2 Approaches to modelling the effects of disturbance on wildlife populations

We provide an overview of the key approaches for understanding and predicting the impacts of disturbance on individuals, populations, and communities. We use a broad definition of human disturbance, wherein we include natural processes (e.g., climate variation, disease, wildfire) that can be exacerbated by human activity. We have categorised the quantitative approaches into four sections based on the general level at which disturbance is usually modelled for each of the modelling approaches. These have been broadly broken down into responses at the individual, population, community, or geographical range scales. We recognise from the outset that some modelling traditions include or link components from multiple scales and that some approaches represent broad categories of model families while others are specific to a single model or method. We also discuss some of the benefits, challenges, and data requirements for specific approaches using case studies. We provide reference to more in-depth reviews in the Supplementary Material.

2.1 Individually-focused dynamics

Below, we describe the most widely used approaches to model the effects of human-related stressors at the individual or group level. These approaches typically allow individuals (or groups of individuals) to vary within a population in terms of a variety of traits related to behaviour, genetics, or energetics. Accounting for such variation may be more representative of real populations than those that assume all individuals are identical (Denny 2017), which can improve predictions of population dynamics (Gerber 2006).

2.1.1 Individual-based models

Individual-based models (IBMs or agent-based models) are a broad class of simulation models that depict relevant processes at the individual or group level (the agent). Population-level properties (e.g., population growth rate) emerge from the behaviour of, and interactions among, discrete agents through time. This key property makes IBMs particularly useful when intraspecific trait variation, local interactions, adaptive behaviour or heterogeneous environments are assumed to influence population level responses to disturbance (Chevy et al. 2025; DeAngelis & Grimm 2014), as well as for small populations (Caughley 1994). Disturbance is typically implemented by comparing different simulation scenarios with varying disturbance levels. IBMs are frequently used to assess the population impacts of disturbance, either as a stand-alone method or in conjunction with other approaches described throughout this section. Such applications include investigating the effects of climate change and habitat connectivity (Andersen et al. 2022) and toxicant exposure (Hall et al. 2018) on population dynamics.

2.1.2 Cell-lattice models

While not technically individually-focused, cell-lattice models analyse spatially-explicit demographic processes through an array of discrete grid cells, that enable fine-scale dynamics to be modelled. Discrete cells can be characterized by variation in important landscape attributes, such as habitat type, food availability, or predation risk, that influence demographic rates. Dispersal between adjacent cells is used to depict simple patterns of redistribution by a fraction of the subpopulations arising from neighbouring cells. Cell-lattice models are a computationally simple way to evaluate the influence of habitat arrangement, mobility, and behavioural decision-making on rates of resource gain and mortality risk among subpopulations occurring in different cells at a given point in time (Tonini et al. 2014). Similar to IBMs, disturbance effects are typically inferred based on comparisons of model outputs among simulation scenarios. Because of their inherent spatial nature, cell-lattice models are particularly relevant for applications involving movement barriers (e.g., road infrastructure; Holdo et al. 2011), the effects of invasive species (Tonini et al. 2014), and disease spread (Jeltschet al. 1997).

2.1.3 Stochastic dynamic programming

Stochastic dynamic programming is an optimization method frequently used to identify optimal decisions and behaviours of individual animals (Houston et al. 1988; Mangel & Clark 1988). As a way to implement state-dependent life-history theory, it is based on the underlying assumption that individuals act to maximize some future expected reward (e.g., Darwinian fitness), which varies depending upon one or more state variables. Energy reserves are often used as physiological state variables, hence there is typically an energetic component when addressing disturbance impacts. Discrete locations characterized by environmental features (e.g., resource availability) can also be included, allowing for spatiotemporally-explicit models. Once identified, optimal decisions for each combination of state variables across the time horizon (e.g., the lifespan of an individual) can be used in an IBM framework to characterize emergent population properties in the presence (and absence) of disturbance scenarios. In the context of disturbance, stochastic dynamic programming has primarily been used to identify optimal movement, habitat, and reproductive decisions to quantify the potential effects of variation in prey resources (e.g., due to climate change; Reimer et al. 2019) and acoustic disturbance (McHuron et al. 2021; Pirotta et al. 2019).

