < 0.001 *
Yearling -0.37224 0.15666 -2.376 0.0187 *
Juvenile 0.41874 0.21960 1.907 0.0584
Senior -0.88662 0.10922 -8.118 < 0.001 *
Rain in January -0.00150 0.00051 -2.955 0.0036 *
Female population -0.00660 0.00198 -3.329 0.0011 *
(Interc ept) 0.11239 0.85486 0.131 0.8957
T° in Sep-Oct -0.04485 0.08335 -0.538 0.5921
Female population -0.00750 0.00218 -3.444 < 0.001 *
(Interc ept) 2.23963 0.39176 5.717 < 0.001 *
Yearling -0.42473 0.15603 -2.722 0.0072 *
Juvenile -0.22263 0.15167 -1.468 0.1442
Senior -0.50217 0.18724 -2.682 0.0081 *
T° in January -0.06336 0.04533 -1.398 0.1643
Female population -0.00456 0.00237 -1.928 0.0557
(Interc ept) 0.04194 0.01586 2.644 0.0099 *
Senior 0.20266 0.03138 6.457 < 0.001 *
a)
b)
c)
d)
Female population
Male population
28
Table 5. Simulations for the density dependent matrices. Section a) shows the simulated values for the female population, b) the differences between
the simulated values of the female population changing the effect of parameters in 1% and the female population with no changes on parameters, c) the
simulated values for the male population, and d) the differences between the simulated values of the male population changing the effect of parameters
in 1% and the male population with no changes on parameters.
Simulations K
nynjnansGyGjPaGaPsFaFs
a) Modelled population (no changes) 243.970 28.008 24.834 115.227 75.902 0.111 0.111 0.432 0.044 0.192 0.067 0.044
Intercept on survival 2.637 -0.078 -0.005 0.602 2.117 -0.001 -0.001 -0.002 0.000 0.004 -0.001 0.000
Fem population on fecundity 1.393 0.313 0.251 0.911 -0.083 0.000 0.000 0.001 0.000 -0.002 0.000 0.000
Fem population on survival 1.057 -0.030 -0.001 0.245 0.844 0.000 0.000 -0.001 0.000 0.002 0.000 0.000
Survival of seniors 0.210 -0.005 -0.008 -0.076 0.299 0.000 0.000 -0.001 0.000 0.001 0.000 0.000
Intercept on fecundity 0.085 0.019 0.015 0.056 -0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Survival of yearlings 0.037 -0.002 0.008 0.030 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Sep-Oct on fecundity 0.034 0.008 0.006 0.022 -0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Survival of juveniles 0.020 0.000 -0.001 0.019 0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Rain Jan on survival 0.001 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000
c) Modelled population (no changes) 221.499 61.382 41.578 101.259 17.279 0.171 0.171 0.408 0.027 0.052 0.144 0.027
Intercept survival 4.912 1.361 0.922 2.246 0.383 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Fem population on survival 2.237 0.620 0.420 1.023 0.175 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Survival of yearlings 0.235 0.053 0.078 0.115 -0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Jan on survival 0.139 0.039 0.026 0.064 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Survival of juveniles 0.107 0.031 0.015 0.064 -0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Survival of seniors 0.088 0.027 0.013 0.003 0.045 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Intercept fecundity 0.035 0.017 0.009 0.011 -0.003 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Fecundity of seniors 0.024 0.012 0.006 0.008 -0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Carrying capacity and age structure
Elasticities
b)
d)
Female population
Male population
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