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.