How do animal territories form and change? Lessons from 20 years of mechanistic modelling

Towards transient space-use dynamics: re-envisioning models of utilization distribution and their applications

BACKGROUND

Models of utilization distribution in the form of partial differential equations have long contributed to our understanding of organismal space use patterns. In studies of infectious diseases, they are also being increasingly adopted in support of epidemic forecasting and scenario planning. However, as movement research shifts its focus towards large data collection and statistical modeling of movement trajectories, the development of such models has notably slowed.

METHODS

Here, we demonstrate the continued importance of modeling utilization distribution to predict variation in space-use patterns over time. We highlight the considerable, yet largely untapped, potential of such models, which have historically been limited by the steady-state assumption due to longstanding technical constraints. Now, by adapting existing computational tools primarily developed for material science and engineering, we can probe beyond the steady states and unlock from them a broad spectrum of complex, transient space-use dynamics. Our approach requires little experience in numerical analysis and is readily accessible to model practitioners in ecology and epidemiology across diverse systems where movement is a critical feature.

RESULTS

We illustrated our approach using a mix of canonical and novel case studies, covering topics from wildlife translocation to vaccine deployment. First, we revisited a classical model of canid territorial formation driven by scent-mediated conspecific avoidance. Transient space-use analysis uncovered previously hidden spatial dynamics that are ecologically informative. Next, we applied our approach to long-distance movement on realistic landscapes. Habitat and land-use heterogeneities markedly affected the transient space-use dynamics and short-term forecasts, even when the steady state remained unchanged, with direct implications for conservation management. Finally, we modeled transient space-use dynamics as both a response to and a driver of transient population dynamics. The importance of this interdependence was shown in the context of epidemiology, in a scenario where the movement of healthcare personnel is influenced by local outbreak conditions that are stochastically evolving.

CONCLUSIONS

By facilitating transient space-use analysis, our approach could lead to reevaluations of foundational ecological concepts such as home range and territory, replacing static with dynamic definitions that more accurately reflect biological realities. Furthermore, we contend that a growing interest in transient space-use dynamics, spurred by this work, could have transformative effects, stimulating new research avenues in ecology and epidemiology.

Voronoi diagrams and Delaunay triangulation for modelling animal territorial behaviour

We explore the use of movable automata in numerical modelling of male competition for territory. We used territorial dragonflies as our biological inspiration for the model, assuming two types of competing males: (a) faster and larger males that adopt a face-off strategy and repulse other males; (b) slower and smaller males that adopt a non-aggressive strategy. The faster and larger males have higher noise intensity, leading to faster motion and longer conservation of motion direction. The velocity distributions resemble the Maxwell distributions of velocity, expected in Brownian dynamics, with two probable velocities and distribution widths for the two animal subpopulations. The fast animals' trajectories move between visually fixed density folds of the slower animal subpopulation. A correlation is found between individual velocity and individual area distribution, with smaller animals concentrated in a region of small velocities and areas. Attraction between animals results in a modification of the system behaviour, with larger animals spending more time being surrounded by smaller animals and being slowed down by their interaction with the surroundings. Overall, the study provides insights into the dynamics of animal competition for territory and the impact of attraction between animals.

Random walks with spatial and temporal resets can explain individual and colony-level searching patterns in ants

Central place foragers, such as many ants, exploit the environment around their nest. The extent of their foraging range is a function of individual movement, but how the movement patterns of large numbers of foragers result in an emergent colony foraging range remains unclear. Here, we introduce a random walk model with stochastic resetting to depict the movements of searching ants. Stochastic resetting refers to spatially resetting at random times the position of agents to a given location, here the nest of searching ants. We investigate the effect of a range of resetting mechanisms and compare the macroscopic predictions of our model to laboratory and field data. We find that all returning mechanisms very robustly ensure that scouts exploring the surroundings of a nest will be exponentially distributed with distance from the nest. We also find that a decreasing probability for searching ants to return to their nest is compatible with empirical data, resulting in scouts going further away from the nest as the number of foraging trips increases. Our findings highlight the importance of resetting random walk models for depicting the movements of central place foragers and nurture novel questions regarding the searching behaviour of ants.

Intraguild processes drive space-use patterns in a large-bodied marine predator community

Interspecific interactions, including predator-prey, intraguild predation (IGP) and competition, may drive distribution and habitat use of predator communities. However, elucidating the relative importance of these interactions in shaping predator distributions is challenging, especially in marine communities comprising highly mobile species. We used individual-based models (IBMs) to predict the habitat distributions of apex predators, intraguild (IG) prey and prey. We then used passive acoustic telemetry to test these predictions in a subtropical marine predator community consisting of eight elasmobranch (i.e. shark and ray) species in Bimini, The Bahamas. IBMs predicted that prey and IG prey will preferentially select habitats based on safety over resources (food), with stronger selection for safe habitat by smaller prey. Elasmobranch space-use patterns matched these predictions. Species with predator-prey and asymmetrical IGP (between apex and small mesopredators) interactions showed the clearest spatial separation, followed by asymmetrical IGP among apex and large mesopredators. Competitors showed greater spatial overlap although with finer-scale differences in microhabitat use. Our study suggests space-use patterns in elasmobranchs are at least partially driven by interspecific interactions, with stronger spatial separation occurring where interactions include predator-prey relationships or IGP.

