How range residency and long-range perception change encounter rates

How resource abundance and resource stochasticity affect organisms' range sizes

BACKGROUND

From megafauna to amoebas, the amount of space heterotrophic organisms use is thought to be tightly linked to the availability of resources within their habitats, such that organisms living in productive habitats generally require less space than those in resource-poor habitats. This hypothesis has widespread empirical support, but existing studies have focused primarily on responses to spatiotemporal changes in mean resources, while responses to unpredictable changes in resources (i.e., variance in resources or resource stochasticity) are still largely unknown. Since organisms adjust to variable environmental conditions, failing to consider the effects of resource unpredictability can result in an insufficient understanding of an organism's range size.

METHODS

We leverage the available literature to provide a unifying framework and hypothesis for the effects of resource abundance and stochasticity on organisms' range sizes. We then use simulated movement data to demonstrate how the combined effects of resource abundance and stochasticity interact to shape predictable patterns in range size. Finally, we test the hypothesis using real-world tracking data on a lowland tapir (Tapirus terrestris) from the Brazilian Cerrado.

RESULTS

Organisms' range sizes decrease nonlinearly with resource abundance and increase nonlinearly with resource stochasticity, and the effects of resource stochasticity depend strongly on resource abundance. Additionally, the distribution and predictability of resources can exacerbate the effects of other drivers of movement, such as resource depletion, competition, and predation.

CONCLUSIONS

Accounting for resource abundance and stochasticity is crucial for understanding the movement behavior of free-ranging organisms. Failing to account for resource stochasticity can lead to an incomplete and incorrect understanding of how and why organisms move, particularly during periods of rapid change.

Nonlocal models in biology and life sciences: Sources, developments, and applications

Mathematical modeling is one of the fundamental techniques for understanding biophysical mechanisms in developmental biology. It helps researchers to analyze complex physiological processes and connect like a bridge between theoretical and experimental observations. Various groups of mathematical models have been studied to analyze these processes, and the nonlocal models are one of them. Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances (e.g., cell-cell, cell-tissue adhesions, neural networks, the spread of diseases, intra-specific competition, nanobeams, etc.). This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including brain dynamics models that provide an important tool to understand neurodegenerative diseases better. In addition, we have discussed nonlocal modeling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales, including nanotechnology, where classical local models often fail to capture the complexities of nanoscale interactions, applied to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.

How do non-independent host movements affect spatio-temporal disease dynamics? Partitioning the contributions of spatial overlap and correlated movements to transmission risk

BACKGROUND

Despite decades of epidemiological theory making relatively simple assumptions about host movements, it is increasingly clear that non-random movements drastically affect disease transmission. To better predict transmission risk, theory is needed that quantifies the contributions of both fine-scale host space use and non-independent, correlated host movements to epidemiological dynamics.

METHODS

We developed and applied new theory that quantifies relative contributions of fine-scale space use and non-independent host movements to spatio-temporal transmission risk. Our theory decomposes pairwise spatio-temporal transmission risk into two components: (i) spatial overlap of hosts-a classic metric of spatial transmission risk - and (ii) pairwise correlations in space use - a component of transmission risk that is almost universally ignored. Using analytical results, simulations, and empirical movement data, we ask: under what ecological and epidemiological conditions do non-independent movements substantially alter spatio-temporal transmission risk compared to spatial overlap?

RESULTS

Using theory and simulation, we found that for directly transmitted pathogens even weak pairwise correlations in space use among hosts can increase contact and transmission risk by orders of magnitude compared to independent host movements. In contrast, non-independent movements had reduced importance for transmission risk for indirectly transmitted pathogens. Furthermore, we found that if the scale of pathogen transmission is smaller than the scale where host social decisions occur, host movements can be highly correlated but this correlation matters little for transmission. We applied our theory to GPS movement data from white-tailed deer (Odocoileus virginianus). Our approach predicted highly seasonally varying contributions of the spatial and social drivers of transmission risk - with social interactions augmenting transmission risk between hosts by greater than a factor of 10 in some cases, despite similar degrees of spatial overlap. Moreover, social interactions could lead to a distinct shift in the predicted locations of transmission hotspots, compared to joint space use.