2.1.4 Dynamic energy budget models

Dynamic energy budget (DEB) theory (Kooijman 2010) provides a mechanistic basis to model the acquisition and allocation of energy by organisms across their lifespan. DEB thus allows for the study of density-dependent feedback effects between a population and its environment, and resulting patterns of life-history evolution (de Roos & Persson 2013). This approach is based on the concept that rates of basic physiological processes are proportional to surface area or body volume, which differs from other energetic approaches like the Metabolic Theory of Ecology (van der Meer 2006). The generalised nature of the framework allows for easy adaptation to a range of disturbance types and taxonomic groups. Because DEB models are specified at the individual level, we need other tools to extrapolate to the population level. As such, DEB theory has been integrated into IBMs (DEB-IBMs), matrix models (Klanjscek et al. 2006), integral projection models (Smallegangeet al. 2017; Thunell et al. 2023), and physiologically structured population models (Metz & Diekmann 1986; de Roos 1997). In particular, DEB-IBMs allow for explicit consideration of individual variation, local interactions and/or adaptation (Martin et al. 2012). DEB-IBMs have been applied to investigate the impact of toxicant exposure and disease (Silva et al. 2020), acoustic disturbance (Soudijn et al. 2020) and habitat loss due to climate change (Johnson et al. 2024) through explicit changes in an individual’s physiology resulting from these disturbances.

2.2 Population dynamics

Modelling human impacts at the population level has a long history (Boyce 1992; Lande 1993). These approaches directly link human disturbances to population viability by quantifying how shifts in key demographic processes (Morris & Doak 2002), such as survival and reproduction, influence population growth and structure (Caswell 2000). As a result, these approaches have been widely applied to project long-term population viability under various disturbance scenarios (Engelen et al. 2025; Morris & Doak 2002) and to assess the evolutionary consequences of human activities (Palstra and Ruzzante 2008; Hendry et al. 2008). More recently, frameworks have been developed to integrate biological mechanisms underpinning responses to anthropogenic threats, highlighting the role of mechanisms in conservation planning (Urban et al. 2016).

2.2.1 Matrix population models

Matrix population models are structured population models that describe the dynamics of a given population in discrete time and stages (e.g., developmental stage) (Caswell 2001). By providing a direct link between age and/or stage-structured vital rates and population dynamics in a relatively simplistic framework, matrix population models are an accessible tool to project population trends under alternate environmental conditions (Fieberg & Ellner 2001). Matrix population models have been applied extensively to explore population response, for example under land-use change (Tucker et al. 2021), climate change (Penman et al. 2015) and hunting (Simon & Fortin 2019), with the effects of disturbance typically included via changes in vital rates. Matrix models are also often integrated with other modelling approaches, such as DEB models (Billoir et al. 2007), to examine population-level consequences of vital rate changes on population dynamics.

2.2.2 Integral projection models

Similar to matrix population models, integral population models track population dynamics in discrete time, but along a continuous stage classification (e.g., size) to describe how an individual’s state influences its vital rates. Integral population models are constructed from regression models that predict vital rates from state variables, and can incorporate factors such as density dependence (Metcalf et al. 2008), environmental drivers (Merow et al. 2014), and stochastic dynamics (Ellner & Rees 2006). By integrating vital rates with environmental covariates, integral population models provide semi-mechanistic insight into ecological patterns including population dynamics, species distributions or life-history strategies (Merowet al. 2014). Integral population models have been applied directly to explore the eco-evolutionary dynamics of populations under a range of human pressures, including size-selective hunting (Wallaceet al. 2013). Integral population models have also been integrated with DEB theory to provide additional mechanistic insights into ecological patterns under disturbance (Smallegange et al. 2017; Thunell et al. 2023). This approach allows for the investigation of ecological and evolutionary patterns from an energy budget perspective, such as sensitivity to shifts in environmental variability (Smallegange et al. 2020; Rademaker et al. 2024) or the eco-evolutionary consequences of climate change for populations (Thunell et al. 2023).

2.2.3 Physiologically structured population models

Physiologically structured population models can describe a population’s demography using DEB theory, but differ by treating time as continuous rather than discrete (Metz & Diekmann 1986; de Roos 1997). This approach has been applied to investigate the population-level impacts of food limitation (e.g., Hin et al. 2019) and environmental stress (Silva et al. 2020). Finally, a computational approach (de Roos 2021) exists that merges discrete and continuous DEB population modelling approaches that can be used for life histories with continuous development through time (de Roos et al. 2008). For example, this approach has been applied to show how habitat deterioration impacts life history evolution in metamorphosing species (ten Brink et al. 2020).