The role of memory-based movements in the formation of animal home ranges

Most animals live in spatially-constrained home ranges. The prevalence of this space-use pattern in nature suggests that general biological mechanisms are likely to be responsible for their occurrence. Individual-based models of animal movement in both theoretical and empirical settings have demonstrated that the revisitation of familiar areas through memory can lead to the formation of stable home ranges. Here, we formulate a deterministic, mechanistic home range model that includes the interplay between a bi-component memory and resource preference, and evaluate resulting patterns of space-use. We show that a bi-component memory process can lead to the formation of stable home ranges and control its size, with greater spatial memory capabilities being associated with larger home range size. The interplay between memory and resource preferences gives rise to a continuum of space-use patterns-from spatially-restricted movements into a home range that is influenced by local resource heterogeneity, to diffusive-like movements dependent on larger-scale resource distributions, such as in nomadism. Future work could take advantage of this model formulation to evaluate the role of memory in shaping individual performance in response to varying spatio-temporal resource patterns.

How territoriality and sociality influence the habitat selection and movements of a large carnivore

While territoriality is one of the key mechanisms influencing carnivore space use, most studies quantify resource selection and movement in the absence of conspecific influence or territorial structure. Our analysis incorporated social information in a resource selection framework to investigate mechanisms of territoriality and intra-specific competition on the habitat selection of a large, social carnivore. We fit integrated step selection functions to 3-h GPS data from 12 collared African wild dog packs in the Okavango Delta and estimated selection coefficients using a conditional Poisson likelihood with random effects. Packs selected for their neighbors' 30-day boundary (defined as their 95% kernel density estimate) and for their own 90-day core (defined as their 50% kernel density estimate). Neighbors' 30-day boundary had a greater influence on resource selection than any habitat feature. Habitat selection differed when they were within versus beyond their neighbors' 30-day boundary. Pack size, pack tenure, pup presence, and seasonality all mediated how packs responded to neighbors' space use, and seasonal dynamics altered the strength of residency. While newly-formed packs and packs with pups avoided their neighbors' boundary, older packs and those without pups selected for it. Packs also selected for the boundary of larger neighboring packs more strongly than that of smaller ones. Social structure within packs has implications for how they interact with conspecifics, and therefore how they are distributed across the landscape. Future research should continue to investigate how territorial processes are mediated by social dynamics and, in turn, how territorial structure mediates resource selection and movement. These results could inform the development of a human-wildlife conflict (HWC) mitigation tool by co-opting the mechanisms of conspecific interactions to manage space use of endangered carnivores.

Home is where the home range is: Identifying territoriality and exhibit preferences in an ex-situ group of all-male Nile crocodiles (Crocodylus niloticus)

Here, the presence or absence of territoriality was evaluated in an all-male Nile crocodile (Crocodylus niloticus) group living in an ex-situ environment. Location data for each crocodile within the exhibit were collected three times per day over a two-year period, including two warm seasons and two cold seasons. A geographic information system (GIS) was used to create seasonal home ranges and core areas for each crocodile, to quantify the overlap of these home ranges and core areas to assess potential territoriality, and to calculate exhibit preferences of the group. Core area overlap was significantly lower than home range overlap, suggesting the crocodiles established territories within their exhibit. This pattern of behavior was similar across seasons, though it moderately intensified during the cold season. The crocodiles appeared to be more territorial in water, as overlap was most concentrated on the central beach, the only feature utilized more than expected based in its availability in the exhibit. These findings highlight the behavioral complexity of Nile crocodiles in human care, specifically the ability of Nile crocodiles to adapt to ex-situ environments similar to their wild counterparts by forming territories despite spatial constraints. Identifying the presence of territorial behavior is important for the care and welfare of ex-situ animals, as territorial animals have specific requirements that may result in increased agonism when unmet. It can also provide valuable context to aid in mitigation strategies, for example, when undesirable levels of agonism do occur. The findings here provide an example of how methodology from the wildlife ecology field can be adapted to ex-situ settings using a GIS and contributes to the current understanding of crocodilian behavior in human care.

Bat Motion can be Described by Leap Frogging

We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.

Should sons breed independently or help? Local relatedness matters

In cooperatively breeding birds, why do some individuals breed independently but others have to help at home? This question has been rarely addressed despite its fundamental importance for understanding the evolution of social cooperation. We address it using 15 years of data from Tibetan ground tits Pseudopodoces humilis where helpers consist of younger males. Since whether younger males successfully breed depends critically on their chances to occupy territories nearby home, our analytic strategy is to identify the determinants of individual differences in gaining territory ownership among these ready-to-breed males. Across widowed, last-year helper and yearling males, an age advantage was evident in inheriting resident territories, occupying adjacent vacancies and budding off part of adjacent territories, which left some last-year helpers and most yearling males to take the latter two routes. These males were more likely to acquire a territory if they were genetically related to the previous or current territory owners; otherwise they remained on natal territories as helpers. The relatedness effect can arise from the prior residence advantage established in the preceding winter when younger males followed their parents to perform kin-directed off-territory forays. Our research highlights the key role of local kinship in determining younger males' territory acquisition and thus their fate in terms of independent reproduction versus help. This finding provides insight into the formation of kin-based, facultative cooperative societies prevailing among vertebrates.