CONCLUSIONS

Our theory provides clear expectations for when non-independent movements alter spatio-temporal transmission risk, showing that correlated movements can reshape epidemiological landscapes, creating transmission hotspots whose magnitude and location are not necessarily predictable from spatial overlap.

An evolutionary game theory for event-driven ecological population dynamics

Despite being a powerful tool to model ecological interactions, traditional evolutionary game theory can still be largely improved in the context of population dynamics. One of the current challenges is to devise a cohesive theoretical framework for ecological games with density-dependent (or concentration-dependent) evolution, especially one defined by individual-level events. In this work, I use the notation of reaction networks as a foundation to propose a framework and show that classic two-strategy games are a particular case of the theory. The framework exhibits a strong versatility and provides a standardized language for model design, and I demonstrate its use through a simple example of mating dynamics and parental care. In addition, reaction networks provide a natural connection between stochastic and deterministic dynamics and therefore are suitable to model noise effects on small populations, also allowing the use of stochastic simulation algorithms such as Gillespie's with game models. The methods I present can help to bring evolutionary game theory to new reaches in ecology, facilitate the process of model design, and put different models on a common ground.

Intraspecific encounters can lead to reduced range overlap

Direct encounters, in which two or more individuals are physically close to one another, are a topic of increasing interest as more and better movement data become available. Recent progress, including the development of statistical tools for estimating robust measures of changes in animals' space use over time, facilitates opportunities to link direct encounters between individuals with the long-term consequences of those encounters. Working with movement data for coyotes (Canis latrans) and grizzly bears (Ursus arctos horribilis), we investigate whether close intraspecific encounters were associated with spatial shifts in the animals' range distributions, as might be expected if one or both of the individuals involved in an encounter were seeking to reduce or avoid conflict over space. We analyze the movement data of a pair of coyotes in detail, identifying how a change in home range overlap resulting from altered movement behavior was apparently a consequence of a close intraspecific encounter. With grizzly bear movement data, we approach the problem as population-level hypothesis tests of the spatial consequences of encounters. We find support for the hypotheses that (1) close intraspecific encounters between bears are, under certain circumstances, associated with subsequent changes in overlap between range distributions and (2) encounters defined at finer spatial scales are followed by greater changes in space use. Our results suggest that animals can undertake long-term, large-scale spatial changes in response to close intraspecific encounters that have the potential for conflict. Overall, we find that analyses of movement data in a pairwise context can (1) identify distances at which individuals' proximity to one another may alter behavior and (2) facilitate testing of population-level hypotheses concerning the potential for direct encounters to alter individuals' space use.

Sequential epidemic-like spread between agglomerates of self-propelled agents in one dimension

Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate between them, and disease recovery rate. While the emergence of agglomerates permits early interventions, it also explains longer real epidemics. In this work, we study the spread of susceptible-infected-recovered (SIR) epidemics (or any sort of information exchange by contact) in one-dimensional spatially structured systems. By working in one dimension, we establish a necessary foundation for future investigation in higher dimensions and mimic micro-organisms in narrow channels. We employ a model of self-propelled particles which spontaneously form multiple clusters. For a lower rate of stochastic reorientation, particles have a higher tendency to agglomerate and therefore the clusters become larger and less numerous. We examine the time evolution averaged over many epidemics and how it is affected by the existence of clusters through the eventual recovery of infected particles before reaching new clusters. New terms appear in the SIR differential equations in the last epidemic stages. We show how the final number of ever-infected individuals depends nontrivially on single-individual parameters. In particular, the number of ever-infected individuals first increases with the reorientation rate since particles escape sooner from clusters and spread the disease. For higher reorientation rate, travel between clusters becomes too diffusive and the clusters too small, decreasing the number of ever-infected individuals.

