Animal space use: distinguishing a two‐level superposition of scale‐specific walks from scale‐free Lévy walk

How to differentiate between scale‐free space use like Lévy walk and a two‐level scale‐specific process like composite random walk (mixture of intra‐ and inter‐patch habitat movement) is surrounded by controversy. Composite random walk may under some parameter conditions appear Lévy walk‐like from the perspective of the path’s distribution of step lengths due to superabundance of very long steps relative to the expectation from a classic (single‐level) random walk. However, a more explicit focus on the qualitative differences between studying movement at a high resolution mechanistic (behavioral) level and the more coarse‐grained statistical mechanical level may contribute to resolving both this and other issues related to scaling complexity. Specifically, a re‐sampling of a composite random walk at larger time lags than the micro‐level unit time step for the simulation makes a Lévy‐look‐alike step length distribution re‐shaping towards a Brownian motion‐like pattern. Conversely, a true Levy walk maintains its scaling characteristics upon re‐sampling. This result illustrates how a confusing pattern at the mechanistic level may be resolved by changing observational scale from the micro level to the coarser statistical mechanical meso‐ or macro‐scale. The instability of the composite random walk pattern under rescaling is a consequence of influence of the central limit theorem. I propose that a coarse‐graining test – studying simulated animal paths at a coarsened temporal scale by re‐sampling a series – should be routinely performed prior to comparing theoretical results with those patterns generated from GPS data describing animal movement paths. Fixes from terrestrial mammals are often collected at hourly intervals or larger, and such a priori coarse‐grained series may thus comply better with the statistical mechanical meso‐ or macro‐level of analysis than the behavioral mechanics observed at finer resolutions typically in the range of seconds and minutes. If fixes of real animals are collected at this high frequency, coarse graining both the simulated and real series is advised in order to bring the analysis into a temporal scale domain where analytical methods from statistical mechanics can be applied.     

Memory keeps you at home: a mechanistic model for home range emergence

Despite its central place in animal ecology no general mechanistic movement model with an emergent home-range pattern has yet been proposed. Random walk models, which are commonly used to model animal movement, show diffusion instead of a bounded home range and therefore require special modifications. Current approaches for mechanistic modeling of home ranges apply only to a limited set of taxa, namely territorial animals and/or central place foragers. In this paper we present a more general mechanistic movement model based on a biased correlated random walk, which shows the potential for home-range behavior. The model is based on an animal tracking a dynamic resource landscape, using a biologically plausible two-part memory system, i.e. a reference- and a working-memory. Our results show that by adding these memory processes the random walker produces home-range behavior as it gains experience, which also leads to more efficient resource use. Interestingly, home-range patterns, which we assessed based on home-range overlap and increase in area covered with time, require the combined action of both memory components to emerge. Our model has the potential to predict home-range size and can be used for comparative analysis of the mechanisms shaping home-range patterns.     

From random walks to informed movement

The analysis of animal movement is a large and continuously growing field of research. Detailed knowledge about movement strategies is of crucial importance for understanding eco‐evolutionary dynamics at all scales – from individuals to (meta‐)populations. This and the availability of detailed movement and dispersal data motivated Nathan and colleagues to published their much appreciated call to base movement ecology on a more thorough mechanistic basis. So far, most movement models are based on random walks. However, even if a random walk might describe real movement patterns acceptably well, there is no reason to assume that animals move randomly. Therefore, mechanistic models of foraging strategies should be based on information use and memory in order to increase our understanding of the processes that lead to animal movement decisions. We present a mechanistic movement model of an animal with a limited perceptual range and basic information storage capacities. This ‘spatially informed forager’ constructs an internal map of its environment by using perception, memory and learned or evolutionarily acquired assumptions about landscape attributes. We analyse resulting movement patterns and search efficiencies and compare them to area restricted search strategies (ARS) and biased correlated random walks (BCRW) of omniscient individuals. We show that, in spite of their limited perceptual range, spatially informed individuals boost their foraging success and may perform much better than the best ARS. The construction of an internal map and the use of spatial information results in the emergence of a highly correlated walk between patches and a rather systematic search within resource clusters. Furthermore, the resulting movement patterns may include foray search behaviour. Our work highlights the strength of mechanistic modelling approaches and sets the stage for the development of more sophisticated models of memory use for movement decisions and dispersal.     