Habitat detection, habitat choice copying or mating benefits: What drives conspecific attraction in a nomadic songbird?

Conspecific attraction during habitat selection is common among animals, but the ultimate (i.e. fitness-related) reasons for this behaviour often remain enigmatic. We aimed to evaluate the following three hypotheses for conspecific attraction during the breeding season in male Wood Warblers (Phylloscopus sibilatrix): the habitat detection hypothesis, the habitat choice copying hypothesis and the female preference hypothesis. These hypotheses make different predictions with respect to the relative importance of social and nonsocial information during habitat assessment, and whether benefits accrue as a consequence of aggregation. We tested the above hypotheses using a combination of a 2-year playback experiment, spatial statistics and mate choice models. The habitat detection hypothesis was the most likely explanation for conspecific attraction and aggregation in male Wood Warblers, based on the following results: (1) males were attracted to conspecific song playbacks, but fine-scale habitat heterogeneity was the better predictor of spatial patterns in the density of settling males; (2) male pairing success did not increase, but instead slightly decreased, as connectivity with other males (i.e. the number and proximity of neighbouring males) increased. Our study highlights how consideration of the process by which animals detect and assess habitat, together with the potential fitness consequences of resulting aggregations, are important for understanding conspecific attraction and spatially clustered distributions.

The evolution of monogamy in cichlids and marine reef fishes

Although several hypotheses have been proposed to explain the emergence of social monogamy, its origin is still intensely debated. Monogamy has many potential drivers, but evolutionary causality among them remains unclear. Using phylogenetic comparative methods within a Bayesian framework we explored the evolution of monogamy in cichlids and in marine reef fishes because, while both groups are characterised by unusually high incidence of social monogamy, they face very different ecological challenges. For each group, we examined four classic hypotheses that explain the evolution of monogamy: female dispersal, male mate guarding, female–female intolerance, and the biparental care hypotheses. We also explored whether the ecological traits of diet and shelter use are evolutionarily coupled with these hypotheses or with monogamy. First, we found that the evolution of monogamy was predicted by male territoriality in cichlids and simultaneous male and female territoriality in marine reef fishes. We suggest that these results provide support for the male mate guarding hypothesis in cichlids and female–female intolerance hypothesis in marine reef fishes. Second, we demonstrate clear evidence against the biparental care hypothesis, as biparental care was a consequence, not a cause, of monogamy in our analyses. Third, as female dispersal drove the loss of monogamy in both cichlids and marine reef fishes, this suggests the female dispersal hypothesis is not driving the evolution of monogamy in either group. These findings in two highly-monogamous fish taxa largely support prior findings from primate and bird comparative studies and provide novel large-scale evidence for a link between mate guarding and the evolution of monogamy.

Confronting spatial capture-recapture models with realistic animal movement simulations

Spatial capture-recapture (SCR) models have emerged as a robust method to estimate the population density of mobile animals. However, model evaluation has generally been based on data simulated from simplified representations of animal space use. Here, we generated data from animal movement simulated from a mechanistic individual-based model, in which movement emerges from the individual's response to a changing environment (i.e., from the bottom-up), driven by key ecological processes (e.g., resource memory and territoriality). We drew individual detection data from simulated movement trajectories and fitted detection data sets to a basic, resource selection and transience SCR model, as well as their variants accounting for resource-driven heterogeneity in density and detectability. Across all SCR models, abundance estimates were robust to multiple, but low-degree violations of the specified movement processes (e.g., resource selection). SCR models also successfully captured the positive effect of resource quality on density. However, covariate models failed to capture the finer scale effect of resource quality on detectability and space use, which may be a consequence of the low temporal resolution of SCR data sets and/or model misspecification. We show that home-range size is challenging to infer from the scale parameter alone, compounded by reliance on conventional measures of "true" home-range size that are highly sensitive to sampling regime. Additionally, we found the transience model challenging to fit, probably due to data sparsity and violation of the assumption of normally distributed inter-occasion movement of activity centers, suggesting that further development of the model is required for general applicability. Our results showed that further integration of complex movement into SCR models may not be necessary for population estimates of abundance when the level of individual heterogeneity induced by the underlying movement process is low, but appears warranted in terms of accurately revealing finer scale patterns of ecological and movement processes. Further investigation into whether this holds true in populations with other types of realistic movement characteristics is merited. Our study provides a framework to generate realistic SCR data sets to develop and evaluate more complex movement processes in SCR models.

Time-dependent memory and individual variation in Arctic brown bears (Ursus arctos)

BACKGROUND

Animal movement modelling provides unique insight about how animals perceive their landscape and how this perception may influence space use. When coupled with data describing an animal's environment, ecologists can fit statistical models to location data to describe how spatial memory informs movement.

METHODS

We performed such an analysis on a population of brown bears (Ursus arctos) in the Canadian Arctic using a model incorporating time-dependent spatial memory patterns. Brown bear populations in the Arctic lie on the periphery of the species' range, and as a result endure harsh environmental conditions. In this kind of environment, effective use of memory to inform movement strategies could spell the difference between survival and mortality.

