AbstractTerritorial behavior plays a key role in shaping the emergent population dynamics and spatial distribution of animal species, yet given its complexity, our understanding of the mechanisms driving territorial formation remains limited. This study used an integrated step selection analysis and a complete territorial location dataset to parameterize a mechanistic home range analysis (MHRA) model, allowing an examination of territorial dynamics in Canada lynx (Lynx canadensis) at a population peak. MHRA models were parameterized using data from two study sites, allowing an analysis of territorial formation and movement under contrasting harvest regimes. In an unharvested region, the model successfully predicted the behavior of a nonterritorial individual that used a mix of territorial space and poor-quality (unoccupied) habitat. In the high-harvest region, the model correctly predicted neighboring lynx response to an observed territorial shift following the harvest of a territorial lynx. This predictive accuracy suggests that territorial behaviors in this cyclically fluctuating species are driven by the interplay among territorial saturation, prey availability, and human exploitation. This approach provides a framework for understanding territorial processes grounded in individual movement patterns while offering insights relevant to population ecology and wildlife management across territorial species.

Abstract Animal movement paths display substantial complexity and variability, promoting efforts to identify universal rules and models that best describe them. Using high‐resolution (≥10 Hz) movement from 43 vertebrate species spanning diverse taxa, body sizes, and lifestyles, we show that paths are universally composed of straight‐line steps interspersed with sharp turns, echoing patterns documented in lower taxa such as bacteria. We report how vertebrate “fundamental steps”—straight travel segments between successive detected turns (with F stepduration as the turn‐to‐turn interval and F steplength as the corresponding distance when displacement is available)—and “fundamental turn angles” ( F turnangles ; net changes in travel heading between successive steps) vary with species' mass, locomotor mode, behavior, and environment. Here, “fundamental” denotes the finest scale step/turn events resolvable under our sampling rate and turn‐detection criteria; these event‐scale steps/turns are intrinsically different from the straight‐line segments inferred from low‐resolution position data. To explain these relationships, we posit that animals inherently move in a straight line until sensory information signals a better heading, triggering a turn. Across all species examined, animals spent the vast majority of their travel time moving in straight lines (species‐level means >90%), with turns representing discrete decision points influenced by body size, locomotor mode, and ecological context. Larger animals turned less frequently, consistent with biomechanical constraints of mass and rotational inertia, while aerial species often exhibited higher turning rates driven by soaring flight demands. We further show that turns can be linked to diverse behavioral drivers, including prey pursuit, obstacle avoidance, predator evasion, and exploitation of environmental energy. By explicitly quantifying turns, we clarify how distributions of step durations and turn angles interact to shape movement patterns and why different statistical models (e.g., correlated random walks, Lévy flights) emerge when lower resolution data are analyzed. Finally, we demonstrate how fundamental steps and turns can be incorporated into an agent‐based modeling framework using penguins as a case study, enabling reconstruction of realistic tracks and prediction of movement responses to environmental change. Straight‐line travel punctuated by decision‐driven turns thus emerges as a fundamental principle of vertebrate movement, linking fine‐scale movement structure, ecological context, and emergent patterns of space use.

Individuals face a trade-off between allocating resources to reproduction or self-maintenance, yet the drivers of the existence and strength of such trade-off have been hard to determine. Environmental conditions are thought to play a crucial role, as long-lived species are predicted to favour more precautionary life-history strategies in variable environments. However, empirical evidence remains limited. Using long-term monitoring of two black-browed albatross Thalassarche melanophris populations, we investigated variation in life-history strategies under contrasting environmental conditions, through reproductive senescence. In more variable environments, individuals displayed generally slower life histories (i.e., slow, late-onset senescence) and greater among-individual variation in life-history strategies. Interestingly, earlier and faster reproductive senescence correlated with higher lifetime reproductive success regardless of environmental variability, suggesting that either faster life histories incur higher fitness or successful reproduction accelerates reproductive senescence. These findings reveal how environmental variability shapes life-history strategies, highlighting potential responses to increasing environmental variability in a changing world.