2.2.4 State-space models

State-space modelling is a highly flexible hierarchical framework used to estimate parameters while explicitly separating the underlying ecological process (the true, unobserved state) from the observation process (measurements). This distinction allows for the independent estimation of uncertainties arising from biological stochasticity and sampling-related measurement errors, therefore reducing bias in parameter estimates compared to models that account for only a single source of uncertainty (Auger-Méthé et al. 2021). Ecological applications of state-space models include estimating demographic rates, assessing population abundance, and projecting population growth and viability (Buckland et al. 2004), using a range of datatypes (e.g., capture-recapture, abundance data). State-space models are highly adaptable, allowing structuring by age (Bret et al. 2017), life stage (McCaffery et al. 2012), or spatial location (Rogerset al. 2017). State-space models can also capture temporal trends and density-dependence effects (Lebreton & Gimenez 2013). In addition to studying the effects of a variety of disturbances, such as climate change and habitat destruction (e.g., Westcott et al. 2018; McCaffery et al. 2012), they can also model host-parasite dynamics (Karban & De Valpine 2010) and be combined with population models such as integrated population models (White et al. 2016).

2.2.5 Integrated population models

Integrated population models (IPMs) combine population count data and demographic data within a single statistical model to infer population dynamics. These models are frequently implemented using Bayesian methods with a state-space model formulation to deal with uncertainties in parameter estimates. Typically, the core of an IPM is a matrix model (or integral projection model; Plard et al. 2019) that is formulated in discrete time to describe changes in age- or stage-structured population sizes. IPMs can help reduce uncertainty in parameter estimates, estimate confounded or hidden parameters, and disentangle sources of uncertainty when forecasting population trajectories (Schaub & Abadi 2011). Disturbance applications of IPMs include climate change (Gamelon et al. 2023), land use changes (Zhao et al. 2019), invasive species (Oppel et al. 2022), and electrocution on power poles or collision with wind turbines (Millsap et al. 2022). Some work has also focused on extending these models to multiple species, incorporating interactions such as competition (Péron & Koons 2012) and predation (Quéroué et al. 2021).

2.2.6 Machine learning models

Machine learning algorithms are computational approaches that learn patterns from large and complex datasets capturing non-linearities and complex interactions between variables to generate accurate predictive models without explicit programming (Pichler & Hartig 2023). In the context of disturbance, machine learning models are most commonly used in correlative SDMs, but they have also been used to predict population dynamics under various pressures (e.g., climate change; Amstrup et al. 2008), and to understand the impact of disturbance on animal behaviour (Berger et al. 2020; Fardell et al. 2021; Tédonzong et al. 2020).

2.2.7 Partial differential equations

Partial differential equations are a class of mathematical equations used to describe systems where variables change continuously over both time and space. A partial differential equation expresses relationships between the rates of change of these variables with respect to time, spatial dimensions, or both. A typical partial differential equation in ecology might describe how the rate of change in animal population density at a specific location depends on factors like the movement of individuals (diffusion), behavioural interactions, and local birth and death rates (Moorcroft & Lewis 2006; Otto & Day 2011). There have been several applications of partial differential equations to study the consequences of human disturbance on populations, including climate change (Chhaytle et al. 2023; Goel et al. 2020), invasive species (Laplanche et al. 2018) and pest control (Banks et al. 2020).

2.3 Range dynamics

This section reviews some of the methods used to understand and predict the effects of human disturbance on the range dynamics of wildlife populations. From a disturbance ecology perspective, range dynamics can tell us where populations may be at greater risk of exposure to stressors, highlight potential areas of refuge, and identify key habitat requirements for a population to persist. This information can be used to prioritise, for example, areas for protection or management.

2.3.1 Species distribution models

Correlative species distribution models (a.k.a. ecological niche models or habitat suitability models; hereafter, SDMs) identify statistical relationships between species occurrence or abundance to spatio-temporal patterns of environmental variation to explain or predict species distributions (Elith & Leathwick 2009). Habitat suitability is typically predicted from static physical features (e.g., land use type, topography) and/or dynamic environmental variables (e.g., temperature, precipitation). Data can be fitted using a range of approaches, including generalized linear and additive models, boosted regression trees, and machine learning algorithms (Guisan et al. 2017). Disturbance can be incorporated as an additional predictor variable (e.g., urbanization; Russo et al. 2023) or effects can be inferred based on spatial or temporal shifts in habitat suitability (e.g., climate change; Russo et al. 2023). They are also frequently integrated as a spatial layer for other modelling approaches, such as connectivity models (e.g., Rezaei et al. 2022) and IBMs (e.g., Andersen et al. 2022; Jordt et al. 2016), providing boundaries for movement or dispersal.