RESULTS

The model we fit tests four alternate hypotheses (some incorporating memory; some not) against each other, and we found a high degree of individual variation in how brown bears used memory. We found that 71% (15 of 21) of the bears used complex, time-dependent spatial memory to inform their movement decisions.

CONCLUSIONS

These results, coupled with existing knowledge on individual variation in the population, highlight the diversity of foraging strategies for Arctic brown bears while also displaying the inference that can be drawn from this innovative movement model.

Memory drives the formation of animal home ranges: Evidence from a reintroduction

Most animals live in home ranges, and memory is thought to be an important process in their formation. However, a general memory-based model for characterising and predicting home range emergence has been lacking. Here, we use a mechanistic movement model to: (1) quantify the role of memory in the movements of a large mammal reintroduced into a novel environment, and (2) predict observed patterns of home range emergence in this experimental setting. We show that an interplay between memory and resource preferences is the primary process influencing the movements of reintroduced roe deer (Capreolus capreolus). Our memory-based model fitted with empirical data successfully predicts the formation of home ranges, as well as emergent properties of movement and spatial revisitation observed in the reintroduced animals. These results provide a mechanistic framework for combining memory-based movements, resource preferences, and the formation of home ranges in nature.

Economical defence of resources structures territorial space use in a cooperative carnivore

Ecologists have long sought to understand space use and mechanisms underlying patterns observed in nature. We developed an optimality landscape and mechanistic territory model to understand mechanisms driving space use and compared model predictions to empirical reality. We demonstrate our approach using grey wolves (Canis lupus). In the model, simulated animals selected territories to economically acquire resources by selecting patches with greatest value, accounting for benefits, costs and trade-offs of defending and using space on the optimality landscape. Our approach successfully predicted and explained first- and second-order space use of wolves, including the population's distribution, territories of individual packs, and influences of prey density, competitor density, human-caused mortality risk and seasonality. It accomplished this using simple behavioural rules and limited data to inform the optimality landscape. Results contribute evidence that economical territory selection is a mechanistic bridge between space use and animal distribution on the landscape. This approach and resulting gains in knowledge enable predicting effects of a wide range of environmental conditions, contributing to both basic ecological understanding of natural systems and conservation. We expect this approach will demonstrate applicability across diverse habitats and species, and that its foundation can help continue to advance understanding of spatial behaviour.

Hierarchical, Memory-Based Movement Models for Translocated Elk (Cervus canadensis)

The use of spatial memory is well-documented in many animal species and has been shown to be critical for the emergence of spatial learning. Adaptive behaviors based on learning can emerge thanks to an interdependence between the acquisition of information over time and movement decisions. The study of how spatio-ecological knowledge is constructed throughout the life of an individual has not been carried out in a quantitative and comprehensive way, hindered by the lack of knowledge of the information an animal already has of its environment at the time monitoring begins. Identifying how animals use memory to make beneficial decisions is fundamental to developing a general theory of animal movement and space use. Here we propose several mobility models based on memory and perform hierarchical Bayesian inference on 11-month trajectories of 21 elk after they were released in a completely new environment. Almost all the observed animals exhibited preferential returns to previously visited patches, such that memory and random exploration phases occurred. Memory decay was mild or negligible over the study period. The fact that individual elk rapidly become used to a relatively small number of patches was consistent with the hypothesis that they seek places with predictable resources and reduced mortality risks such as predation.

Learning and Animal Movement

Integrating diverse concepts from animal behavior, movement ecology, and machine learning, we develop an overview of the ecology of learning and animal movement. Learning-based movement is clearly relevant to ecological problems, but the subject is rooted firmly in psychology, including a distinct terminology. We contrast this psychological origin of learning with the task-oriented perspective on learning that has emerged from the field of machine learning. We review conceptual frameworks that characterize the role of learning in movement, discuss emerging trends, and summarize recent developments in the analysis of movement data. We also discuss the relative advantages of different modeling approaches for exploring the learning-movement interface. We explore in depth how individual and social modalities of learning can matter to the ecology of animal movement, and highlight how diverse kinds of field studies, ranging from translocation efforts to manipulative experiments, can provide critical insight into the learning process in animal movement.

Transient disease dynamics across ecological scales

Analyses of transient dynamics are critical to understanding infectious disease transmission and persistence. Identifying and predicting transients across scales, from within-host to community-level patterns, plays an important role in combating ongoing epidemics and mitigating the risk of future outbreaks. Moreover, greater emphases on non-asymptotic processes will enable timely evaluations of wildlife and human diseases and lead to improved surveillance efforts, preventive responses, and intervention strategies. Here, we explore the contributions of transient analyses in recent models spanning the fields of epidemiology, movement ecology, and parasitology. In addition to their roles in predicting epidemic patterns and endemic outbreaks, we explore transients in the contexts of pathogen transmission, resistance, and avoidance at various scales of the ecological hierarchy. Examples illustrate how (i) transient movement dynamics at the individual host level can modify opportunities for transmission events over time; (ii) within-host energetic processes often lead to transient dynamics in immunity, pathogen load, and transmission potential; (iii) transient connectivity between discrete populations in response to environmental factors and outbreak dynamics can affect disease spread across spatial networks; and (iv) increasing species richness in a community can provide transient protection to individuals against infection. Ultimately, we suggest that transient analyses offer deeper insights and raise new, interdisciplinary questions for disease research, consequently broadening the applications of dynamical models for outbreak preparedness and management.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12080-021-00514-w.

