Behavioral intermittence, Lévy patterns, and randomness in 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.

Movement ecology is a rapidly emerging new research field that explores the underlying mechanisms of organism movement, from animals, humans, to plant and microorganisms, across a range of environmental contexts and spatiotemporal scales, from individual behavior to population-level processes. Research in this area draws on a diverse range of disciplines including animal behavior, ecology, biology, geography, physics, mathematics, statistics, and computer science, and utilizes a range of techniques and technologies, including telemetry, remote sensing, and bioacoustics. Animal movements are determined by a combination of both innate individual characteristics and environmental factors, such as food availability, predation risk, and habitat quality. Movements can range from small-scale foraging excursions within a home-range to seasonal migrations over thousands of kilometers, with characteristic patterns at different spatial scales. Animal movement may affect reproductive success, genetic diversity, and disease transmission within populations, and can play a role in wider ecosystem functioning via nutrient cycling or dispersal of seeds and pollen. The rapid growth of movement ecology since the early 2000s has arguably been driven by the increased functionality, availability, and durability of modern biologgers and sensors enabling detailed data sets to be collected from a wide range of species. In turn, this has necessitated the development of new mathematical, statistical, and computational methods for modeling and analyzing these rich, and increasingly very large, data sets. In its broadest sense, movement ecology encompasses a wide-ranging set of concepts, theories, and practical approaches that relate to animal movement. Rather than attempting to cover the entire field, this bibliography specifically focuses on recent developments in modeling and analysis of the most common type of animal movement data, namely (x,y) or (x,y,z) positional data, as collected directly or indirectly over time by spatial tracking systems such as GPS or radio telemetry. Data collected in other forms such as via mark-recapture studies is beyond our scope (although still an important approach within the field). The bibliography highlights the key Movement Ecology Textbooks in the field, explores key Movement Ecology Concepts, and explains methods for Movement Data Collection and Processing and dealing with Circular Statistics. The article gives an overview of Random Walk Models of Movement and how they relate to Movement Path Analysis and Metrics and Statistical Model Fitting of Movement Data in this context. It focuses on several key applications: Foraging and Search, Home-Range, Habitat Space-Use and Resource Selection, and Collective Movement, and finishes with a summary of recent R Packages for Movement Ecology.

Over the last decade, spatial capture–recapture (SCR) models have become widespread for estimating demographic parameters in ecological studies. However, the underlying assumptions about animal movement and space use are often not realistic. This is a missed opportunity because interesting ecological questions related to animal space use, habitat selection, and behavior cannot be addressed with most SCR models, despite the fact that the data collected in SCR studies — individual animals observed at specific locations and times — can provide a rich source of information about these processes and how they relate to demographic rates. We developed SCR models that integrated more complex movement processes that are typically inferred from telemetry data, including a simple random walk, correlated random walk (i.e., short‐term directional persistence), and habitat‐driven Langevin diffusion. We demonstrated how to formulate, simulate from, and fit these models with standard SCR data using data‐augmented Bayesian analysis methods. We evaluated their performance through a simulation study, in which we varied the detection, movement, and resource selection parameters. We also examined different numbers of sampling occasions and assessed performance gains when including auxiliary location data collected from telemetered individuals. Across all scenarios, the integrated SCR movement models performed well in terms of abundance, detection, and movement parameter estimation. We found little difference in bias for the simple random walk model when reducing the number of sampling occasions from T = 25 to T = 15. We found some bias in movement parameter estimates under several of the correlated random walk scenarios, but incorporating auxiliary location data improved parameter estimates and significantly improved mixing during model fitting. The Langevin movement model was able to recover resource selection parameters from standard SCR data, which is particularly appealing because it explicitly links the individual‐level movement process with habitat selection and population density. We focused on closed population models, but the movement models developed here can be extended to open SCR models. The movement process models could also be easily extended to accommodate additional “building blocks” of random walks, such as central tendency (e.g., territoriality) or multiple movement behavior states, thereby providing a flexible and coherent framework for linking animal movement behavior to population dynamics, density, and distribution.

Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.