Abstract The hidden Markov model (HMM) is a central framework for identifying behavioural state changes from animal movement data. In this context, movement is typically represented as a sequence of observed metrics, such as step length and turning angle distributions, generated by an unobserved behavioural state process. Each hidden state corresponds to a distinct behavioural mode (e.g. foraging, resting), and transitions between states are governed by probabilistic rules. Typically, these models have been applied to data collected at relatively low frequency, for example one location every few minutes or hours, so that turning angle and step length distributions are, to some extent, an artefact of the data‐gathering frequency. However, with the growing availability of high‐frequency biologging data (often greater than 1 Hz), it is now possible to determine the precise places where an animal has turned, enabling behaviourally informed step length and turning angle distributions to be fed into HMMs. In this study, we introduce a fast and accurate method for identifying animal behavioural states from high‐frequency data (e.g. ≥1 Hz) within the HMM framework. We first use an existing algorithm to segment the animal's high‐frequency movement path into steps, where each ‘step’ is defined as the straight‐line trajectory between successive real turning points. We then develop a new HMM model for identifying behavioural states that accounts for steps that are of differing durations. We then extend our technique to allow state‐switching to be driven by environmental effects. To evaluate the accuracy of our method, compared with methods that use lower‐frequency data, we apply it to both simulated trajectories and high‐frequency data from free‐ranging goats (Capra aegagrus hircus). Our technique greatly improves the accuracy of inference compared with using step lengths and turning angles derived from fix‐to‐fix steps in lower‐frequency data. Indeed, we demonstrate that the latter can lead to quite notable inaccuracies, and be very sensitive to sampling frequency, in situations where our method achieves >95% accuracy in state identification.

Anthropogenic land conversion is putting increasing pressure on wildlife populations around the world. To mitigate impacts, it is necessary to develop a detailed mechanistic understanding of how animals are affected by different types of human activity. A key challenge is to disentangle the effects of static infrastructure, like roads or buildings, and the presence of humans in the landscape. To address this question, we examined if terrestrial mammals altered their movement behaviour around buildings in response to reduced human mobility during COVID-19 lockdowns. We compiled GPS tracking data from 35 study sites across five continents, for 10 carnivore species and 13 herbivore species, totalling >1 million location records from 586 individuals. For each study, we used integrated step selection analysis to test the extent to which animals changed their avoidance of buildings as lockdown took effect, leveraging the recently released Microsoft MLBuildings dataset of global building locations. Analysis of population-level effects revealed that, in areas with high Human Footprint Index (HFI), animals tended to show a significant reduction in their avoidance of buildings during lockdown, but not in low HFI areas. No such trend was detected during equivalent periods in years other than 2020, indicating that behavioural changes were a result of reduced human mobility during lockdowns. Overall, our findings suggest that animals living alongside humans exhibit greater plasticity when people change their behaviour, likely indicating the combined effects of environmental filtering and habituation. More generally, our study provides a critical first step towards developing evidence-based tools for forecasting how wildlife movement behaviour may change in response to different land-use strategies, human activities, conservation interventions or environmental perturbations.

