4 Discussion

An impressive variety of quantitative modelling approaches are being used to understand and predict wildlife responses to human disturbance – and even to address the same conservation or management problems, as exemplified by our red fox case-study. Understandably, it may be daunting for someone who is not familiar with modelling, or who is only familiar with a specific family of models, to decide on which modelling approach(es) to use. We hope that this manuscript can provide guidance and broaden horizons for those wishing to model the impacts of human disturbance on wildlife. Broadening our perspective of what constitutes disturbance can open ecologists up to other research areas and approaches. For example, some ecologists may not consider disease to be a human-mediated disturbance, since it is a part of the evolutionary history of most organisms, but it is also affected by human-mediated environmental change. Approaches used to model disease impacts, and their associated considerations, may thus provide insights into the modelling of other disturbances that may act via similar mechanisms. A broader perspective can also expose ecologists to some of the ways that modelling approaches can be integrated to overcome the limitations of the different singular approaches. It is interesting how different processes are being pulled into models to address different disturbances. This was illustrated well for red foxes, where dispersal and immigration were explicitly incorporated when assessing the impacts of regulatory management, since these processes appear to drive the difficulties in regulating red fox abundance. Similarly, spatial dynamics, movement, and dispersal were key processes included for predicting disease transmission, because movement of infected individuals drives disease spread. Yet there remains an opportunity to incorporate other processes that impact population responses to human disturbance, including eco-evolutionary feedbacks and sociological processes. Since evolutionary changes following disturbance may enable populations to adapt to disturbances, such as increasing temperatures, eco-evolutionary feedbacks play a crucial role in the long-term responses of populations to disturbance (Loeuille 2019). Social dynamics can also play a key role in population dynamics and although they are sometimes considered for social wildlife (e.g., Brandell et al. 2021; Grente et al. 2024), the human element is often neglected. Not only are human disturbances inherently driven by human behaviour, but so are the perceptions of management actions (Bro-Jørgensen et al. 2019). Such interdisciplinary approaches are already well developed (e.g., Dobson et al. 2019) but greater uptake in disturbance ecology modelling could improve conservation and regulatory management outcomes. We were pleased to see increasing use of energetic modelling applications across a range of quantitative approaches. Since energetics act in a summative way and many non-lethal disturbances have impacts on energy acquisition or use, energetic models can help us better understand the impacts of multiple stressors on wildlife populations. Subsequently, the inclusion of energetic mechanisms represents an important avenue to scale individual-level responses to population-level impacts. By integrating models, energetics can be incorporated into most of the quantitative approaches available for modelling population responses to human disturbance. Perhaps most importantly, energetic models may offer the only viable way both scientists and decision-makers can anticipate the impact of demographic responses to complex patterns of global climate change that will surely continue for the foreseeable future. If we do not accommodate changes in behaviour, space use, and demography that will accompany the relentless change in climatic drivers, even the best of models will only have value for understanding the past rather than predicting the future. While DEB theory is not new (Kooijman 2000), it appears to be having a resurgence to address the growing concerns of human-mediated threats to wildlife. Given the common challenge of data availability, the DEB approach may be more attainable than traditional energetic approaches that require detailed energetic data that may not be readily available. This is one of the reasons why we explored this avenue in our European mink case-study. However, traditional energetics approaches can also utilise data from proxy species and allometric relationships, and may be more intuitive to some ecologists. The intricate tie between individual behaviour and energetics makes these a powerful combination for assessing population responses to disturbance. Despite the developments and integrations of quantitative modelling approaches, models can only ever be a simplified representation of natural systems. All quantitative approaches rely on assumptions, imperfect data, and simplifications of the processes they aim to represent. Consequently, there is a great deal of uncertainty associated with input parameters and data, model structure (Refsgaard et al. 2006), and resulting model predictions (Rounsevell et al. 2021). Several approaches have been developed to minimise or quantify the level of data or model uncertainty. For example, sensitivity analysis aims to determine the influence of uncertain parameters in model outputs, which can highlight priority areas for data collection or model development (Cariboni et al. 2007). Alternatively, ensemble modelling aims to reduce model uncertainty by combining predictions from multiple models. This approach has become more common for species distribution modelling (Hao et al. 2020) but has received criticisms due to the ‘smoothing out’ of model outputs. Challenging models with different assumptions against each other (i.e., robustness analysis (Levins 1966) or model intercomparison) is another approach to quantifying uncertainty in model outputs, as well as investigating the influence of different model structures. With this approach, there is no averaging of model outputs, but the resulting model predictions may be vastly different. Quantifying uncertainty brings about its own challenges. When providing predictions to managers, it is important to highlight the degree of uncertainty in model predictions, yet uncertainty can make it more difficult for managers to make decisions. This makes knowledge transfer crucial, as stakeholders are able to conceptualise uncertainty in model outputs and make informed decisions when clearly communicated (Mahevas & Sigrid 2024). Nonetheless, the acceptance of modelling tools as a decision support tool depends on whether different stakeholders agree with the representation of the system and their understanding of its components. For this purpose, participatory modelling is a widely used approach (Voinov & Bousquet 2010) that aims to increase and share knowledge of a system and its dynamics under different conditions and to anticipate the impact of management actions to support decision-making. However, the involvement of stakeholders is no guarantee for the appropriation of model results, especially if their participation is limited.