Long-term and short-term stability characteristics of receiver inter system bias for BDS3/BDS2

Animal movement and behaviour is fundamental for ecosystem functioning. The process of seed dispersal by frugivorous animals is a showcase for this paradigm since their behaviour shapes the spatial patterns of the earliest stage of plant regeneration. However, we still lack a general understanding of how intrinsic (frugivore and plant species traits) and extrinsic (landscape features) factors interact to determine how seeds of a given species are more likely to be deposited in some places more than in others. We develop a multi-species mechanistic model of seed dispersal based on frugivore behavioural responses to landscape heterogeneity. The model was fitted to data from three-years of spatially-explicit field observations on the behaviour of six frugivorous thrushes and the fruiting patterns of three fleshy-fruited trees in a secondary forest of the Cantabrian range (N Spain). With such model we explore how seed rain patterns arise from the interaction between animal behaviour and landscape heterogeneity. We show that different species of thrushes respond differently to landscape heterogeneity even though they belong to the same genus, and that provide complementary seed dispersal functions. Simulated seed rain patterns are only realistic when at least some landscape heterogeneity (forest cover and fruit abundance) is taken into account. The common and simple approach of re-sampling movement data to quantify seed dispersal produces biases in both the distance and the habitat at which seeds arrive. Movement behaviour not only affects dispersal distance and seed rain patterns but also can affect frugivore diet composition even if there is no built-in preference for fruiting species. In summary, the fate of seeds produced by a given plant species is strongly affected by both the composition of the frugivore assemblage and the landscape-scale context of the plant location, including the presence of fruits from other plants (from the same or different species).

Trait-based approaches are key to understanding eco-evolutionary processes but rarely account for animal behaviour despite its central role in ecosystem dynamics. We propose integrating behaviour into trait-based ecology through movement traits-standardised and comparable measures of animal movement derived from biologging data, such as daily displacements or range sizes. Accounting for animal behaviour will advance trait-based research on species interactions, community structure and ecosystem functioning. Importantly, movement traits allow for quantification of behavioural reaction norms, offering insights into species' acclimation and adaptive capacity to environmental change. We outline a vision for a 'living' global movement trait database that enhances trait data curation by (1) continuously growing alongside shared biologging data, (2) calculating traits directly from individual-level data using standardised, consistent methodology and (3) providing information on multi-level (species, individual, within-individual) trait variation. We present a proof-of-concept 'MoveTraits' database with 52 mammal and 97 bird species, demonstrating calculation workflows for 5 traits across multiple timescales. Movement traits have significant potential to improve trait-based global change predictions and contribute to global biodiversity assessments as Essential Biodiversity Variables. By making animal movement data more accessible and interpretable, this database could bridge the gap between movement ecology and biodiversity policy, facilitating evidence-based conservation.

BackgroundGreen Fluorescent Protein (GFP) is used extensively as a reporter for transgene expression in Drosophila and other organisms. However, GFP has not generally been used as a reporter for circadian patterns of gene expression, and it has not previously been possible to correlate patterns of reporter expression with 3D movement and behavior of transgenic animals.ResultsWe present a video tracking system that allows tissue-specific GFP expression to be quantified and correlated with 3D animal movement in real time. eyeless/Pax6 reporter expression had a 12 hr period that correlated with fly activity levels.hsp70 and hsp22 gene reporters were induced during fly aging in circadian patterns (24 hr and 18 hr periods, respectively), and spiked in the hours preceding and overlapping the death of the animal. The phase of hsp gene reporter expression relative to fly activity levels was different for each fly, and remained the same throughout the life span.ConclusionThese experiments demonstrate that GFP can readily be used to assay longitudinally fly movement and tissue-specific patterns of gene expression. The hsp22-GFP and hsp70-GFP expression patterns were found to reflect accurately the endogenous gene expression patterns, including induction during aging and circadian periodicity. The combination of these new tracking methods with the hsp-GFP reporters revealed additional information, including a spike in hsp22 and hsp70 reporter expression preceding death, and an intriguing fly-to-fly variability in the phase of hsp70 and hsp22 reporter expression patterns. These methods allow specific temporal patterns of gene expression to be correlated with temporal patterns of animal activity, behavior and mortality.