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.     

Step selection techniques uncover the environmental predictors of space use patterns in flocks of Amazonian birds

Understanding the behavioral decisions behind animal movement and space use patterns is a key challenge for behavioral ecology. Tools to quantify these patterns from movement and animal–habitat interactions are vital for transforming ecology into a predictive science. This is particularly important in environments undergoing rapid anthropogenic changes, such as the Amazon rainforest, where animals face novel landscapes. Insectivorous bird flocks are key elements of avian biodiversity in the Amazonian ecosystem. Therefore, disentangling and quantifying the drivers behind their movement and space use patterns is of great importance for Amazonian conservation. We use a step selection function (SSF) approach to uncover environmental drivers behind movement choices. This is used to construct a mechanistic model, from which we derive predicted utilization distributions (home ranges) of flocks. We show that movement decisions are significantly influenced by canopy height and topography, but depletion and renewal of resources do not appear to affect movement significantly. We quantify the magnitude of these effects and demonstrate that they are helpful for understanding various heterogeneous aspects of space use. We compare our results to recent analytic derivations of space use, demonstrating that the analytic approximation is only accurate when assuming that there is no persistence in the animals' movement. Our model can be translated into other environments or hypothetical scenarios, such as those given by proposed future anthropogenic actions, to make predictions of spatial patterns in bird flocks. Furthermore, our approach is quite general, so could potentially be used to understand the drivers of movement and spatial patterns for a wide variety of animal communities.     

Moving GIS Research Indoors: Spatiotemporal Analysis of Agricultural Animals

A proof of concept applying wildlife ecology techniques to animal welfare science in intensive agricultural environments was conducted using non-cage laying hens. Studies of wildlife ecology regularly use Geographic Information Systems (GIS) to assess wild animal movement and behavior within environments with relatively unlimited space and finite resources. However, rather than depicting landscapes, a GIS could be developed in animal production environments to provide insight into animal behavior as an indicator of animal welfare. We developed a GIS-based approach for studying agricultural animal behavior in an environment with finite space and unlimited resources. Concurrent data from wireless body-worn location tracking sensor and video-recording systems, which depicted spatially-explicit behavior of hens (135 hens/room) in two identical indoor enclosures, were collected. The spatial configuration of specific hen behaviors, variation in home range patterns, and variation in home range overlap show that individual hens respond to the same environment differently. Such information could catalyze management practice adjustments (e.g., modifying feeder design and/or location). Genetically-similar hens exhibited diverse behavioral and spatial patterns via a proof of concept approach enabling detailed examinations of individual non-cage laying hen behavior and welfare.     

Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be Lévy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A Lévy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between Lévy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a Lévy walk. However, there is some doubt about the accuracy of early studies that apparently found Lévy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits Lévy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-Lévy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of Lévy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that ‘turns’ or ‘reorientations’ in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-Lévy walks exhibit Lévy-like patterns.     

BEEtag: A Low-Cost,Image-Based Tracking System for the Study of Animal Behavior and Locomotion

A fundamental challenge common to studies of animal movement, behavior, and ecology is the collection of high-quality datasets on spatial positions of animals as they change through space and time. Recent innovations in tracking technology have allowed researchers to collect large and highly accurate datasets on animal spatiotemporal position while vastly decreasing the time and cost of collecting such data. One technique that is of particular relevance to the study of behavioral ecology involves tracking visual tags that can be uniquely identified in separate images or movie frames. These tags can be located within images that are visually complex, making them particularly well suited for longitudinal studies of animal behavior and movement in naturalistic environments. While several software packages have been developed that use computer vision to identify visual tags, these software packages are either (a) not optimized for identification of single tags, which is generally of the most interest for biologists, or (b) suffer from licensing issues, and therefore their use in the study of animal behavior has been limited. Here, we present BEEtag, an open-source, image-based tracking system in Matlab that allows for unique identification of individual animals or anatomical markers. The primary advantages of this system are that it (a) independently identifies animals or marked points in each frame of a video, limiting error propagation, (b) performs well in images with complex backgrounds, and (c) is low-cost. To validate the use of this tracking system in animal behavior, we mark and track individual bumblebees (Bombus impatiens) and recover individual patterns of space use and activity within the nest. Finally, we discuss the advantages and limitations of this software package and its application to the study of animal movement, behavior, and ecology.     