Reinforced diffusions as models of memory-mediated animal movement

How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies suggest that memory has both temporal and spatial components, and can include both attractive and aversive elements. Here, we introduce reinforced diffusions (the continuous time counterpart of reinforced random walks) as a modelling framework for understanding the role that memory plays in determining animal movements. This framework includes reinforcement via functions of time before present and of distance away from a current location. Focusing on the interplay between memory and central place attraction (a component of home ranging behaviour), we explore patterns of space usage that result from the reinforced diffusion. Our efforts identify three qualitatively different behaviours: bounded wandering behaviour that does not collapse spatially, collapse to a very small area, and, most intriguingly, convergence to a cycle. Subsequent applications show how reinforced diffusion can create movement trajectories emulating the learning of movement routes by homing pigeons and consolidation of ant travel paths. The mathematically explicit manner with which assumptions about the structure of memory can be stated and subsequently explored provides linkages to biological concepts like an animal's 'immediate surroundings' and memory decay.

Deriving spatially explicit direct and indirect interaction networks from animal movement data

Quantifying spatiotemporally explicit interactions within animal populations facilitates the understanding of social structure and its relationship with ecological processes. Data from animal tracking technologies (Global Positioning Systems ["GPS"]) can circumvent longstanding challenges in the estimation of spatiotemporally explicit interactions, but the discrete nature and coarse temporal resolution of data mean that ephemeral interactions that occur between consecutive GPS locations go undetected. Here, we developed a method to quantify individual and spatial patterns of interaction using continuous-time movement models (CTMMs) fit to GPS tracking data. We first applied CTMMs to infer the full movement trajectories at an arbitrarily fine temporal scale before estimating interactions, thus allowing inference of interactions occurring between observed GPS locations. Our framework then infers indirect interactions-individuals occurring at the same location, but at different times-while allowing the identification of indirect interactions to vary with ecological context based on CTMM outputs. We assessed the performance of our new method using simulations and illustrated its implementation by deriving disease-relevant interaction networks for two behaviorally differentiated species, wild pigs (Sus scrofa) that can host African Swine Fever and mule deer (Odocoileus hemionus) that can host chronic wasting disease. Simulations showed that interactions derived from observed GPS data can be substantially underestimated when temporal resolution of movement data exceeds 30-min intervals. Empirical application suggested that underestimation occurred in both interaction rates and their spatial distributions. CTMM-Interaction method, which can introduce uncertainties, recovered majority of true interactions. Our method leverages advances in movement ecology to quantify fine-scale spatiotemporal interactions between individuals from lower temporal resolution GPS data. It can be leveraged to infer dynamic social networks, transmission potential in disease systems, consumer-resource interactions, information sharing, and beyond. The method also sets the stage for future predictive models linking observed spatiotemporal interaction patterns to environmental drivers.

Foraging behaviour and patch size distribution jointly determine population dynamics in fragmented landscapes

Increased fragmentation caused by habitat loss represents a major threat to the persistence of animal populations. How fragmentation affects populations depends on the rate at which individuals move between spatially separated patches. Whereas negative effects of habitat loss on biodiversity are well known, the effects of fragmentation per se on population dynamics and ecosystem stability remain less well understood. Here, we use a spatially explicit predator-prey model to investigate how the interplay between fragmentation and optimal foraging behaviour affects predator-prey interactions and, subsequently, ecosystem stability. We study systems wherein prey occupies isolated patches and are consumed by predators that disperse following Lévy random walks. Our results show that the Lévy exponent and the degree of fragmentation jointly determine coexistence probabilities. In highly fragmented landscapes, Brownian and ballistic predators go extinct and only scale-free predators can coexist with prey. Furthermore, our results confirm that predation causes irreversible habitat loss in fragmented landscapes owing to overexploitation of smaller patches of prey. Moreover, we show that predator dispersal can reduce, but not prevent or minimize, the amount of lost habitat. Our results suggest that integrating optimal foraging theory into population and landscape ecology is crucial to assessing the impact of fragmentation on biodiversity and ecosystem stability.

Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework

Understanding whether a population will survive or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where migration is usually represented as a linear diffusion term, and birth-death is represented with a nonlinear source term. While linear diffusion is most commonly employed to study migration, there are several limitations of this approach, such as the inability of linear diffusion-based models to predict a well-defined population front. One way to overcome this is to generalize the constant diffusivity, D , to a nonlinear diffusivity function D ( C ) , where C > 0 is the population density. While the choice of D ( C ) affects long-term survival or extinction of a bistable population, working solely in a continuum framework makes it difficult to understand how the choice of D ( C ) affects survival or extinction. We address this question by working with a discrete simulation model that is easy to interpret. This approach provides clear insight into how the choice of D ( C ) either encourages or suppresses population extinction relative to the classical linear diffusion model.

Estimation of the maximum utilization area including home range and peripheral sites

There is increasing evidence that occasional utilization area (peripheral sites), in addition to typical utilization area (home range), is important for wildlife conservation and management. Here we estimated the maximum utilization area (MUA), including both typical and occasional utilization areas, based on asymptotic curves of utilization area plotted against sample size. In previous studies, these curves have conventionally been plots of cumulative utilization area versus sample size, but this cumulative method is sensitive to stochastic effects. We propose a new method based on simulation studies where outcomes of replicated simulations are averaged to reduce stochastic effects. In this averaged method, possible combinations of sample size with the same number of location data replicated from a dataset were averaged and applied to the curves of utilization area. The cumulative method resulted in a large variation of MUA estimates, depending on the start date as well as total sample size of the dataset. In the averaged method, MUA estimates were robust against changes in the start date and total sample size. The large variation of MUA estimates arose because location data on any day including the start date are affected by unpredictable effects associated with animal activity and environmental conditions. In the averaged method, replicates of sample size resulted in a reduction of temporal stochasticity, suggesting that the method stably provides reliable estimates for MUA.

Movement ecology of vulnerable lowland tapirs between areas of varying human disturbance

BACKGROUND

Animal movement is a key ecological process that is tightly coupled to local environmental conditions. While agriculture, urbanisation, and transportation infrastructure are critical to human socio-economic improvement, these have spurred substantial changes in animal movement across the globe with potential impacts on fitness and survival. Notably, however, human disturbance can have differential effects across species, and responses to human activities are thus largely taxa and context specific. As human disturbance is only expected to worsen over the next decade it is critical to better understand how species respond to human disturbance in order to develop effective, case-specific conservation strategies.

METHODS

Here, we use an extensive telemetry dataset collected over 22 years to fill a critical knowledge gap in the movement ecology of lowland tapirs (Tapirus terrestris) across areas of varying human disturbance within three biomes in southern Brazil: the Pantanal, Cerrado, and Atlantic Forest.

RESULTS

From these data we found that the mean home range size across all monitored tapirs was 8.31 km² (95% CI 6.53-10.42), with no evidence that home range sizes differed between sexes nor age groups. Interestingly, although the Atlantic Forest, Cerrado, and Pantanal vary substantially in habitat composition, levels of human disturbance, and tapir population densities, we found that lowland tapir movement behaviour and space use were consistent across all three biomes. Human disturbance also had no detectable effect on lowland tapir movement. Lowland tapirs living in the most altered habitats we monitored exhibited movement behaviour that was comparable to that of tapirs living in a near pristine environment.

CONCLUSIONS

Contrary to our expectations, although we observed individual variability in lowland tapir space use and movement, human impacts on the landscape also had no measurable effect on their movement. Lowland tapir movement behaviour thus appears to exhibit very little phenotypic plasticity in response to human disturbance. Crucially, the lack of any detectable response to anthropogenic disturbance suggests that human modified habitats risk being ecological traps for tapirs and this information should be factored into conservation actions and species management aimed towards protecting lowland tapir populations.