Recent years have seen a proliferation of high-frequency animal movement data, often at greater than 1 Hz, allowing us to gain much greater insight into behaviour than with lower frequency data. In particular, it is becoming possible to detect the precise points at which animals are making decisions to turn, thus placing the idea that the animals move in 'steps and turns' onto rigorous grounding. Despite this, current efforts to ascertain the points at which animals turn tend to rely on the user making pre-determined choices of certain model parameter values. Furthermore, whilst they may give good results, there is often no theory explaining why the inferred turning points are most likely to be correct, for example by maximising a likelihood function. Here, we propose a theoretically grounded statistical technique to find turning points in high-frequency movement data that does not require any a priori choices of parameter values. By testing our algorithm on simulated data, we show that our technique is both fast (e.g. 3 s to parse 106$$ {10}<^>6 $$ data points) and accurate. For example, when the standard deviation of the noise is less than around pi 12$$ \frac{\pi }{12} $$ radians then our algorithm correctly identifies nearly 100%$$ 100\% $$ of the turning points, providing the noise is not heavily autocorrelated. Additionally, we demonstrate the effectiveness of our technique on magnetometer data from free-ranging Arabian oryx (Oryx leucoryx). Overall, our work gives a fast, accurate and statistically grounded algorithm for turning point detection in high-frequency data. The resulting model of straight-line steps and turns provides a biologically meaningful summary of the animal's movement behaviour, which has potential to be used as an input to the wide range of step-and-turn techniques used in movement ecology, such as step selection analysis and hidden Markov models of behavioural states.

Predictions of animal movement are vital for understanding and managing wild populations. However, the fine-scale, complex decision-making of animals can pose challenges for the accurate prediction of trajectories. Integrated step selection functions (iSSFs), a common tool for inferring relationships between animal movement and the environment, are also increasingly used to simulate animal trajectories for prediction. Although admitting a lot of flexibility, the iSSF framework is limited to its reliance on pre-defined functional forms for fitting to data, and iSSFs that involve complex functional forms to model detailed processes can be prohibitively difficult to fit and interpret. Here, we present deepSSF, an approach to fit and predict animal movement data using deep learning. The deepSSF approach replaces the log-linear model of an iSSF with a neural network architecture that receives multiple environmental layers and scalar values as inputs and outputs a single layer representing the next-step probability. We demonstrate an example deepSSF model, built in PyTorch, consisting of distinct but interacting habitat selection and movement subnetworks. This allows for explicit representation of both selection and movement processes, thus giving interpretable intermediate outputs. We apply our model to GPS data of introduced water buffalo (Bubalus bubalis) in the tropical savannas of Northern Australia. Our deepSSF model was able to learn features that are present in the habitat covariate layers, such as linear features (rivers, forest edges) and the composition of certain habitat areas, without having to specify them pre-emptively within the model framework. It was able to capture complex interactions between the habitat covariates as well as temporal dynamics across time of day and year. Finally, our deepSSF model generally had better in- and out-of-sample predictive accuracy than the analogous iSSF model. We expect that the deepSSF approach will generate accurate and informative predictions about animal movement, which can be used for deepening our understanding of animal-environment systems and for the practical management of species. We discuss how the wide range of existing deep learning tools could enable the deepSSF approach to be extended to represent memory and social dynamic processes, with the potential for integrating non-spatial data sources such as accelerometers and physiological sensors.

Aggregation–diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical way. However, most existing studies do not account for the effect of the underlying environment on organism movement. In reality, the environment is often a key determinant of emergent space use patterns, albeit in combination with collective aspects of motion. This work studies aggregation–diffusion equations in a heterogeneous environment in one spatial dimension. Under certain assumptions, it is possible to find exact analytic expressions for the steady-state solutions when diffusion is quadratic. Minimising the associated energy functional across these solutions provides a rapid way of determining the likely emergent space use pattern, which can be verified via numerical simulations. This energy-minimisation procedure is applied to a simple test case, where the environment consists of a single clump of attractive resources. Here, self-attraction and resource-attraction combine to shape the emergent aggregation. Two counter-intuitive findings emerge from these analytic results: (a) a non-monotonic dependence of clump width on the aggregation width, (b) a positive correlation between self-attraction strength and aggregation width when the resource attraction is strong. These are verified through numerical simulations. Overall, the study shows rigorously how environment and collective behaviour combine to shape organism space use, sometimes in counter-intuitive ways.

We study a broad class of nonlocal advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the nonlocal presence of others. Our model allows for different nonlocal interaction kernels for each species and arbitrarily many spatial dimensions. We prove the global existence of both non-negative weak solutions in any spatial dimension and positive classical solutions in one spatial dimension. These results generalise and unify various existing results regarding existence of nonlocal advection-diffusion equations. We demonstrate that solutions can blow up in finite time when the detection radius becomes zero, i.e. when the system is local, thus showing that nonlocality is essential for the global existence of solutions. We verify our results with numerical simulations on 2D spatial domains.