2.3.2 Process-explicit range models

Process-explicit range models extend correlative SDMs to explicitly model the underlying processes that drive population dynamics, such as physiology, dispersal, demography, and evolution (Briscoe et al. 2019). There are a broad range of modelling approaches that can be categorised as process-explicit range models, including occupancy or abundance dynamics models, coupled SDM-population models, demographic distribution models, eco-physiological models, and IBMs (Briscoeet al. 2019). Applications of process-explicit range models are limited but they have increased in recent years (Kelleher et al. 2024; Uribe‐Rivera et al. 2023), particularly as they are often assumed to provide more accurate range prediction when extrapolating to novel conditions (Evans et al. 2015, but see Uribe‐Rivera et al. 2023). For example, demographic-based process-explicit range models have been used to assess the effect of wind farms (Bastos et al. 2016), movement barriers (Pratzeret al. 2023), and climate change (Mathewson et al. 2017; Santika et al. 2014).

2.4 Community and ecosystem dynamics

While ecological models often focus on a single species, unintended management outcomes can result when species are viewed in isolation (Buckley and Han 2014). Models that explicitly consider the interactions and feedback among species can help better inform population-level responses to disturbance and management. Community and ecosystem models vary substantially in their complexity, from simple food webs (e.g., Varriale and Gomes 1998) to complex end-to-end ecosystem models (e.g., Fulton 2010). Here, we focus on metacommunity and food web models as these approaches are more frequently applied to disturbance studies, though their application is still relatively rare.

2.4.1 Metacommunity models

Metacommunity models represent the multiscale dynamics of species inhabiting discrete habitat patches, where populations face measurable extinction risk, can recolonize after local extinction, and experience asynchronous local population dynamics. Patterns in local extinctions versus regional survival are central to these models and are driven by processes such as environmental filtering, biotic interactions, dispersal, and drift (Chase et al. 2020; Lerch et al. 2023). As these models are united by underlying theory rather than a standard method, there exists a wide variety of modelling approaches that may represent time and space differently (Ovaskainen and Hanski 2001; Bond et al. 2023; Souto-Veiga et al . 2024). Dynamics may be represented using IBMs (e.g., Radchuk et al. 2013) and matrix population models (e.g., Takashina 2016), among others (e.g., Brandell et al. 2021; Zhang et al. 2021). Metacommunity models are still rarely used to study disturbances (but see Duggeret al. 2011); however, the theory is analogous to metapopulation models that have been used to address how changes in landscape structure influence colonization and extinction dynamics (Bond et al. 2023) and the impacts of broader environmental changes (e.g., extreme weather) across metapopulations (Radchuk et al. 2013).

2.4.2 Food web models

Food web models aim to represent the demographic impact and rates of transfer of material or energy between different elements of the community matrix as a result of trophic interactions such as predation, parasitism, or mutualism (e.g., Baudrot et al. 2020). These models encompass a wide variety of computational approaches, ranging from partial differential equations (e.g., Lusardi et al. 2024) to individual-based or cell-lattice models (e.g., Fryxell et al. 2020). Community structure, behavioural details (e.g., decision-making, mobility, and cognition), sources of heterogeneity affecting interaction rates, and landscape configuration are often key components influencing model outcomes. The response to disturbance in food web models, such as that caused by invasive species or habitat loss (e.g., Roemer et al. 2002), is often determined through impacts on community structure or changes in the functional relationships between community components.

2.4.3 Structural equation models

Structural equation models aim to capture the complex interactions that are inherent in communities and ecosystems. By integrating multiple processes, structural equation models can help disentangle the relative influences of many processes on community or ecosystem dynamics. As in food web models, structural equation models allow researchers to assess both direct and indirect effects of disturbance on trophic interactions, such as the cascading impacts of habitat loss or invasive species (e.g., Curveira-Santos et al. 2024; Schwensow et al. 2022). Their ability to account for multiple causal pathways makes them a valuable tool for predicting community-level responses to disturbance (Schweigeret al. 2016). However, relationships are assumed linear which may not always be appropriate in real world systems.