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.