The home range fractal: From random walk to memory-dependent space use

We present theoretical developments of the multi-scaled random walk (MRW) model for cognitive map-influenced space use by animals. The extensions include a unified space–time scaling function, and further details with respect to statistical properties of the spatial distribution of a set of locations. Supported by numeric simulations we show how memory effects may open for a complex, multi-scaled and self-organized – i.e., intrinsically driven – habitat utilization pattern with fractal dimensional properties. These properties allow for testing for MRW compliance by using parameters from classic movement models like Brownian motion, correlated random walk and Levy walks as null models. In terms of applied ecology, empirical confirmation of memory-influenced space use by individuals will have consequences for interpretation and statistical analyses of habitat utilization. For example, under memory map influence, re-visits to intra-home range locations do not represent independent events. Further, the MRW formulation specifically implies home range movements over a continuum of process rates, spanning a range of spatio-temporal scales in parallel, in violation of the traditional low order Markovian (scale-specific) model architecture. The MRW approach requires an extension of classic Boltzmann–Gibbs statistical mechanics, which rests on the premise that spatio-temporal memory effects are averaged out beyond micro-scales. We suggest that the emergent coherence between spatial and temporal scaling from the MRW approach may open for a more realistic statistical mechanics theory for population processes under terms of memory-influenced space use by individuals.     

Understanding movement data and movement processes: current and emerging directions

Animal movement has been the focus on much theoretical and empirical work in ecology over the last 25 years. By studying the causes and consequences of individual movement, ecologists have gained greater insight into the behavior of individuals and the spatial dynamics of populations at increasingly higher levels of organization. In particular, ecologists have focused on the interaction between individuals and their environment in an effort to understand future impacts from habitat loss and climate change. Tools to examine this interaction have included: fractal analysis, first passage time, Lévy flights, multi‐behavioral analysis, hidden markov models, and state‐space models. Concurrent with the development of movement models has been an increase in the sophistication and availability of hierarchical bayesian models. In this review we bring these two threads together by using hierarchical structures as a framework for reviewing individual models. We synthesize emerging themes in movement ecology, and propose a new hierarchical model for animal movement that builds on these emerging themes. This model moves away from traditional random walks, and instead focuses inference on how moving animals with complex behavior interact with their landscape and make choices about its suitability.     

Behavioral states help translate dispersal movements into spatial distribution patterns of floaters

Within the field of spatial ecology, it is important to study animal movements in order to better understand population dynamics. Dispersal is a nonlinear process through which different behavioral mechanisms could affect movement patterns. One of the most common approaches to analyzing the trajectories of organisms within patches is to use random-walk models to describe movement features. These models express individual movements within a specific area in terms of random-walk parameters in an effort to relate movement patterns to the distributions of organisms in space. However, only using the movement trajectories of individuals to predict the spatial spread of animal populations may not fit the complex distribution of individuals across heterogeneous environments. When we empirically tested the results from a random-walk model (a residence index) used to predict the spatial equilibrium distribution of individuals, we found that the index severely underestimated the spatial spread of dispersing individuals. We believe this is because random-walk models only account for the effects of environmental conditions on individual movements, completely overlooking the crucial influence of behavior changes over time. In the future, both aspects should be accounted for when predicting general rules of (meta)population abundance, distribution, and dynamics from patterns of animal movements.     