From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly recognised as powerful tools for capturing such phenomena. However, most research has focused on one-dimensional domains, leaving their two-dimensional behaviour largely unexplored. Here, we present a detailed numerical study of the patterns formed by these systems on 2D domains. Depending on the underlying mechanisms, a wide variety of spatial patterns can emerge - including segregated clusters, stripes, volcanos, and polygonal mosaics - many of which have been observed in natural systems. By systematically varying model parameters, we classify the links between emergent patterns and their underlying movement mechanisms. In comparing these patterns with empirical observations, we show how this modelling framework can help reveal possible mechanisms of self-organisation in various situations within the life sciences, from ecology and developmental biology to cancer research.

Predicting animal movements and spatial distributions is crucial for our comprehension of ecological processes and provides key evidence for conserving and managing populations, species and ecosystems. Notwithstanding considerable progress in movement ecology in recent decades, developing robust predictions for rapidly changing environments remains challenging. To accurately predict the effects of anthropogenic change, it is important to first identify the defining features of human-modified environments and their consequences on the drivers of animal movement. We review and discuss these features within the movement ecology framework, describing relationships between external environment, internal state, navigation and motion capacity. Developing robust predictions under novel situations requires models moving beyond purely correlative approaches to a dynamical systems perspective. This requires increased mechanistic modelling, using functional parameters derived from first principles of animal movement and decision-making. Theory and empirical observations should be better integrated by using experimental approaches. Models should be fitted to new and historic data gathered across a wide range of contrasting environmental conditions. We need therefore a targeted and supervised approach to data collection, increasing the range of studied taxa and carefully considering issues of scale and bias, and mechanistic modelling. Thus, we caution against the indiscriminate non-supervised use of citizen science data, AI and machine learning models. We highlight the challenges and opportunities of incorporating movement predictions into management actions and policy. Rewilding and translocation schemes offer exciting opportunities to collect data from novel environments, enabling tests of model predictions across varied contexts and scales. Adaptive management frameworks in particular, based on a stepwise iterative process, including predictions and refinements, provide exciting opportunities of mutual benefit to movement ecology and conservation. In conclusion, movement ecology is on the verge of transforming from a descriptive to a predictive science. This is a timely progression, given that robust predictions under rapidly changing environmental conditions are now more urgently needed than ever for evidence-based management and policy decisions. Our key aim now is not to describe the existing data as well as possible, but rather to understand the underlying mechanisms and develop models with reliable predictive ability in novel situations.

We investigate a nonlocal single-species reaction-diffusion-advection model that integrates the spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE-ODE system reflective of several existing models found in spatial ecology. We prove the existence and uniqueness of a H\"older continuous weak solution in one spatial dimension under some general conditions, allowing for discontinuous kernels such as the top-hat detection kernel. A robust spectral and bifurcation analysis is also performed, providing the rigorous analytical study not yet found in the existing literature. In particular, the essential spectrum is shown to be entirely negative, and we classify the nature of the bifurcation near the critical values obtained via a linear stability analysis. A pseudo-spectral method is used to solve and plot the steady states near and far away from these critical values, complementing the analytical insights.

Animal movement paths display substantial complexity and variability, leading researchers to seek underlying rules that govern these patterns and mathematical models that best describe them. Using high-resolution (≥ 10 Hz) movement from 43 vertebrate species across diverse taxa, mass, and lifestyles, we show that movement paths are universally composed of straight-line steps interspersed with sharp turns, echoing a pattern documented for lower taxa such as bacteria. We report how these vertebrate ‘fundamental step lengths’ and ‘fundamental turn angles’, which are intrinsically different from the straight-line paths detailed in studies using low resolution position data, vary with species’ mass, lifestyle, behaviour, and environmental context. To explain these, we posit that animals inherently move in a straight line until sensory information signals a perceived better heading, which instigates a turn. The constellation of fundamental step lengths and turn angles over varying time intervals affects how well different models of animal movement (such as random walk or Lévy flight) fit lower resolution data. By examining turns as decision points, we can seek drivers of animal movement patterns and thereby work to predict future paths under varying conditions.

Step selection functions (SSFs) are flexible models to jointly describe animals' movement and habitat preferences. Their popularity has grown rapidly and extensions have been developed to increase their utility, including various distributions to describe movement constraints, interactions to allow movements to depend on local environmental features, and random effects and latent states to account for within- and among-individual variability. Although the SSF is a relatively simple statistical model, its presentation has not been consistent in the literature, leading to confusion about model flexibility and interpretation. We believe that part of the confusion has arisen from the conflation of the SSF model with the methods used for parameter estimation. Notably, conditional logistic regression can be used to fit SSFs in exponential form, and this approach is often presented interchangeably with the actual model (the SSF itself). However, reliance on conditional logistic regression reduces model flexibility, and suggests a misleading interpretation of step selection analysis as being equivalent to a case-control study. In this review, we explicitly distinguish between model formulation and inference technique, presenting a coherent framework to fit SSFs based on numerical integration and maximum likelihood estimation. We provide an overview of common numerical integration techniques, and explain how they relate to step selection analyses. This framework unifies different model fitting techniques for SSFs, and opens the way for improved inference. In particular, it makes it straightforward to model movement with distributions outside the exponential family, and to apply different SSF formulations to a data set and compare them with AIC. By separating the model formulation from the inference technique, we hope to clarify many important concepts in step selection analysis.

Animals determine their daily movement trajectories in response to a network of ecological processes, including interactions with other organisms, their memories of previous events, and the changing environment. These combine to cause the emergent space use patterns observed over longer periods of time, such as a whole season. Understanding which processes cause these patterns to emerge, and how, requires a process-based modelling approach. Individual-based decisions can be described as a system of partial-differential equations (PDEs) to produce a dynamic description of space use built from the underlying movement process. Here we combine PDE-based models with step-selection analysis to investigate the combined effects of three established ecological processes that partially shape movement and space use: 1) a heterogeneous environment; 2) the environmental markings of moving conspecifics; and 3) the memory of direct interactions with conspecifics. We apply this framework to a large GPS-based dataset of white-tailed deer Odocoileus virginianus in the southeastern US. We fit models at the population level to provide predictive models, then tailor these to fit individual deer. We specifically incorporate relationships between each possible pair of deer and define each animal's responses to their unique local environments using separate integrated step-selection analyses. We show how individual movements and decisions yield emergent patterns in animal distributions, and we provide a full generalised description of the framework so that it may be applied to any species simultaneously responding to multiple potentially interacting stimuli (e.g. sociality, morphology, etc.). We found that the population of bucks had highly varied preferences for vegetation, but were shaping their space use in response to conspecific interactions, dependent on the individual relationships between two deer. We advocate for increased consideration of individual-based movement rules as determinants of realized animal space use, and particularly how these affect emergent distributions of entire species.

Untangling the abiotic and biotic feedback mechanisms driving animal movements and ranges is a core question in ecology, yet progress is hampered by inadequate modelling procedures. Here we show how a recently developed process-based modelling approach, combining step-selection functions and individual-based models, enables a flexible method to infer movement drivers and multi-scale emergent space use patterns. As a case study, we examine the movement behaviours of a highly invasive social generalist (wild pigs, Sus scrofa) in relation to conspecific space use and multiple land cover types in a complex agricultural landscape, showing that social interactions are predominantly more important to this species than selection for land cover. Thus, animal movement studies should not neglect the effects of sociality when inferring resource driven movements and, crucially, use multi-scale techniques that incorporate movement processes to untangle drivers of animal space use.