A model for leveraging animal movement to understand spatio-temporal disease dynamics

The ongoing explosion of fine-resolution movement data in animal systems provides a unique opportunity to empirically quantify spatial, temporal and individual variation in transmission risk and improve our ability to forecast disease outbreaks. However, we lack a generalizable model that can leverage movement data to quantify transmission risk and how it affects pathogen invasion and persistence on heterogeneous landscapes. We developed a flexible model 'Movement-driven modelling of spatio-temporal infection risk' (MoveSTIR) that leverages diverse data on animal movement to derive metrics of direct and indirect contact by decomposing transmission into constituent processes of contact formation and duration and pathogen deposition and acquisition. We use MoveSTIR to demonstrate that ignoring fine-scale animal movements on actual landscapes can mis-characterize transmission risk and epidemiological dynamics. MoveSTIR unifies previous work on epidemiological contact networks and can address applied and theoretical questions at the nexus of movement and disease ecology.

Enhanced species coexistence in Lotka-Volterra competition models due to nonlocal interactions

We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the nonlocal interactions. In both cases, nonlocal interactions can create spatial patterns of population densities in which highly populated clumps alternate with unpopulated regions. These non-populated regions provide spatial niches for a weaker competitor to establish in the community and persist in conditions in which local models predict competitive exclusion. Moreover, depending on the balance between local and nonlocal competition intensity, the clumps of the weaker competitor vary from M-like structures with higher densities of individuals accumulating at the edges of each clump to triangular structures with most individuals occupying their centers. These results suggest that long-range competition, through the creation of spatial patterns in population densities, might be a key driving force behind the rich diversity of species observed in natural ecological communities.

Exploring the Evolution of Perception: An Agent-Based Approach

Perception is central to the survival of an individual for many reasons, especially as it affects the ability to gather resources. Consequently, costs associated with perception are partially shaped by resource availability. Understanding the interplay of environmental factors (such as the density and distribution of resources) with species-specific factors (such as growth rate, mutation, and metabolic costs) allows the exploration of possible trajectories by which perception may evolve. Here, we used an agent-based foraging model with a context-dependent movement strategy in which each agent switches between undirected and directed movement based on its perception of resources. This switching behavior is central to our goal of exploring how environmental and species-specific factors determine the evolution and maintenance of perception in an ecological system. We observed a non-linear response in the evolved perceptual ranges as a function of parameters in our model. Overall, we identified two groups of parameters, one of which promotes evolution of perception and another group that restricts it. We found that resource density, basal energy cost, perceptual cost and mutation rate were the best predictors of the resultant perceptual range distribution, but detailed exploration indicated that individual parameters affect different parts of the distribution in different ways.

Jaguar movement behavior: using trajectories and association rule mining algorithms to unveil behavioral states and social interactions

Animal movement data are widely collected with devices such as sensors and collars, increasing the ability of researchers to monitor animal movement and providing information about animal behavioral patterns. Animal behavior is used as a basis for understanding the relationship between animals and the environment and for guiding decision-making by researchers and public agencies about environmental preservation and conservation actions. Animal movement and behavior are widely studied with a focus on identifying behavioral patterns, such as, animal group formation, the distance between animals and their home range. However, we observed a lack of research proposing a unified solution that aggregates resources for analyses of individual animal behavior and of social interactions between animals. The primary scientific contribution of this work is to present a framework that uses trajectory analysis and association rule mining [Jaiswal and Agarwal, 2012] to provide statistical measures of correlation and dependence to determine the relationship level between animals, their social interactions, and their interactions with other environmental factors based on their individual behavior and movement data. We demonstrate the usefulness of the framework by applying it to movement data from jaguars in the Pantanal, Brazil. This allowed us to describe jaguar behavior, social interactions among jaguars and their behavior in different landscapes, thus providing a highly detailed investigation of jaguar movement decisions at the fine scale.

Population dynamics with spatial structure and an Allee effect

Population dynamics including a strong Allee effect describe the situation where long-term population survival or extinction depends on the initial population density. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to extinction, whereas initial densities above the threshold lead to survival. Mean-field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as competition and dispersal. The influence of non-mean-field effects has not been studied in the presence of an Allee effect. To address this, we develop an individual-based model that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure neglected by mean-field models. For example, there are cases where the mean-field model predicts extinction but the population actually survives. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.