Inherent high correlation of individual motility enhances population dispersal in a heterotrophic, planktonic protist

Quantitative linkages between individual organism movements and the resulting population distributions are fundamental to understanding a wide range of ecological processes, including rates of reproduction, consumption, and mortality, as well as the spread of diseases and invasions. Typically, quantitative data are collected on either movement behaviors or population distributions, rarely both. This study combines empirical observations and model simulations to gain a mechanistic understanding and predictive ability of the linkages between both individual movement behaviors and population distributions of a single-celled planktonic herbivore. In the laboratory, microscopic 3D movements and macroscopic population distributions were simultaneously quantified in a 1L tank, using automated video- and image-analysis routines. The vertical velocity component of cell movements was extracted from the empirical data and used to motivate a series of correlated random walk models that predicted population distributions. Validation of the model predictions with empirical data was essential to distinguish amongst a number of theoretically plausible model formulations. All model predictions captured the essence of the population redistribution (mean upward drift) but only models assuming long correlation times (minute), captured the variance in population distribution. Models assuming correlation times of 8 minutes predicted the least deviation from the empirical observations. Autocorrelation analysis of the empirical data failed to identify a de-correlation time in the up to 30-second-long swimming trajectories. These minute-scale estimates are considerably greater than previous estimates of second-scale correlation times. Considerable cell-to-cell variation and behavioral heterogeneity were critical to these results. Strongly correlated random walkers were predicted to have significantly greater dispersal distances and more rapid encounters with remote targets (e.g. resource patches, predators) than weakly correlated random walkers. The tendency to disperse rapidly in the absence of aggregative stimuli has important ramifications for the ecology and biogeography of planktonic organisms that perform this kind of random walk.     

Primates got personality,too: Toward an integrative primatology of consistent individual differences in behavior

In recent years, research on animal personality has exploded within the field of behavioral ecology. Consistent individual differences in behavior exist in a wide range of species, and these differences can have fitness consequences and influence several aspects of a species' ecology. In comparison to studies of other animals, however, there has been relatively little research on the behavioral ecology of primate personality. This is surprising given the large body of research within psychology and biomedicine showing that primate personality traits are heritable and linked to health and life history outcomes. In this article, I bring together theoretical perspectives on the ecology and evolution of animal personality with an integrative review of what we know about primate personality from studies conducted on captive, free‐ranging, and wild primates. Incorporating frameworks that emphasize consistency in behavior into primate behavioral ecology research holds promise for improving our understanding of primate behavioral evolution.     

Breeding habitat selection behaviors in heterogeneous environments: implications for modeling reintroduction

Animal movement and habitat selection behavior are important considerations in ecology, and remain a major issue for successful animal reintroductions. However, simple rules are often used to model movement or focus only on intrinsic environmental cues, neglecting recent insights in behavioral ecology on habitat selection processes. In particular, social information has been proposed as a widespread source of information for habitat evaluation.
We investigated the role of explicit breeding habitat selection strategies on the establishment pattern of reintroduced populations and their persistence. We considered local movement at the scale of a single population. We constructed a spatially-implicit demographic model that considered five breeding habitat selection rules: 1) random, 2) intrinsic habitat quality, 3) avoidance of conspecifics, 4) presence of conspecifics and 5) reproductive success of conspecifics. The impact of breeding habitat selection was examined for different release methods under various levels of environmental heterogeneity levels, for both long and short-lived monogamous species.
When heterogeneity between intrinsic habitat patch qualities is high, the persistence of reintroduced populations strongly depends on habitat selection strategies. Strategies based on intrinsic quality and conspecific reproductive success lead to a lower reintroduction failure risk than random, conspecific presence or avoidance-based strategies. Conspecific presence or avoidance-based strategies may aggregate individuals in suboptimal habitats. The release of adults seems to be more efficient independent of habitat selection strategy.
We emphasize the crucial role of oriented habitat selection behavior and non ideal habitat selection in movement modeling, particularly for reintroduction.     

How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein''s original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern.     