Recent developments in animal tracking technology have permitted the collection of detailed data on the movement paths of individuals from many species. However, analysis methods for these data have not developed at a similar pace, largely due to a lack of suitable candidate models, coupled with the technical difficulties of fitting such models to data. To facilitate a general modeling framework, we propose that complex movement paths can be conceived as a series of movement strategies among which animals transition as they are affected by changes in their internal and external environment. We synthesize previously existing and novel methodologies to develop a general suite of mechanistic models based on biased and correlated random walks that allow different behavioral states for directed (e.g., migration), exploratory (e.g., dispersal), area‐restricted (e.g., foraging), and other types of movement. Using this “toolbox” of nested model components, multistate movement models may be custom‐built for a wide variety of species and applications. As a unified state‐space modeling framework, it allows the simultaneous investigation of numerous hypotheses about animal movement from imperfectly observed data, including time allocations to different movement behavior states, transitions between states, the use of memory or navigation, and strengths of attraction (or repulsion) to specific locations. The inclusion of covariate information permits further investigation of specific hypotheses related to factors driving different types of movement behavior. Using reversible‐jump Markov chain Monte Carlo methods to facilitate Bayesian model selection and multi‐model inference, we apply the proposed methodology to real data by adapting it to the natural history of the grey seal (Halichoerus grypus) in the North Sea. Although previous grey seal studies tended to focus on correlated movements, we found overwhelming evidence that bias toward haul‐out or foraging locations better explained seal movement than did simple or correlated random walks. Posterior model probabilities also provided evidence that seals transition among directed, area‐restricted, and exploratory movements associated with haul‐out, foraging, and other behaviors. With this intuitive framework for modeling and interpreting animal movement, we believe that the development and application of custom‐made movement models will become more accessible to ecologists and non‐statisticians.

Quantifying animal movements is necessary for answering a wide array of research questions in ecology and conservation biology. Consequently, ecologists have made considerable efforts to identify the best way to estimate an animal's home range, and many methods of estimating home ranges have arisen over the past half a century. Most of these methods fall into two distinct categories of estimators that have only recently been described in statistical detail: those that measure range distributions (methods such as kernel density estimation that quantify the long-run behavior of a movement process that features restricted space use) and those that measure occurrence distributions (methods such as Brownian bridge movement models and the Correlated Random Walk Library that quantify uncertainty in an animal movement path during a specific period of observation). In this paper, we use theory, simulations, and empirical analysis to demonstrate the importance of appropriately using these two categories of distributions and their estimators. Conflating range and occurrence distributions can have serious consequences for ecological inference and conservation practice. For example, in most situations, home ranges estimated using estimators of occurrence distributions are too small, and this problem is exacerbated by ongoing improvements in tracking technology that enable more frequent and more accurate data on animal movements. We encourage researchers to use estimators of range distributions to quantify home ranges and estimators of occurrence distributions to answer other questions in movement ecology, such as when and where an animal crossed a linear feature, visited a location of interest, or interacted with other animals.

Improving the realism of random walk movement analyses through the incorporation of habitat bias

Knowing the influence of intrinsic and environmental traits on animals’ movement is a central interest of ecology and can aid to enhance management decisions. The giant anteater (Myrmecophaga tridactyla) is a vulnerable mammal that presents low capacity for physiological thermoregulation and uses forests as thermal shelters. Here, we aim to provide reliable estimates of giant anteaters’ movement patterns and home range size, as well as untangle the role of intrinsic and environmental drivers on their movement. We GPS-tracked 19 giant anteaters in Brazilian savannah. We used a continuous-time movement model to estimate their movement patterns (described by home range crossing time, daily distance moved and directionality), and provide an autocorrelated kernel density estimate of home range size. Then, we used mixed structural equations to integratively model the effects of sex, body mass and proportion of forest cover on movement patterns and home range size, considering the complex net of interactions between these variables. Male giant anteaters presented more intensive space use and larger home range than females with similar body mass, as it is expected in polygynous social mating systems. Males and females increased home range size with increasing body mass, but the allometric scaling of intensity of space use was negative for males and positive for females, indicating different strategies in search for resources. With decreasing proportion of forest cover inside their home ranges, and, consequently, decreasing thermal quality of their habitat, giant anteaters increased home range size, possibly to maximize the chances of accessing thermal shelters. As frequency and intensity of extreme weather events and deforestation are increasing, effective management efforts need to consider the role of forests as an important thermal resource driving spatial requirements of this species. We highlight that both intrinsic and environmental drivers of animal movement should be integrated to better guide management strategies.

