3H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
 ACTA BIOLOGICA SLOVENICA 
 LJUBLJANA 2009             Vol. 52, [t. 1: 3–18
Sprejeto (accepted): 02. 02. 2009
The reintroduced Dinaric lynx population dynamics in PVA simulation,
The 30 years retrospection and the future viability
Modeli razvoja in analiza viabilnosti re-introducirane dinarske populacije risa,
30-letni pogled nazaj ter možnosti preživetja v prihodnosti
Hubert Potočnik*, Tomaž Skrbinšek & Ivan koS
Biotechnical Faculty, Department of Biology, Večna pot 111, SI-1001 Ljubljana
Corresponding author: H. Potočnik, E-mail: hubert.potocnik@bf.uni-lj.si
Abstract. In the study, we modelled population dynamics of the reintroduced Dinaric lynx 
population. We used data obtained by monitoring to estimate population dynamics – spatial 
expansion, abundance estimates, and mortalities – since the reintroduction in 1973 and up to 
the present day, and then looked for demographic and habitat parameters that would provide 
the best fit of a lynx population model to this data. We tried to evaluate the importance of these 
parameters for future population dynamics and viability (PVA) of this lynx population. We con-
structed a number of 100-year simulations using a range of demographic parameters, different 
prey availabilities and simulating other potential human related factors that might affect the 
lynx population. We found that the reintroduced lynx population must have had high fecundity 
rates with more than 1.6 kittens survived per female and per litter to reach abundances over 100 
individuals despite the high human related mortality. The elasticity analysis revealed that adult 
survival is by far the most important demographic parameter for the lynx population dynamics. 
PVA highlighted two important factors that had a major impact on population growth dynamics 
and related risk of population extinction: changes in the survival rates of subadult and adult in-
dividuals and, especially, the quality of habitat with regard to prey availability. Survival rates of 
subadult and adult lynx are directly influenced by human activities, mainly manifested through 
illegal shooting, and are difficult to control. Quite opposite to that, the quality of habitat with 
regard to prey availability can be directly influenced through management. Since habitat quality 
can have a significant role for the lynx population dynamic and viability, even in presence of 
minor, difficult to control changes in survival rates of subadults and adults, adequate prey species 
management might be one of the most important short-term conservation priorities.
Keywords. Eurasian lynx, Lynx lynx, population dynamics, PVA simulation, reintroduction, 
Dinaric region
Izvleček. V raziskavi smo zgradili modele populacijske dinamike ponovno naseljene po-
pulacije risa v Dinaridih. Pri oblikovanju modelov smo uporabili podatke, ki so bili pridobljeni 
pri spremljanju razvoja populacije od leta 1973 kot so: prostorsko širjenje, ocena številčnosti in 
smrtnost ter nato poiskali ustrezne demografske in prostorske parametre s katerimi smo dobili 
populacijski model, ki v največji meri ustreza zbranim podatkom. Poskušali smo oceniti pomen 
teh parametrov za razvoj in viabilnost populacije v prihodnje. Pripravili smo serijo simulacij 100 
letne populacijske dinamike risa pri čemer smo variirali demografske parametre, razpoložljivost 
plena ter odsimulirali druge antropogene dejavnike, ki bi lahko vplivali na populacijo risa. Ugo-
tovili smo, da je morala biti stopnja rodnosti ponovno naseljene populacije visoka z več kot 1.6 
4 Acta Biologica Slovenica, 52 (1), 2009
Introduction
The reintroduction of individual animals of a 
certain species to an area where the species has 
become extinct in the recent past has become 
one of the most important, albeit controversial, 
approaches to conservation of threatened species 
over the last few decades (breitenmoSer & al. 
2001, bekoff 2001). The current presence of the 
Eurasian lynx (Lynx lynx) in Slovenia is a direct 
result of a successful reintroduction. The reintro-
duction project was started in 1972, when expe-
riences with carnivore recovery programs were 
still very limited. Considering the contemporary 
requirements that such reintroduction projects 
should meet (IUCN/SSC, 1998), the reintroduc-
tion program had many deficiencies, especially 
from valuational and organisational point of view. 
However, the reintroduction was performed with 
consent and cooperation of hunters, the most 
important interest group that had the power to 
directly affect the success of the reintroduction. 
This was of great importance, since review 
analyses show that in successful reintroductions 
a human – carnivore conflict either did not exist, 
or had been reasonably solved (reading & Clark 
1996, Wolf & al. 1996, breitenmoSer & al. 
2001). Besides, the newly established population 
had favourable habitat and prey conditions (čoP 
1994), which can be considered of key importance 
for the reintroduction’s success. Since only three 
pairs of lynx were introduced, there can be no 
doubt that the population experienced the founder 
effect through the genetic drift (breitenmoSer-
WürSten & obexer-ruff 2003), a reduction of 
heterozygosity, a loss of alleles and a further de-
preživelih mladičev na samico. Le tako bi lahko populacija dosegla številčnost preko 100 osebkov 
ob hkratni visoki antropogeni smrtnosti risov. Analiza elastičnosti populacije je pokazala, da je 
preživetje odraslih osebkov daleč najpomembnejši demografski parameter, ki v največji meri 
vpliva na populacijsko dinamiko. Z analizo populacijske viabilnosti (PVA) smo ugotovili dva 
pomembna dejavnika, ki imata največji vpliv na dinamiko populacijske rasti in z njo povezana 
tveganja za izumrtje populacije. To sta preživetje doraščajočih in odraslih osebkov ter kvaliteta 
risovega habitata z vidika razpoložljivosti (gostote) plena. Na spreminjanje stopnje preživetja ima 
največji vpliv človek s svojim neposrednim vplivom (zakoniti in nezakoniti lov, promet), ki ga 
je težko regulirati. Ravno nasprotno pa lahko upravljalci z ustreznim upravljanjem s plenskimi 
vrstami v veliki meri vplivajo na  kvaliteto risovega prostora z vidika dostopnosti hrane. Zato je 
lahko zadnje  eden izmed najpomembnejših kratkoročnih varstvenih ukrepov pri upravljanju s 
populacijo risa v Sloveniji v prihodnje.