Evidence of economical territory selection in a cooperative carnivore

As an outcome of natural selection, animals are probably adapted to select territories economically by maximizing benefits and minimizing costs of territory ownership. Theory and empirical precedent indicate that a primary benefit of many territories is exclusive access to food resources, and primary costs of defending and using space are associated with competition, travel and mortality risk. A recently developed mechanistic model for economical territory selection provided numerous empirically testable predictions. We tested these predictions using location data from grey wolves (Canis lupus) in Montana, USA. As predicted, territories were smaller in areas with greater densities of prey, competitors and low-use roads, and for groups of greater size. Territory size increased before decreasing curvilinearly with greater terrain ruggedness and harvest mortalities. Our study provides evidence for the economical selection of territories as a causal mechanism underlying ecological patterns observed in a cooperative carnivore. Results demonstrate how a wide range of environmental and social conditions will influence economical behaviour and resulting space use. We expect similar responses would be observed in numerous territorial species. A mechanistic approach enables understanding how and why animals select particular territories. This knowledge can be used to enhance conservation efforts and more successfully predict effects of conservation actions.

Reconstructing the Intrinsic Statistical Properties of Intermittent Locomotion Through Corrections for Boundary Effects

Locomotion characteristics are often recorded within bounded spaces, a constraint which introduces geometry-specific biases and potentially complicates the inference of behavioural features from empirical observations. We describe how statistical properties of an uncorrelated random walk, namely the steady-state stopping location probability density and the empirical step probability density, are affected by enclosure in a bounded space. The random walk here is considered as a null model for an organism moving intermittently in such a space, that is, the points represent stopping locations and the step is the displacement between them. Closed-form expressions are derived for motion in one dimension and simple two-dimensional geometries, in addition to an implicit expression for arbitrary (convex) geometries. For the particular choice of no-go boundary conditions, we demonstrate that the empirical step distribution is related to the intrinsic step distribution, i.e. the one we would observe in unbounded space, via a multiplicative transformation dependent solely on the boundary geometry. This conclusion allows in practice for the compensation of boundary effects and the reconstruction of the intrinsic step distribution from empirical observations.

Animal intermittent locomotion: A null model for the probability of moving forward in bounded space

We present a null model to be compared with biological data to test for intrinsic persistence in movement between stops during intermittent locomotion in bounded space with different geometries and boundary conditions. We describe spatio-temporal properties of the sequence of stopping points r₁,r₂,r₃,… visited by a Random Walker within a bounded space. The path between stopping points is not considered, only the displacement. Since there are no intrinsic correlations in the displacements between stopping points, there is no intrinsic persistence in the movement between them. Hence, this represents a null-model against which to compare empirical data for directional persistence in the movement between stopping points when there is external bias due to the bounded space. This comparison is a necessary first step in testing hypotheses about the function of the stops that punctuate intermittent locomotion in diverse organisms. We investigate the probability of forward movement, defined as a deviation of less than 90° between two successive displacement vectors, as a function of the ratio between the largest displacement between stops that could be performed by the random walker and the system size, α=Δℓ/L_max. As expected, the probability of forward movement is 1/2 when α→0. However, when α is finite, this probability is less than 1/2 with a minimum value when α=1. For certain boundary conditions, the minimum value is between 1/3 and 1/4 in 1D while it can be even lower in 2D. The probability of forward movement in 1D is calculated exactly for all values 0<α⩽1 for several boundary conditions. Analytical calculations for the probability of forward movement are performed in 2D for circular and square bounded regions with one boundary condition. Numerical results for all values 0<α⩽1 are presented for several boundary conditions. The cases of rectangle and ellipse are also considered and an approximate model of the dependence of the forward movement probability on the aspect ratio is provided. Finally, some practical points are presented on how these results can be utilised in the empirical analysis of animal movement in two-dimensional bounded space.

A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns

We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many species and more general kinds of dispersal. We first consider diffusive instabilities, determining that for directed motion along fecundity gradients, the model permits the Turing instability leading to colony formation and persistence provided there are three or more interacting species. We also prove that such patterning is not possible in the model under the Turing mechanism for two species under directed motion along fecundity gradients, confirming earlier findings in the literature. However, when the directed motion is not along fecundity gradients, for instance, if foraging or migration is sub-optimal relative to fecundity gradients, we find that very different colony structures can emerge. This generalization also permits colony formation for two interacting species. In the advection-dominated case, aggregation patterns are more broad and global in nature, due to the inherent non-local nature of the advection which permits directed motion over greater distances, whereas in the diffusion-dominated case, more highly localized patterns and colonies develop, owing to the localized nature of random diffusion. We also consider the interplay between Turing patterning and spatial heterogeneity in resources. We find that for small spatial variations, there will be a combination of Turing patterns and patterning due to spatial forcing from the resources, whereas for large resource variations, spatial or spatiotemporal patterning can be modified greatly from what is predicted on homogeneous domains. For each of these emergent behaviors, we outline the theoretical mechanism leading to colony formation and then provide numerical simulations to illustrate the results. We also discuss implications this model has for studies of directed motion in different ecological settings.