Within‐Individual Correlations Reveal Link Between a Behavioral Syndrome,Condition, and Cortisol in Free‐Ranging Belding's Ground Squirrels

Animals often exhibit consistent individual differences in behavior (i.e., animal personality) and correlations between behaviors (i.e., behavioral syndromes), yet the causes of those patterns of behavioral variation remain insufficiently understood. Many authors hypothesize that state‐dependent behavior produces animal personality and behavioral syndromes. However, empirical studies assessing patterns of covariation among behavioral traits and state variables have produced mixed results. New statistical methods that partition correlations into between‐individual and residual within‐individual correlations offer an opportunity to more sufficiently quantify relationships among behaviors and state variables to assess hypotheses of animal personality and behavioral syndromes. In a population of wild Belding's ground squirrels (Urocitellus beldingi), we repeatedly measured activity, exploration, and response to restraint behaviors alongside glucocorticoids and nutritional condition. We used multivariate mixed models to determine whether between‐individual or within‐individual correlations drive phenotypic relationships among traits. Squirrels had consistent individual differences for all five traits. At the between‐individual level, activity and exploration were positively correlated whereas both traits negatively correlated with response to restraint, demonstrating a behavioral syndrome. At the within‐individual level, condition negatively correlated with cortisol, activity, and exploration. Importantly, this indicates that although behavior is state‐dependent, which may play a role in animal personality and behavioral syndromes, feedback mechanisms between condition and behavior appear not to produce consistent individual differences in behavior and correlations between them.     

Dynamical aspects of animal grouping: Swarms,schools, flocks,and herds

Grouping of animals is a natural phenomenon in which a number of animal individuals are involved in movement as forming a group. Examples are insect swarms and fish schools. In this article an attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes. Also presented is dynamical modeling for the group size distribution as a result of amalgamation and splitting processes of groups.Examples of animal grouping are described in detail. They are insect swarms, zooplankton swarms, fish schools, bird flocks, and mammal herds. The presented mathematical models are compared with data of these animal groupings.     

“Micropersonality” traits and their implications for behavioral and movement ecology research

1. Many animal personality traits have implicit movement‐based definitions and can directly or indirectly influence ecological and evolutionary processes. It has therefore been proposed that animal movement studies could benefit from acknowledging and studying consistent interindividual differences (personality), and, conversely, animal personality studies could adopt a more quantitative representation of movement patterns.
2. Using high‐resolution tracking data of three‐spined stickleback fish (Gasterosteus aculeatus), we examined the repeatability of four movement parameters commonly used in the analysis of discrete time series movement data (time stationary, step length, turning angle, burst frequency) and four behavioral parameters commonly used in animal personality studies (distance travelled, space use, time in free water, and time near objects).
3. Fish showed repeatable interindividual differences in both movement and behavioral parameters when observed in a simple environment with two, three, or five shelters present. Moreover, individuals that spent less time stationary, took more direct paths, and less commonly burst travelled (movement parameters), were found to travel farther, explored more of the tank, and spent more time in open water (behavioral parameters).
4. Our case study indicates that the two approaches—quantifying movement and behavioral parameters—are broadly equivalent, and we suggest that movement parameters can be viewed as “micropersonality” traits that give rise to broad‐scale consistent interindividual differences in behavior. This finding has implications for both personality and movement ecology research areas. For example, the study of movement parameters may provide a robust way to analyze individual personalities in species that are difficult or impossible to study using standardized behavioral assays.

     

Linking rates of diffusion and consumption in relation to resources

The functional response is a fundamental model of the relationship between consumer intake rate and resource abundance. The random walk is a fundamental model of animal movement and is well approximated by simple diffusion. Both models are central to our understanding of numerous ecological processes but are rarely linked in ecological theory. To derive a synthetic model, we draw on the common logical premise underlying these models and show how the diffusion and consumption rates of consumers depend on elementary attributes of naturally occurring consumer-resource interactions: the abundance, spatial aggregation, and traveling speed of resources as well as consumer handling time and directional persistence. We show that resource aggregation may lead to increased consumer diffusion and, in the case of mobile resources, reduced consumption rate. Resource-dependent movement patterns have traditionally been attributed to area-restricted search, reflecting adaptive decision making by the consumer. Our synthesis provides a simple alternative hypothesis that such patterns could also arise as a by-product of statistical movement mechanics.