Ključne besede. Evrazijski ris, Lynx lynx, populacijska dinamika, PVA simulacija, reintro-
dukcija, dinarska regija
pletion of its gene pool through inbreeding. These 
negative predispositions aside, the monitoring of 
the population shows that the population has un-
dergone a rapid expansion into Croatia and Bosnia 
and Herzegovina, and also expansion towards 
the north into Austria and towards the northwest 
into Italy. The long term monitoring effort has 
been initiated soon after the reintroduction, and 
several comprehensive papers and internal reports 
have been published (eg. čoP 1994, 1997, čoP 
& frković 1998, frković 2003, Staniša & al. 
2001, Jonozovič 2004). However, the monitoring 
has been mainly oriented in collection of spatial 
distribution of lynx signs of presence and on 
recording of killed (culled) lynxes. According to 
these, the expansion into the unoccupied areas 
came to a halt in the early nineties. 
Although the monitoring effort is very 
important, other population studies should also 
be considered. Telemetry (Huber & al. 1995), 
population modelling and population viability 
analysis (PVA) may prove to be of great value 
for management of the Dinaric lynx population, 
since we still cannot be confident in its long-term 
survival. 
In general, population viability analysis is a 
useful tool for identification of variables impor-
tant for population growth and the resulting vi-
ability of reintroduced or other small populations. 
We performed the analysis in two parts. In the 
first part, we used the monitoring data to estimate 
population dynamics of the Dinaric lynx popula-
tion (spatial expansion, abundance estimates, and 
mortalities) since the reintroduction up to the 
present day, and then looked for demographic and 
habitat parameters that would provide the best 
5H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
cles in the Norwegian lynx population has shown 
that 50% of males reach sexual maturity at the age 
of 21 months (kvam 1990). However it is unlikely 
that young males would participate in mating, 
since they are being chased away from females 
by older males. This probably means that they 
can mate only a year later, when they are almost 
3 years old (kvam 1991). The females in captivity 
reach sexual maturity at 21 months (lindeman 
1955, HenrikSen & al. 2005). A similar result was 
obtained in Norway through analysis of ovulation 
or presence of corpora lutea, where most females 
also reached sexual maturity by the age of ap-
proximately 21 months. However, roughly half of 
the females were sexually mature already at the 
age of 7.5–11.5 months (kvam 1990).
Reproductive success of a lynx population 
depends primarily on the feeding conditions 
in the environment, usually the density of roe 
deer, Capreolus capreolus, (JedrzeJeWSki & al. 
1996, okarma & al. 1997). When they become 
sexually mature, Eurasian lynx females usually 
mate until the high age of 12–13 years (SteHlik 
1984, StaHl & vandel 1998, HenrikSen & al. 
2005). In a radio-telemetric study in Scandinavia 
they found that 55% of two-year old females and 
72% of older females were with kittens (andren 
& al. 1998, 2002). In the model, we defined this 
proportion of females as reproductively active. 
Subadult (1 year old) females were defined as 
non-reproductive. 
Many European studies of lynx reproduction 
found that the number of kittens per female at the 
end of their first year of life was between 1.6 and 
1.2 (kvam 1991, Pulliainen 1995, JedrzeJeWSki 
& al. 1996, andren & al. 1998, 2002, okarma 
& al. 1997, JedrzeJeWSka & JedrzeJeWSki 1998, 
anderSen & al. 2003, HenrikSen & al. 2005). 
Deviating from this are data from Switzerland, 
where they found only 0.69 kittens per female in 
the studied animals (breitenmoSer & al. 1993). 
Reasons for this may be in different methodolo-
gies used to assess recruitment, or due to lower 
survival of kittens. We chose to use fecundities 
F = 1.2 and F =1.6 for the model, referred to as 
the high and the low reproduction. In RAMAS 
Metapop®, fecundity is defined as the number of 
offspring that survive to the end of their first year 
of life per female. 
fit of a lynx population model to this data. We 
applied different scenarios in modelling of popu-
lation dynamics of the re-introduced lynx from 
1973 to 2003, using different demographic and/or 
environmental parameters. In the second part of 
the analysis we tried to evaluate the importance of 
the same parameters for future population dynam-
ics and viability (PVA) of such a lynx population. 
We constructed a number of 100-year simula-
tions using a range of demographic para meters, 
different prey availabilities and simulating other 
potential human related factors that might affect 
the lynx population.