A mechanistic, stigmergy model of territory formation in solitary animals: Territorial behavior can dampen disease prevalence but increase persistence

Although movement ecology has leveraged models of home range formation to explore the effects of spatial heterogeneity and social cues on movement behavior, disease ecology has yet to integrate these potential drivers and mechanisms of contact behavior into a generalizable disease modeling framework. Here we ask how dynamic territory formation and maintenance might contribute to disease dynamics in a territorial, solitary predator for an indirectly transmitted pathogen. We developed a mechanistic individual-based model where stigmergy—the deposition of signals into the environment (e.g., scent marking, scraping)—dictates local movement choices and long-term territory formation, but also the risk of pathogen transmission. Based on a variable importance analysis, the length of the infectious period was the single most important variable in predicting outbreak success, maximum prevalence, and outbreak duration. Host density and rate of pathogen decay were also key predictors. We found that territoriality best reduced maximum prevalence in conditions where we would otherwise expect outbreaks to be most successful: slower recovery rates (i.e., longer infectious periods) and higher conspecific densities. However, for slower pathogen decay rates, stigmergy-driven movement increased outbreak durations relative to random movement simulations. Our findings therefore support a limited version of the “territoriality benefits” hypothesis—where reduced home range overlap leads to reduced opportunities for pathogen transmission, but with the caveat that reduction in outbreak severity may increase the likelihood of pathogen persistence. For longer infectious periods and higher host densities, key trade-offs emerged between the strength of pathogen load, the strength of the stigmergy cue, and the rate at which those two quantities decayed; this finding raises interesting questions about the evolutionary nature of these competing processes and the role of possible feedbacks between parasitism and territoriality. This work also highlights the importance of considering social cues as part of the movement landscape in order to better understand the consequences of individual behaviors on population level outcomes.

Making decisions about conservation and disease management relies on our understanding of what allows animal populations to be successful, which often depends on when and where animals encounter each other. However, disease ecology often focuses on the social behavior of animals without accounting for their individual movement patterns. We developed a simulation model that bridges the fields of disease and movement ecology by allowing hosts to inform their movement based on the past movements of other hosts. As hosts navigate their environment, they leave behind a scent trail while avoiding the scent trails of other individuals. We wanted to know if this means of territory formation could heighten or dampen disease spread when infectious hosts leave pathogens in their wake. We found that territoriality can inhibit disease spread under conditions that we would normally expect pathogens to be most successful: when there are many hosts on the landscape and hosts stay infectious for longer. This work points to how incorporating movement behavior into disease models can provide improved understanding of how diseases spread in wildlife populations; such understanding is particularly important in the face of combatting ongoing and emerging infectious diseases.

Testosterone-related behavioral and neural mechanisms associated with location preferences: A model for territorial establishment

Territoriality is an adaptive behavioral trait that is important for animal's fitness and there still remains much to learn about the proximate mechanisms underlying the development of territoriality. We speculate that the formation of a conditioned place preference (CPP), an increased time allocation to the environment where a rewarding experience occurred, contributes to territoriality. Testosterone (T) plays an important role in modulating territorial behaviors and T pulses can induce a CPP. We confirmed previous findings in California mice (Peromyscus californicus) that T pulses can induce a CPP in singly-housed, but not group-housed males. Housing singly may be similar enough to dispersal in nature to initiate similar hormonal and neuroanatomical changes needed for the development of territoriality. We further revealed that T pulses interact with the single housing experience and appear to enhance the motivation to be aggressive towards a stimulus male. On a neural level, being singly housed upregulated levels of androgen receptors in the preoptic area, which positively correlated with the strength of the CPP. We speculate that this change in androgen sensitivity in the preoptic area is characteristic of males that have dispersed, making them more sensitive to T pulses. Also, single housing increased markers of synaptic plasticity in the nucleus accumbens, ventral and dorsal hippocampus, neural changes that may be associated with dispersal, reproduction and territory establishment. These behavioral and neural changes may reflect the life history transition from residing in the natal territory to dispersing and establishing a new territory.

Optimizing the use of biologgers for movement ecology research

The paradigm-changing opportunities of biologging sensors for ecological research, especially movement ecology, are vast, but the crucial questions of how best to match the most appropriate sensors and sensor combinations to specific biological questions and how to analyse complex biologging data, are mostly ignored. Here, we fill this gap by reviewing how to optimize the use of biologging techniques to answer questions in movement ecology and synthesize this into an Integrated Biologging Framework (IBF). We highlight that multisensor approaches are a new frontier in biologging, while identifying current limitations and avenues for future development in sensor technology. We focus on the importance of efficient data exploration, and more advanced multidimensional visualization methods, combined with appropriate archiving and sharing approaches, to tackle the big data issues presented by biologging. We also discuss the challenges and opportunities in matching the peculiarities of specific sensor data to the statistical models used, highlighting at the same time the large advances which will be required in the latter to properly analyse biologging data. Taking advantage of the biologging revolution will require a large improvement in the theoretical and mathematical foundations of movement ecology, to include the rich set of high-frequency multivariate data, which greatly expand the fundamentally limited and coarse data that could be collected using location-only technology such as GPS. Equally important will be the establishment of multidisciplinary collaborations to catalyse the opportunities offered by current and future biologging technology. If this is achieved, clear potential exists for developing a vastly improved mechanistic understanding of animal movements and their roles in ecological processes and for building realistic predictive models.