Animal behavior is a complex trait known to have strong feedbacks with environmental conditions across all ecosystems. Understanding how animals interact with their environment is therefore a key element for gaining new insights on how ecosystem landscapes develop and what is the potential environmental degradation caused by different species of animals. Within animal behavioral traits, characterizing animal movement has received attention because it is relatively easy to monitor. Despite the widely differing conditions in which different species of animals exist, it has been demonstrated that statistical models of animal movement based on random walks (e.g., Brownian and Lévy walks) often offer a consistent and accurate representation of animal movement in diverse ecosystems. Grazing livestock systems are particularly interesting to explore as they play an important role in the context of climate change and agricultural sustainability. Movement of grazing livestock has not been fully explored nor described, and knowledge on the way they impact the environment temporally and spatially is often empirical and remains largely unknown. To fill these gaps and to provide new insights on spatio-temporal impacts of grazing animals on soil structure, we characterized daily and seasonal patterns of grazing livestock using GPS (Global Positioning System) data from conventionally grazed and cell-grazed paddocks. In addition, we used a soil compaction model to predict changes in bulk density due to grazing. We found that the way grazing livestock move is consistent with a Lévy walk and that Lévy properties depend on the dimensions of the grazing cells (constraints and attractors). The combination of an animal movement model and a soil compaction model allowed us to obtain treatment-specific spatially explicit maps of soil properties affected by grazing that are consistent with observations.

In order to make quantitative statements regarding behavior patterns in animals, it is important to establish whether new observations are statistically consistent with the animal's equilibrium behavior. For example, traumatic stress from the presence of a telemetry transmitter may modify the baseline behavior of an animal, which in turn can lead to a bias in results. From the perspective of information theory such a bias can be interpreted as the amount of information gained from a new measurement, relative to an existing equilibrium distribution. One important concept in information theory is the relative entropy, from which we develop a framework for quantifying time-dependent differences between new observations and equilibrium. We demonstrate the utility of the relative entropy by analyzing observed speed distributions of Pacific bluefin tuna, recorded within a 48-hour time span after capture and release. When the observed and equilibrium distributions are Gaussian, we show that the tuna's behavior is modified by traumatic stress, and that the resulting modification is dominated by the difference in central tendencies of the two distributions. Within a 95% confidence level, we find that the tuna's behavior is significantly altered for approximately 5 hours after release. Our analysis reveals a periodic fluctuation in speed corresponding to the moment just before sunrise on each day, a phenomenon related to the tuna's daily diving pattern that occurs in response to changes in ambient light.

Artificial food supplementation of wildlife is an increasing practice for species conservation, as well as for hunting and viewing tourism. Yet, our understanding of the implications of wildlife supplementary feeding is still very limited. Concerns have been raised over the potential negative impact of artificial feeding, but the effects of this practice on animal movements and rhythms of activity are just beginning to be investigated. Here, with the aim of studying whether the artificial feeding of brown bears may affect their behaviour, we analysed (1) the probability and intensity of feeding site use at different temporal scales, (2) how the use of artificial feeding sites is related to the bear's age and sex, main periods of the bear's annual cycle (i.e. mating and hyperphagia) and characteristics of the feeding sites, and (3) how the use of artificial feeding may be affecting bear movement patterns. We analysed the movements of 71 radio-collared brown bears in southern-central Finland and western Russian Karelia. Artificial feeding sites had several effects on brown bears in boreal habitats. The probability of a feeding site being used was positively correlated to the stability of this food resource over time, whereas sexes and bear classes (subadults, adults and females with cubs) did not show significant differences in the use of feeding sites, which were visited predominantly at night and slightly more during hyperphagia. The probability of using an artificial feeding site affected the daily net distance only (bears using feeding sites: 3.5 ± 4.5 km, range: 0–29 km; bears not using feeding sites: 4.4 ± 4.9 km, range: 0–47 km). Those brown bears using artificial feeding more intensively moved shorter distances at a lower speed within smaller home ranges compared to bears that used this food sources less. Highly predictable and continuously available anthropogenic food may therefore have substantial impacts on brown bear movement patterns, ecology and health. The recorded changes in movement patterns support the evidence that artificial feeding may have important implications for bear ecology and conservation.