Methods
PVA software and model parameters
The data on demographic attributes for 
the Dinaric lynx population are scarce, if not 
non-existent. To be able to model the develop-
ment of the Dinaric lynx population, we estimated 
its population parameters from knowledge of 
lynx biology from other parts of the species’ 
range.The simulations were performed using the 
RAMAS Metapop® software package (Applied 
Biomathematics, USA). All analyses and models 
were produced for the Dinaric lynx population 
as a whole and in its entire geographic range 
(Slovenia, Croatia and Bosnia and Herzegovina), 
since doing population dynamics and viability for 
individual parts of the population doesn’t make 
much sense. Each scenario used for modelling 
of the population dynamics was run with 1000 
iterations. The birth sex ratio used for the model-
ling was 1:1, since the sex structure in stable lynx 
populations shows a balanced ratio between males 
and females (kvam 1991). We designed a post-
reproductive Leslie matrix for both, males and 
females in seven separate stages, three for females 
and four for males. For both, we applied three age 
categories: yearlings, subadults and adults. Male 
subadults were placed in two stages. Although 
they can become sexually mature at the end of 
their second year of life, it is unlikely for them to 
breed until the end of their third year. The age at 
first reproduction is the demographic parameter 
that significantly affects the population dynamics 
(akCakaya 2002). Histological analysis of testi-
6 Acta Biologica Slovenica, 52 (1), 2009
Pre-dispersal and dispersal mortalities have 
been researched for many felid species, and they 
seem to vary between species (breitenmoSer & 
al. 1993). Survival rates of dispersing or subadult 
lynx in Europe range from 36 % to 62 % (SteHlik 
1984, breitenmoSer & al. 1993, andren & al. 
1998, HenrikSen & al. 2005). Although there are 
some data on survival rates of resident lynx in Eu-
rope (JedrzeJeWSki & al. 1996, kramer-SCHadt 
& al. 2005, andren & al. 1998, 2006), the rather 
low statistical power of the data is common for 
all the studies. For the model, we used survival 
rates of subadult and adult lynx obtained from 
the survival data of 245 animals radio-tracked 
in the Scandinavian Lynx Project (andren & al. 
1998, 2006). The survival rates used were 62% 
for subadult males and females (one to two years 
old), 81% for two to three years old females and 
83% for the males of the same age. 
We are fully aware that these values might be 
biased due to small sample size and the limited 
time of the study. Additionally, these data are from 
the boreal region found in the northern part of 
the lynx areal in Europe, and we are using them 
to model population dynamics in a mountainous 
region of mixed forests in the southern part of 
the species’ areal. However, all the values used 
in the model are rather high, since they should 
represent only background survival rates without 
the influence of human-related mortality which 
was modelled separately. We must consider that 
population models and PVA require information 
on many variables that are difficult to estimate 
for low-density populations (beiSSinger & 
WeStPHal 1998). 
Even the simplest deterministic models need 
information regarding age structure, breeding 
schedule, and vital rates (mCkelvey & al. 2000). 
These models assume that demographic rates 
are constant, which is certainly not true for lynx. 
Small populations are more sensitive to stochastic 
events, which usually make them more vulner-
able to various detrimental factors and can sig-
nificantly decrease their viability. Demographic 
and environmental stochasticity were included 
in our model to simulate variation in population 
size under natural conditions. Accordingly, we 
modelled lynx population dynamics stochasti-
cally by generating random annual lynx vital rates 
from the normal distribution curve according to 
the values defined above, using the coefficient of 
variability (CV) of 0.2 for fecundities and 0.1 for 
survival rates, which covers a substantial part of 
the variation in lynx vital rates known from the 
literature considered above.
Modelling historical 30-year population 
dynamics
In January 1973, three adult male and three 
adult female lynx were transferred to a quarantine 
enclosure in Slovenia from a quarantine enclosure 
in the Stromovka Zoo near Ostrava (in today’s 
Slovak Republic). After 46 days they spent there 
separated in pairs, the lynx were released into 
the wild. According to direct observations and 
observations of signs of presence (čoP 1994), 
none of the animals exhibited homing behaviour. 
Snow tracking of presumably all six animals was 
reported in November 1973. Thus, as the initial 
population size, three adult females and three 
adult males were modelled in our model.
In the years that followed the population 
grew and expanded. The initial development of 
the population showed a low mortality of indi-
viduals (koS & krofel 2004). We can assume 
this to be of key importance for survival of the 
newly established population through the initial 
phase (koS & krofel 2004). The population 
continued to grow despite legal culling of lynx 
being introduced in 1978, and also expanded in 
the northwestern direction towards Italy and the 
Alps (čoP 1994). It seems that the rapid spatial 
expansion of the population that took place until 
the middle of the eighties of the previous century 
slowed down by the end of the decade, and came 
to a halt in the beginning of the 90s (čoP 1997, 
čoP & frković 1998, frković 2003). To be able 
to model the development of the population, we 
had to determine the population ceiling (K). The 
ceiling in RAMAS Metapop® is the population 
size above which all individuals are killed or have 
died, and it does not act like usually an environ-
mental carrying capacity would act. We defined 
the ceiling as the population size at its highest 
point in the last 30 years, which was most likely 
reached at the end of the spatial expansion (17 to 
18 years after reintroduction). 