Spatial Memory and Taxis-Driven Pattern Formation in Model Ecosystems

Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births and deaths are negligible. This phenomenon is particularly prevalent in populations of larger, vertebrate animals who often reproduce only once per year or less. To understand spatial arrangements of animal communities on such timescales, we use a class of diffusion-taxis equations for modelling inter-population movement responses between [Formula: see text] populations. These systems of equations incorporate the effect on animal movement of both the current presence of other populations and the memory of past presence encoded either in the environment or in the minds of animals. We give general criteria for the spontaneous formation of both stationary and oscillatory patterns, via linear pattern formation analysis. For [Formula: see text], we classify completely the pattern formation properties using a combination of linear analysis and nonlinear energy functionals. In this case, the only patterns that can occur asymptotically in time are stationary. However, for [Formula: see text], oscillatory patterns can occur asymptotically, giving rise to a sequence of period-doubling bifurcations leading to patterns with no obvious regularity, a hallmark of chaos. Our study highlights the importance of understanding between-population animal movement for understanding spatial species distributions, something that is typically ignored in species distribution modelling, and so develops a new paradigm for spatial population dynamics.

SiMRiv: an R package for mechanistic simulation of individual, spatially-explicit multistate movements in rivers, heterogeneous and homogeneous spaces incorporating landscape bias

BACKGROUND

Lack of suitable analytical software and computational power constrains the comprehension of animal movement. In particular, we are aware of no tools allowing simulating spatially-explicit multistate Markovian movements constrained to linear features or conditioned by landscape heterogeneity, which hinders movement ecology research in linear/dendritic (e.g. river networks) and heterogeneous landscapes.SiMRiv is a novel, fast and intuitive R package we designed to fill such gap. It does so by allowing continuous-space mechanistic spatially-explicit simulation of multistate Markovian individual movements incorporating landscape bias on local behavior.

RESULTS

We present SiMRiv and its main functionalities, illustrate its simulation capabilities and easy-of-use, and discuss its limitations and potential improvements. We further provide examples of use and a preliminary evaluation, using real and simulated data, of a parameter approximation experimental method. SiMRiv allowed us to generate increasingly complex movements of three theoretical species (aquatic, semiaquatic and terrestrial), showing the effects of input parameters and water-dependence on emerging movement patterns, and to parameterize a high-frequency simulation model from real, low-frequency movement (telemetry) data. Typical running times for conducting 1000 simulations with 10,000 steps each, of two-state movement trajectories in a river network, were of ca. 3 min in an Intel Core i7 CPU X990 @ 3.47 GHz.

CONCLUSIONS

SiMRiv allows simulation of movements constrained to linear habitats or conditioned by landscape heterogeneity, therefore enhancing the application of movement ecology to linear/dendritic and heterogeneous landscapes. Importantly, the software is flexible enough to be used in linear, heterogeneous, as well as homogeneous landscapes. Using the same software, algorithm and approach, one can therefore use SiMRiv to study the movement of different organisms in a variety of landscapes, facilitating comparative research.SiMRiv balances ease and speed with high realism of the movement models obtainable, constituting a fast, powerful, yet intuitive tool, which should contribute exploring several movement-related questions. Its applications depart from the generation of mechanistic null movement models, up to population level (e.g. landscape connectivity) analyses, holding potential for all fields requiring the simulation of random trajectories.

Resource-Area-Dependence Analysis: Inferring animal resource needs from home-range and mapping data

An animal's home-range can be expected to encompass the resources it requires for surviving or reproducing. Thus, animals inhabiting a heterogeneous landscape, where resource patches vary in size, shape and distribution, will naturally have home-ranges of varied sizes, so that each home-range encompasses a minimum required amount of a resource. Home-range size can be estimated from telemetry data, and often key resources, or proxies for them such as the areas of important habitat types, can be mapped. We propose a new method, Resource-Area-Dependence Analysis (RADA), which uses a sample of tracked animals and a categorical map to i) infer in which map categories important resources are accessible, ii) within which home range cores they are found, and iii) estimate the mean minimum areas of these map categories required for such resource provision. We provide three examples of applying RADA to datasets of radio-tracked animals from southern England: 15 red squirrels Sciurus vulgaris, 17 gray squirrels S. carolinensis and 114 common buzzards Buteo buteo. The analyses showed that each red squirrel required a mean (95% CL) of 0.48 ha (0.24--0.97) of pine wood within the outermost home-range, each gray squirrel needed 0.34 ha (0.11-1.12) ha of mature deciduous woodland and 0.035-0.046 ha of wheat, also within the outermost home-range, while each buzzard required 0.54 ha (0.35-0.82) of rough ground close to the home-range center and 14 ha (11-17) of meadow within an intermediate core, with 52% of them also relying on 0.41 ha (0.29-0.59) of suburban land near the home-range center. RADA thus provides a useful tool to infer key animal resource requirements during studies of animal movement and habitat use.

