3 Case-studies
To illustrate how quantitative approaches can be selected for a given
application, we highlight two case-studies: 1) the ever-abundant red fox
and 2) the critically endangered European mink. The red fox is a
well-studied species that has been modelled extensively to address a
range of management purposes. The European mink, on the other hand, is a
data limited species of high conservation concern, with only one
modelling application. Through this endeavour, we hope to illustrate
some of the decisions that are made in the model development process,
how others have overcome the limitations of different approaches, and
how mechanistic pathways can be used to help address data scarcity
challenges.
3.1 Case-study 1: Red fox
Disturbances of wildlife populations are often unintentional, occurring
as a by-product of other human activities. In some cases, however, they
may result from targeted management actions that may occur in isolation
or conjunction with other disturbances. One example species is the red
fox, a small carnivore that has a wide distribution across the northern
hemisphere (Box 2). Foxes are often perceived as a nuisance species, are
potential vectors of zoonotic disease, but also play important
ecological roles (e.g., prey regulation). As a relatively well-studied
species of high management interest, a range of modelling approaches
have been used to address disturbances in red fox populations. Here, we
provide a brief overview of some of these models, focusing on two
disturbances where multiple methods have been used to address similar
questions, namely rabies and harvesting/culling.
3.1.1 Rabies/Disease
Rabies, a zoonotic disease, is often viewed as a natural feature in the
environment. However, its dynamics, along with those of other diseases,
can be shaped by human influences, including spill-over from domestic
species, shifts in wildlife densities driven by urbanization, and
changes in behaviour or ranges associated with climate or land use
change. Rabies has been extensively studied in red foxes, which serve as
critical hosts and vectors for specific strains of the disease. Although
now eradicated in many regions, rabies remains a valuable case study due
to the diverse modelling efforts it has inspired, offering opportunities
to compare alternative approaches that may be applied to other diseases
of interest.
Here, we compare two methods for modelling rabies dynamics: 1) an IBM
with a cell-lattice framework (Tischendorf et al. 1998) and 2) a
combined Bayesian state-space and metapopulation model (Baker et
al. 2020). Tischendorf et al . (1998) employed spatially-explicit
grid cells to simulate localised interactions, transmission
heterogeneity, and clustering effects in highly immunized fox
populations, offering insights into fine-scale processes and enabling
targeted interventions. In contrast, Baker et al. (2020) used
three decades of rabies case data to assess regional spatial coupling,
density-dependent dynamics, and localized transmission to capture
broader trends and demographic influences of rabies on fox populations.
These methods provide complementary insights into rabies dynamics by
focusing on different scales and mechanisms of disease spread.
Both models incorporated seasonality and dispersal, essential for
capturing temporal variations in long-distance transmission and changes
in the number of susceptible individuals. However, their use of
empirical data differed. Tischendorf et al . (1998) relied on
literature-derived movement patterns, while Baker et al . (2020)
used Bayesian approaches to estimate dispersal rates from observed
rabies cases. Tischendorf et al. (1998) also used theoretical
landscapes, while Baker et al. (2020) represented regions as five
German states between which dispersal could occur. Notably, only Bakeret al. (2020) explicitly integrated density dependence
(represented as declines in survival and reproduction as metapopulations
approach carrying capacity) and demographic processes, critical for
realistic modelling of contact rates, with parameters informed by
studies on urban foxes. In Tischendorf et al. (1998), these
processes were somewhat implicitly represented through the number of
occupied cells, mortality rates due to infection, and dispersal rates of
subadult foxes.
The use of integrated models in both cases demonstrates the benefits of
integration for addressing disease dynamics, while managing the
trade-offs inherent with modelling complex systems. For example, both
approaches captured spatial elements of rabies dynamics and tracked
disease progression over time, demonstrating that different approaches
can achieve similar goals. Both approaches also emphasised the
importance of spatio-temporal processes in understanding rabies
dynamics. Both studies found that incorporating dispersal-mediated
transmission across habitat regions was important to reproduce key
empirical patterns. Despite these strengths, both models faced
challenges with missing data, such as population size and fine scale
distribution of foxes and vaccination campaigns. Ultimately, each
approach underscored the necessity of accounting for local interactions
and spatial heterogeneity to model the complex fox-rabies system,
strengthening the conclusions despite data limitations.
3.1.2 Culling
Foxes are subject to lethal predator control through harvesting,
fertility control, and poisoning due to their perceived negative impacts
on wildlife, livestock, and human health, with the aim to limit
depredation impacts and/or reduce disease spread (Hoffmann &
Sillero-Zubiri 2021). However, the impact of culling on fox population
dynamics remains unclear due to a lack of evidence of potential
compensatory mechanisms (Lieury et al. 2015). Beyond foxes,
understanding the effectiveness of predator control remains a key issue
in conservation management.
Here we discuss two approaches used to evaluate the impact of culling on
fox population dynamics: 1) a spatially-explicit IBM (Hradsky et
al. 2019) and 2) a Bayesian state-space IPM (Nater et al. 2024).
These two approaches had different management purposes and thus required
different data and considered different processes. Hradsky et al. (2019) focused on the impact of poisoning to evaluate population
responses to diverse baiting designs at scales relevant to management,
while Nater et al . (2024) assessed the impact of harvesting on
vital rates, population structure, and rate of population change in an
expanding fox population.
To evaluate and plan effective fox baiting programs, Hradsky et
al. (2019) used customisable habitat-cells to specify habitat patches
and indicate the location and type of bait stations. The model used a
relatively fine temporal scale that allowed for fox sociality and
territoriality to be incorporated. At each time step, foxes could
disperse and, depending on their sex and social status, join a
fox-family and reproduce. In contrast, Nater et al. (2024) used a
non-spatial, female only model to understand the drivers of fox
population dynamics. The model was built on an annual time step, during
which the population changes in response to natural mortality,
harvesting, immigration, and reproduction. The impact of seasonal and
inter-annual changes in food availability on local demography and
immigration rates were also investigated.
To investigate the effects of culling in their respective contexts, the
authors utilised different data and evaluated their models in different
ways. Hradsky et al. (2019) parameterised their IBM using
site-specific data from the literature, including population density and
dispersal distances. Their model was applied to four case-studies and
model outputs were validated against individual- and population-level
empirical estimates. Nater et al. (2024), on the other hand, used
a range of disparate data streams to estimate age-specific demographic
rates (number, age, and reproductive status of harvested foxes),
reproductive rates (placental scar data and opportunistic pup counts
from hunters and camera traps), immigration rates (genetic data). Data
on food availability (rodent abundances and reindeer carcasses) at
different spatial and temporal scales were also used to infer natural
mortality and immigration. The IPM was then evaluated by comparing model
predictions with genetic data on emigration.
Overall, both approaches provided complementary insights on the impact
of culling on fox populations. Hradsky et al. (2019) showed that
fox density is more sensitive to the frequency of baiting than the
spatial density of baits, due to the recruitment of individuals from
neighbouring patches. In contrast, Nater et al. (2024) identified
the key drivers of year-to-year population change, highlighting the
interactive role of food availability, showing that harvesting is more
efficient when it coincides with low rodent abundance. Both studies
highlighted the importance of better understanding density-dependent and
compensatory fecundity and immigration, which appear to be key drivers
of fox population dynamics. Potential immigration-mediated compensation
for intentional mortality has rarely been investigated due to the lack
of data on dispersal. In this regard, the IPM developed by Nateret al. (2024) shows a very promising use of genetic data for
estimating migration rates.
3.2 Case-study 2: European
mink
Many species are subject to data limitation challenges, making it
difficult to assess conservation status and to identify the associated
drivers of population decline. Regardless, management decisions are
needed, often at timescales that are much shorter (years) than it takes
to amass the data to conduct robust analyses on population dynamics
(decades). Rare species present a particular challenge because their
scarcity makes data inherently difficult to collect, while also being at
high risk of extinction (Davidson et al. 2009). The European
mink, a mustelid that has been extirpated across much of its historic
range, is one example of this dilemma. Remaining local populations are
critically endangered and active intervention to prevent extinction and
promote recovery is ongoing (Box 3).
For understanding disturbance impacts and informing management decisions
for European mink, correlative SDMs are an obvious first choice as
presence data exist and remote sensing and climate modelling make it
possible to include dynamic and disturbance-relevant predictor
variables. SDMs have been developed to predict habitat suitability for
European mink (and American mink, Neovison vison , an invasive
competitor) in Spain under historical conditions and various
socioeconomic and emissions pathways (Goicolea et al. 2023).
Spatial maps produced from SDMs can help identify areas for protection,
restoration, and captive release, and illustrate changes in habitat
suitability and interspecific overlap under climate change. The latter
relies on assumptions that correlative relationships remain unchanged in
time, accurately represent species requirements, and hold when
extrapolated outside the range of input data. However, in many
instances, these assumptions are likely to be violated.
Many of the potential causes of the decline in the European mink could
have strong impacts on energy balance (Fig. 3, Box 3). Energetic
modelling approaches are well suited to data limited species because
many energetic processes scale allometrically or are evolutionarily
conserved (McGrosky and Pontzer 2023; Kooijman and Augustine 2022),
allowing models to be parameterized in the absence of species-specific
data. In addition, while energetic measurements from data-limited
populations may be difficult to obtain, data collected from proxy
species or animals managed in human care may be more readily available.
For example, metabolism and reproductive energetics have been measured
in American mink and other terrestrial mustelids (e.g., Iversen 1972;
Wamberg and Tauson 1998; Chappell et al. 2013), while data
relevant to energetic models have been collected from European mink in
captive breeding programs (Kiik et al. 2017). These data can thus
inform the energetic requirements and challenges of the European mink.
There are a range of energetic modelling frameworks that can be used
including traditional bioenergetics models and DEB models. One key
advantage of DEB framework is that it is grounded in the first
principles of fundamental biological and physical laws. It assumes that
all organisms (regardless of their taxonomy) follow the same basic
principles of energy acquisition, allocation, and expenditure. DEB
therefore allows for the transfer of information across species by
leveraging standardized allometric relationships and shared biological
principles, allowing for predictions even in species for data are
lacking (Lika et al. 2011). This assumption also facilitates the
application of existing models to new species, as could be the case with
American and European mink (Desforges et al. 2017). By capturing
the underlying processes of energy flow, DEB models can make useful
predictions about organism responses to environmental changes such as
resource availability, temperature, and stress (e.g., Molnár et
al . 2010; Harwood et al. 2020), providing an explanatory
framework linking physiology and ecology.
For the European mink, DEB models could be used to investigate the
effects of habitat loss and fragmentation including reduced prey
availability, interspecific competition, altered activity budgets due to
habitat fragmentation, and antagonistic interactions with American mink
(Fig. 2). Other disturbances indirectly related to energetics could be
incorporated, such as pollution or reduced mating opportunities, to
understand synergistic impacts. Such models could help identify
thresholds at which resource scarcity begins to negatively affect
individual survival, assess the long-term impacts of disturbances, and
quantify the impacts of stressor removal (e.g., eradication of American
mink). By combining DEB with individual-based movement models and
habitat suitability maps (from SDMs), spatially-explicit DEB models
could be used to evaluate the potential outcomes of management
decisions. For example, this approach, coupled with targeted surveys,
would allow for the identification of suitable areas to release
captive-bred individuals based on resource availability. It could also
inform habitat restoration efforts by highlighting areas where
interventions would likely have the greatest impact on the species’
recovery.