7H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
Effects of recorded human-related mortality
Two scenarios were applied for simulation of 
the thirty year population growth of the Dinaric 
lynx population using the ceiling growth model: 
(1) a population with high reproduction (F = 1.6) 
and (2) a population with low reproduction (F 
= 1.2). Deterministic growth rate (lambda) and 
elasticity analysis were performed for each of the 
fecundity values. Additionally, human-related 
mortality was included as a relative decrease of 
annual vital rates, determined as a percentage of 
killed lynx with regard to the mean population 
sizes in particular years with no additional mor-
tality modelled. Thirty percent of the decreases 
were modelled as decreases of fecundities, and 
70% as decreases of survival rates. This cor-
responds to the ratio between kittens and older 
animals killed in this population between 1973 
and 2003 (frković 2003). During this period, 
there are 375 lynx recorded as harvested, poached, 
and killed in traffic accidents or found dead in 
Slovenia, Croatia, and Bosnia and Herzegovina 
(Potočnik 2004). 
Effects of prey density
Following conclusion of the spatial expan-
sion, and re-adaptation of the prey to the new 
predator, is the second phase of population 
dynamics, with a decrease in population density 
and the end of population growth (breitenmoSer 
& Haller 1987, 1993). In this phase, if there are 
no other direct factors like hunting and poaching, 
the density of prey becomes the most important 
factor, affecting mainly the survival rate of the 
young, and trough it directly the reproductive suc-
cess of the lynx population (brand & keitH 1979, 
kvam 1991, JedrzeJeWSki & al. 1996, okarma 
& al. 1997, fuller & Sievert 2001, Steury & 
murray 2004). Although there are a number of 
carnivore species, especially those with cyclical 
populations, like for example the Canadian lynx 
(Lynx canadensis) for which we have a good 
understanding of the effects the food/prey has 
on demography (e.g. mCCord & Cardoza 1982, 
breitenmoSer & al. 1993, SlougH & moWat 
1996, o’donogHue & al. 1997, moWat & al. 
2000), such knowledge is surprisingly poor for 
the Eurasian lynx. Data exist from Poland, where 
a deliberate reduction of roe deer (35 – 40%) 
and red deer, Cervus elaphus, (30%) densities in 
Bialowieza forest by game managers resulted in 
a 50% reduction of the reproductive success of 
the lynx (okarma & al. 1997, JedrzeJeWSka & 
JedrzeJeWSki 1998). 
Effects of illegal hunting
The lynx has never been protected in Bosnia 
and Herzegovina. In the Serbian Republic of 
Bosnia and Herzegovina it used to be listed as a 
protected species between 1994 and 2001, but the 
effectiveness of the legal protection in the post-
war political situation is questionable. According 
to reports, lynx are hunted whenever seen (Soldo 
2001). Until 2001, 25 lynx have been killed, with 
the first lynx killed in 1983 (Soldo 2001). This 
represents 7% of all killed lynx reported for the 
entire Dinaric population. We can assume that 
Bosnia and Herzegovina represents a sink area 
with a low population density. In 1993, Slovenia 
passed a Decree on the Protection of Endangered 
Animal and Plant Species, and the lynx received 
the status of a species under strict protection. In 
1998 it received a complete legal protection in 
Croatia as well. A year before that a new Hunting 
Act was passed in Croatia, introducing a leas-
ing system for hunting grounds and effectively 
making hunting primarily an economic activity. 
Because of the complete legal protection the 
lynx lost its trophy value for hunters, which 
was possibly an important mechanism of the 
so-called active protection. All this made preda-
tors, especially the large carnivores, indirectly 
characterized as economic pests. A sentiment 
that there is no influence or control over the 
population size of a predator, and consequently 
no control over the effects it has on the prey 
species, certainly bears negative consequences 
for conservation of the predator. This is most 
often manifested through an increase of illegal 
hunting of the predator (breitenmoSer & al. 
2001, červeny 2002). Illegal shooting of lynx 
is a considerable mortality factor and a threat to 
a small population (breitenmoSer & al., 1998). 
The data on illegal hunting or poaching of lynx in 
Switzerland and Poland confirm this, as poaching 
in Poland contributed to 75% of all known lynx 
mortality and posed the most important mortality 
8 Acta Biologica Slovenica, 52 (1), 2009
factor in Switzerland (breitenmoSer & al. 1993, 
SCHmidt-PoStHauS & al. 2002, JedrzeJeWSki & 
al. 1996, okarma & al. 1997). 
Prey density and additional mortality as im-
portant factors for future viability
As a theoretical starting point for the Dinaric 
lynx PVA, we can use the estimate that the current 
lynx population numbers 100 individuals that live 
in an area of 20,000 km2 (frković 2003, firšt & 
al., 2003, koS & al., 2004). The initial population 
size used in the model was 100 individuals, with 
a stage structure equal to the calculated stable 
stage structure rounded to the closest integer. 
The population was limited just above the initial 
population size with a ceiling at K = 110 (SD ± 
20). Allee effects in RAMAS Met&apop® were 
determined by the function N/(N+A), representing 
a relative decrease in fecundity with regard to the 
population size. A value of A = 2 was chosen, 
which decreased the vital rates for more than 5% 
when the population fell below the density of 1 
individual per 500 km2, which was double the 
size of an adult male home range radio-tracked 
in the region (Huber & al. 1995). 
Results
Modelling historical 30-year population dyna-
mics
We ran simulations of an exponential popu-
lation growth for 17 and 18 model years. We 
included effects of recorded human-caused mor-
tality (čoP 1997, čoP & frković 1998, frković 
2003, Potočnik 2004), modelled as a removal of 
the specific number of individuals per each year. 
The simulated population reached mean sizes 
between 90 and 130 individuals. Therefore, we 
determined the population ceiling at K = 110 with 
a standard error (SE +/– 20) to simulate variation 
due to environmental stochasticity. These results 
are supported by estimations from the population 
monitoring reports of Slovenian Forest Service 
and frković (2003). Judging by the results of 
simulations of potential inbreeding coefficients 
expected in the Dinaric lynx population 30 years 
after the reintroduction (Potočnik 2005), the 
inbreeding depression is not expected to have 
an important role in population dynamics during 
that period. However, for the simulations the 
founder animals were assumed unrelated and with 
a random choice of reproductive mates which is 
unlikely. So far there has been no evidence of 
the inbreeding depression (beside population 
decline), so we didn’t include it in the models. 
However, since there is definitely inbreeding in 
the population, and there is recent genetic data to 
confirm it (MaJić & al. unpubl.), this factor should 
be included in future modelling exercises as it can 
soon become of major importance for viability of 
the Dinaric lynx population. 
Effects of recorded human-related mortality
Values obtained for lambda at high and low 
reproduction were 1.2 and 1.15, respectively. The 
elasticity analysis showed survival of adult indi-
viduals to be the most important parameter, with 
proportional contributions to population growth 
rates of 0.46 and 0.49 (Table 1).
Simulations showed that the modelled 
population with high reproduction would grow 
relatively fast until the year 1991. Afterwards, 
the population growth slows down, reaching 
high reproduction F = 1.6 low reproduction F = 1.2
fecundity (kitten recruitment) 0.19 0.18
survival of 1 - 2 year old individuals 0.17 0.16
survival of 2 - 3 year old individuals 0.18 0.17
survival of adults 0.46 0.49
Elasticity
Demographic parameter
Table 1: Elasticity, the relative contribution of demographic parameters to the population growth.
Tabela 1: Elastičnost demografskih parametrov modela populacijske dinamike risa pri visokem oziroma nizkem 
reprodukcijskem uspehu. 
9H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
the ceiling in 2003 (Figure 1). As a contrast, 
the population with low reproduction would 
grow slowly until 1991, and would not reach 
the ceiling within 30 years despite faster growth 
in the years that follow. Thus, the population 
dynamics of the population with high reproduc-
tion was closer to the dynamics observed in the 
monitoring reports, and although the model did 
not include some mechanisms that are important 
for reintroduced populations, it was retained for 
further analysis.
These mechanisms were studied during 
expansion of a reintroduced lynx population in 
Switzerland (breitenmoSer & Haller 1987, 
Haller 1992, breitenmoSer & al. 1993). The 
mechanisms affecting population dynamics of a 
reintroduced lynx population can be divided into 
two phases. The dispersion of young animals is 
an important factor in the first phase of popula-
tion growth, enabling a high survival rate and 
rapid spatial expansion of the population. It is a 
simple mathematical phenomenon, additionally 
amplified by naive prey that is not adapted to the 
new predator (breitenmoSer & Haller 1987, 
Haller 1992). We can assume that the first phase, 
the rapid expansion of the Dinaric lynx popula-
tion, took place until the end of the eighties or the 
beginning of the nineties of the previous century, 
when it slowed down or stopped.
Effects of prey density
To simulate the effects of prey density and 
availability on reproductive success of the Di-
naric lynx population, we included the data on 
roe deer harvest in the model as a prey density 
parameter for the years after 1993, when the lynx 
expansion presumably stopped. We can assume 
that the harvest of roe deer population decreased 
with a decrease in roe deer population. The rea-
sons for the decrease are various, including the 
effects of the presumable increase of the wolf 
population as well as the significant change in 
sex structure of the harvest with a much larger 
proportion of females being harvested. According 
to the Slovenian Forest Service and the Slovenian 
Hunters Association’s harvest data, there was 
40% decrease in the roe deer population size 
0
20
40
60
80
100
120
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00. 01. 02. 03.
(Simulation) years
M
ea
n 
ly
nx
 p
op
ul
at
io
n 
si
ze
/L
yn
x 
ki
lle
d 
( n
)
lynx killed
high fecundity
low fecundity
Fig. 1: Stochastic population growth models over a 30–year period with an initial population of three adult females 
and three adult males, taking into account the recorded lynx mortality.
Slika 1: Stohastični modeli populacijske dinamike risa v 30–letnem obdobju z začetno populacijo treh odraslih 
samcev in treh samic, upoštevajoč vpliv znanih izgub na celotnem območju.
10 Acta Biologica Slovenica, 52 (1), 2009
between 1993 and 2003. Following the results 
from Bialowieza, we modelled the effects of 
prey density as a reduction in fecundity relative 
to the decrease in the harvest in a particular year 
with regard to the harvest in 1993. The maximum 
reduction of fecundity was down to 60% of the 
initial fecundity when the reduction of roe deer 
population was 40%. Simulations of population 
dynamics that included the effects of prey density 
showed that the population would stop growing 
after 1993 at a mean population size of approxi-
mately 100 individuals (Figure 2).
Effects of illegal hunting
In contrast to the prey density, the illegal hunt-
ing is very difficult to measure or estimate. How-
ever, we assume that the strict protection of the 
lynx and the new hunting legislation in Slovenia 
and Croatia have caused a progressive increase 
in illegal hunting of this species. The effect was 
modelled, in addition to the prey density effect, 
as a 10–year linear decrease of survival rates from 
1 to 10% and from 1 to 15% (Figure 2). In both 
simulations the populations started declining in 
a year when progressive effect of illegal hunting 
reached a 5% decrease in survival rates of all age 
and sex categories (Figure 2). Obtained mean 
population sizes at the end of simulations were 81 
and 91 lynx, respectively. On basis of the avail-
able lynx monitoring data the Slovenian Forest 
Service estimated the number of lynx in Slovenia 
in 2003 to be approximately 45 individuals. The 
estimate for Croatia is 50 individuals (frković 
2003, firšt & al. 2003). The data available on 
the recent population status of lynx in Bosnia and 
Herzegovina are scarce. Since the number of re-
corded dead lynx is low (% of all recorded losses 
in the Dinaric population) despite extremely re-
laxed hunting regulations, we believe the estimate 
of 40 individuals, from the country report (cf. von 
arx & al. 2004) to be quite exaggerated. With all 
that in mind and, despite the constructed model is 
being a simplified description of relations in the 
real population, we assume that it can be used as 
0
20
40
60
80
100
120
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00. 01. 02. 03.
Simulation years 
M
ea
n 
ly
nx
 p
op
ul
at
io
n 
si
ze
 ( n
)
roe deer density
roe deer + 10% S decline 
roe deer + 15% S decline
Fig. 2: Stochastic lynx population growth models over a 30–year period with high reproduction, taking into ac-
count changes in roe deer abundance (roe deer density) and a gradual decrease in survival rates (S decline) 
caused by increased human related mortality in the last 10 years.
Slika 2: Stohastični modeli populacijske dinamike risa v 30–letnem obdobju ob visoki reprodukciji, upoštevajoč 
spreminjanje številčnosti srnjadi (roe deer density) in postopno zmanjševanje preživetvene stopnje (S 
decline) risov zaradi povečane antropogene smrtnosti v zadnjih 10. letih.
11H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
a helpful basis for population viability analysis 
for the Dinaric lynx population.
Prey density and additional mortality as im-
portant factors for future viability 
In simulations of population dynamics and 
viability analysis for the next 100 years, we ex-
posed the population to different situations in the 
environment: (1) an environment with high prey 
density, simulated as high fecundity (F = 1.6), 
(2) an environment with medium prey density, 
simulated as medium fecundity (F = 1.2, –25%), 
and (3) an environment where prey density is 
low, simulated as low fecundity (F = 1.0, –40%). 
In all three cases we studied the effects of the 
decrease in lynx survival rates resulting from 
additional mortality (Figure 3) on the associated 
risks of population extinction over a 100-year 
period (Figure 3). To determine the acceptable, 
non-detrimental level of additional mortality, in 
the model considered as the effect of culling (il-
legal shooting), the population was considered 
viable if the risk of its extinction over a 100 years 
period was below 5% (SHaffer 1981). 
In different prey density scenarios, the 
simulations showed substantial differences in the 
decline of survival rates. There was no extinction 
risk in any of the scenarios when no additional 
mortality was included in the model. That means 
that in the absence of additional mortality a 
decline in fecundities as severe as 40% would 
not pose a threat to the Dinaric lynx population. 
On the other hand, the prey density had a drastic 
influence on the extinction risk dynamics in pres-
ence of progressive decreases of survival rates. 
In the high prey density scenario, the limit of 
the population viability was reached at a 10.5% 
decrease in survival rates. On the contrary in 
the medium and the low prey density conditions 
the risk of extinction reached the threshold of 
viability at 6% and 3%, respectively (Figure 3). 
Results of the model indicate that the population 
is much more sensitive to even minimal changes 
in survival rates of adults and subadults (as a 
result of additional human related mortality) 
under the low prey density conditions than when 
the prey density is high.
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Survival rate decrease (%)
E
xt
in
ct
io
n 
ri
sk
 (%
) 
low prey density (F=1.0)
medium prey density (F=1.2)
high prey density (F=1.6)
extinction line
viability limit
Fig. 3: Extinction risk dynamics influenced by decreasing survival rates caused by human related mortality in 
subadult and adult lynx at different fecundities, simulating different prey densities.
Slika 3: Dinamika tveganja za izumrtje populacije ob zmanjševanju stopnje preživetja doraščajočih in odraslih 
risov, kot posledice povečane antropogene smrtnosti ob različni reproduktivni uspešnosti s katero smo 
simulirali različno gostoto plena v okolju.
12 Acta Biologica Slovenica, 52 (1), 2009
Discussion
Carnivores, especially lynx, are elusive 
animals, and to monitor the progress and the suc-
cess of a reintroduction programme is a difficult, 
expensive and long lasting task (breitenmoSer 
& al. 2001). There is a clear need to improve the 
efficiency of reintroductions. By simulating popu-
lation dynamics and viability of the Dinaric lynx 
population we tried to contribute to understanding 
of the reintroduction mechanisms. The thirty year 
retrospective models simulating the Dinaric lynx 
population growth indicate that the reintroduced 
population must have had high fecundity rates (F 
> 1.6) to reach abundances over 100 individuals 
despite the high human related mortality. The 
high human related mortality, especially in Bosnia 
and Herzegovina, might be one of the reasons for 
the slow down of lynx expansion (von arx & al. 
2004) or probably low dispersion to the southern 
Dinaric Mountains. An expansion toward north 
and northwest into the Alps in Slovenia has been 
probably slowed down due to significant spatial 
obstacles (traffic infrastructure, urban areas, open 
habitat) separating the Alps from the Dinaric re-
gion (Skrbinšek 2004). In Slovenia, no reproduc-
tion has been recorded in the Alps (Staniša &al. 
2001). We can assume these obstacles to have an 
important effect on local oscillations in popula-
tion size and may obstruct the population flow. 
This would have a d&rimental effect on viability 
of the entire population and increase the risk of 
local extinctions. The effect of the matrix obstacle 
increases when a dispersion pressure from the 
core area of the population is decreased.
Approximately 20 years after the reintro-
duction, when the intensive expansion of the 
population into new, unoccupied habitats came to 
an end, the population probably culminated and 
habitat quality parameters, like the prey density, 
became important density dependant factors. 
Changes in reproductive output are certainly a 
major potential response, and the relationship of 
nutrition and both reproduction and recruitment 
is well documented in mammals (Sadleir 1969). 
Since recruitment to a population is a function of 
the proportion of productive females, litter size, 
and offspring survival, these demographic pa-
rameters should be higher when prey is relatively 
abundant (fuller & Sievert 2001). Changes 
in food abundance can drastically affect the 
survival of new-borns. Post-partum mortality of 
Canadian lynx kittens during a snowshoe hare, 
Lepus americanus, population decline was the 
main factor responsible for a lack of recruitment 
to the lynx population in Alberta (brand & keitH 
1979). A slower increase of home-range sizes 
with a decrease in prey density in female than in 
male lynx (Herfindal & al. 2005) might be, as an 
alternative to the Sandell’S (1989) prediction of 
a change in the mating tactics of males, explained 
by a decreased reproductive output of females, 
resulting in lower food requirements during the 
low prey density. However, even considerable 
decline in prey density in the third decade after 
the lynx reintroduction in Slovenia, simulated as 
a up to 40% decrease in fecundity, i.e. production 
of only one kitten that survives until end of its 
first year per female, did not lead to a population 
decrease.
The elasticity analysis revealed that adult 
survival is by far the most important demographic 
parameter for the lynx population dynamics. 
This is not surprising, considering the fact that 
lynx have a relatively long reproductive period 
(SteHlik 1984). Therefore, even minor decreases 
in survival rates could cause a decrease in 
population. Throughout history, carnivores have 
been perceived as man’s competitors for prey 
and consequently directly persecuted (Sillero-
zubiri & laurenSon 2001). We presume that 
the controlled harvest of lynx as a trophy animal 
produced relatively positive attitudes of hunters 
toward the lynx in Slovenia and Croatia, which 
probably changed after its strict protection was 
put in place, and especially after the new hunting 
legislation has been adopted in Croatia. 
Conclusions
Our 30–year simulations revealed that the 
reintroduced lynx population started declining 
when its survival rates were gradually decreased 
for 5%, simulating increased human related mor-
tality in that period. breitenmoSer & al. (1999) 
believe that in Switzerland the expansion of lynx 
after reintroduction has ceased due to illegal 
killings. Even insignificant decreases in game 
densities or minor losses of livestock caused by 
lynx can make illegal killing the most important 
13H. Potočnik, T. Skrbinšek & I. Kos: The reintroduced Dinaric lynx population dynamics …
mortality factor, as has probably happened in the 
case of the lynx in the Swiss Alps (breitenmoSer 
& al., 1998). 
The hypothetical models of lynx population 
dynamics over a 100–year period highlighted 
two important factors that had a major impact 
on population growth dynamics and the related 
risk of population extinction: (1) changes in the 
survival rates of subadult and adult individuals 
in the population that are directly influenced by 
human activities and are difficult to control, and 
(2) the quality of habitat with regard to prey avail-
ability (density), which is relatively controllable 
parameter trough management of prey species in 
the lynx areal. The changes in the survival rate 
are by and large governed by the direct influence 
of man (legal hunting, illegal hunting, traffic 
mortality). Of these factors, legal hunting is the 
only one over that we can exert direct control or 
management. The other two factors, especially 
illegal hunting, can be affected only indirectly 
through long-term education and actions that 
decrease predator-caused conflicts.
Effects of habitat quality can have a major 
impact even when there is a minimal change in 
the survival rate of subadults and adults in the 
population. The most important factor affecting 
prey availability is the regulation of population 
size of prey species by man. Natural competi-
tors for food, especially wolves (JedrzeJeWSki 
& al. 1993), also affect prey availability. Quite 
opposite to the adult survival parameter, the 
quality of habitat with regard to prey availability 
can be directly influenced through management. 
Since habitat quality can have a significant role 
for the lynx population dynamics and viability, 
in presence of even minor changes in survival 
rate of subadults and adults in a population, we 
must consider an adequate prey species manage-
ment to be one of the most important short-term 
conservation priorities. Many values used for the 
PVA model are quite arbitrary, since there are no 
or few hard data for Dinaric lynx population and 
such an approach is the only choice. Therefore, 
the results should be used with caution, as some 
future simulations with new/better data may show 
different results.
Povzetek
Reintrodukcija oziroma ponovna naselitev 
osebkov določene vrste na območje, kjer je bila 
njena populacija v preteklosti iztrebljena (IUCN, 
1995), je postala v zadnjih desetletjih ena izmed 
pomembnejših oblik upravljanja z ogroženimi 
živalskimi vrstami (reading & Clark 1996, 
Wolf & al. 1996). Ponovno naselitev risa v 
Sloveniji leta 1973 lahko torej uvrščamo med 
pionirske naravovarstvene ukrepe, ki jih danes 
ciljno proučuje tudi varstvena biologija. Namen 
tega poglavja je predstaviti pomen posameznih 
demografskih parametrov ter njihov vpliv na 
populacijsko dinamiko in viabilnost dinarske 
populacije risa. Kljub relativno majhnemu številu 
populacijskih parametrov potrebnih za izdelavo 
osnovnih modelov populacijske dinamike je za 
dinarsko populacijo risa znanih le malo para-
metrov. Zato smo bili pri oblikovanju modelov 
prisiljeni uporabiti objavljene podatke o biologiji 
risa iz drugih evropskih populacij.
Za matematično modeliranje populacijske 
dinamike risa smo uporabili programski orodji 
RAMAS Metapop® (Applied Biomathemat-
ics, ZDA). Program omogoča oblikovanje in 
simulacijo (meta)populacijskih modelov s pros-
torsko strukturiranostjo. Vse analize in modeli 
so bili izdelani za dinarsko populacijo risa kot 
celoto na celotnem območju prisotnosti, saj 
populacijske dinamike in analize preživetvenih 
sposobnosti populacije ni mogoče obravnavati 
le za posamezen del populacije. Mehanizme, ki 
vplivajo na populacijsko dinamiko pri reintro-
duciranih populacijah risa delimo v dve fazi. V 
prvi fazi populacijske rasti je disperzija mladih 
osebkov pomemben dejavnik, ki omogoča visoko 
preživetje ter hitro prostorsko širjenje populacije. 
Gre za preprost matematični fenomen, ki ga 
dodatno ojači še naiven plen, ki nima izkušenj 
z novim plenilcem. Prva faza, hitro širjenje di-
narske populacije risa, je najverjetneje potekalo 
do konca 80. oziroma začetka 90. let, ko se je 
upočasnilo oziroma ustavilo.
Po prenehanju prostorskega širjenja ter pri-
lagoditvi plena na novega plenilca sledi druga 
faza populacijske dinamike, v kateri pride do 
zmanjšanje populacijske gostote oziroma us-
tavitve rasti populacije. V tej fazi je gostota plena, 
če niso prisotni drugi neposredni dejavniki, kot 
14 Acta Biologica Slovenica, 52 (1), 2009
so lov in krivolov, najpomembnejši dejavnik, ki 
vpliva predvsem na preživetje mladičev.
Deterministična stopnja rasti populacije je 
bila pri optimalni rasti lambda = 1,2, pri sub-
optimalni pa 1,15. To pomeni, da se v prvem 
primeru populacija vsako leto teoretično poveča 
za 20%, v drugem pa za 15%. Analizirali smo 
elastičnost posameznih demografskih parametrov 
(Tabela 1). Ugotovili smo, podobno kot andren 
& al. (1998), da je največji vpliv na populacijsko 
dinamiko imelo preživetje odraslih osebkov, saj 
je spreminjanje parametra preživetja odraslih 
osebkov prispevalo kar 46–49% k spreminjanju 
populacijske dinamike populacije ter kvaliteta 
prostora z vidika dostopnosti (gostote) plena, ki 
neposredno vpliva na produkcijo mladičev (Tabe-
la 1, Slika 2). Na spreminjanje stopnje preživetja 
ima največji vpliv človek s svojim neposrednim 
vplivom (zakoniti lov, promet, nezakoniti lov). 
Pri tem je le zakoniti lov dejavnik, ki ga lahko 
neposredno kontroliramo oziroma uravnavamo. 
Na ostala dva dejavnika, predvsem na nezakoniti 
lov, lahko vplivamo le posredno z dolgoročnim 
izobraževanjem in ukrepi, ki zmanjšujejo kon-
fliktnost plenilca. Učinki kvalitete prostora so 
lahko izrednega pomena že pri minimalnem 
spreminjanju stopnje preživetja doraščajočih in 
odraslih živali v populaciji. 
S simulacijami populacijske dinamike smo 
predstavili teoretična izhodišča razvoja dinarske 
populacije risa in njihove potencialne posledice 
v prihodnjih 100 letih. Za izhodišče modela smo 
uporabili začetno velikost populacije 100 osebkov 
s starostno in spolno strukturo, ki je bila blizu 
izračunani stabilni populacijski strukturi. Pri 
tem smo uporabili enake populacijske parametre 
kot v prvem delu s povprečno produkcijo 1,6 
mladiča/samico. V model smo vključili Aleejev 
efekt, katerega učinki bi se pokazali šele v 
primeru, ko bi številčnost risa padla pod 20 
osebkov v populaciji. Populacijo smo omejevali 
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