How ecology shapes exploitation: a framework to predict the behavioural response of human and animal foragers along exploration-exploitation trade-offs

Understanding how humans and other animals behave in response to changes in their environments is vital for predicting population dynamics and the trajectory of coupled social-ecological systems. Here, we present a novel framework for identifying emergent social behaviours in foragers (including humans engaged in fishing or hunting) in predator-prey contexts based on the exploration difficulty and exploitation potential of a renewable natural resource. A qualitative framework is introduced that predicts when foragers should behave territorially, search collectively, act independently or switch among these states. To validate it, we derived quantitative predictions from two models of different structure: a generic mathematical model, and a lattice-based evolutionary model emphasising exploitation and exclusion costs. These models independently identified that the exploration difficulty and exploitation potential of the natural resource controls the social behaviour of resource exploiters. Our theoretical predictions were finally compared to a diverse set of empirical cases focusing on fisheries and aquatic organisms across a range of taxa, substantiating the framework's predictions. Understanding social behaviour for given social-ecological characteristics has important implications, particularly for the design of governance structures and regulations to move exploited systems, such as fisheries, towards sustainability. Our framework provides concrete steps in this direction.

What do territory owners defend against?

Theoretical research on evolutionary aspects of territoriality has a long history. Existing studies, however, differ widely in modelling approach and research question. A generalized view on the evolution of territoriality is accordingly still missing. In this review, we show that territorial conflicts can be classified into qualitatively distinct types according to what mode of access to a territory which competitor attempts to gain. We argue that many of the inconsistencies between existing studies can be traced back to the fact that, while using the same terminology, different instances of these types of conflicts have been investigated. We discuss the connections of each type of conflict to existing research within the wider area of animal conflicts. We conclude that a clear conceptual separation of different types of territorial conflicts is helpful but that a more general theory of territoriality has to account for interdependencies between them and that a more mechanistic approach to modelling territoriality is needed.

A camera-based method for estimating absolute density in animals displaying home range behaviour

The measurement of animal density may take advantage of recent technological achievements in wildlife video recording. Fostering the theoretical links between the patterns depicted by cameras and absolute density is required to exploit this potential. We explore the applicability of the Hutchinson-Waser's postulate (i.e. when animal density is stationary at a given temporal and spatial scale, the absolute density is given by the average number of animals counted per frame), which is a counter-intuitive statement for most ecologists and managers who are concerned with counting the same individual more than once. We aimed to reconcile such scepticism for animals displaying home range behaviour. The specific objectives of this paper are to generalize the Hutchinson-Waser's postulate for animals displaying home range behaviour and to propose a Bayesian implementation to estimate density from counts per frame using video cameras. Accuracy and precision of the method was evaluated by means of computer simulation experiments. Specifically, six animal archetypes displaying well-contrasted movement features were considered. The simulation results demonstrate that density could be accurately estimated after an affordable sampling effort (i.e. number of cameras and deployment time) for a great number of animals across taxa. The proposed method may complement other conventional methods for estimating animal density. The major advantages are that identifying an animal at the individual level and precise knowledge on how animals move are not needed, and that density can be estimated in a single survey. The method can accommodate conventional camera trapping data. The major limitations are related to some implicit assumptions of the underlying model: the home range centres should be homogeneously distributed, the detection probability within the area surveyed by the camera should be known, and animals should move independently to one another. Further improvements for circumventing these limitations are discussed.

How memory of direct animal interactions can lead to territorial pattern formation

Mechanistic home range analysis (MHRA) is a highly effective tool for understanding spacing patterns of animal populations. It has hitherto focused on populations where animals defend their territories by communicating indirectly, e.g. via scent marks. However, many animal populations defend their territories using direct interactions, such as ritualized aggression. To enable application of MHRA to such populations, we construct a model of direct territorial interactions, using linear stability analysis and energy methods to understand when territorial patterns may form. We show that spatial memory of past interactions is vital for pattern formation, as is memory of 'safe' places, where the animal has visited but not suffered recent territorial encounters. Additionally, the spatial range over which animals make decisions to move is key to understanding the size and shape of their resulting territories. Analysis using energy methods, on a simplified version of our system, shows that stability in the nonlinear system corresponds well to predictions of linear analysis. We also uncover a hysteresis in the process of territory formation, so that formation may depend crucially on initial space-use. Our analysis, in one dimension and two dimensions, provides mathematical groundwork required for extending MHRA to situations where territories are defended by direct encounters.

Social behavioural epistemology and the scientific community

The progress of science is influenced substantially by social behaviour of and social interactions within the scientific community. Similar to innovations in primate groups, the social acceptance of an innovation depends not only upon the relevance of the innovation but also on the social dominance and connectedness of the innovator. There are a number of parallels between many well-known phenomena in behavioural evolution and various behavioural traits observed in the scientific community. It would be useful, therefore, to use principles of behavioural evolution as hypotheses to study the social behaviour of the scientific community. I argue in this paper that a systematic study of social behavioural epistemology is likely to boost the progress of science by addressing several prevalent biases and other problems in scientific communication and by facilitating appropriate acceptance/rejection of novel concepts.

Partial differential equation techniques for analysing animal movement: A comparison of different methods

Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement.