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.

Sex-specific seasonal variations of wild boar distance traveled and home range size

Distance traveled and home range size describe how animals move in space. The seasonal variations of these parameters are important to comprehensively understand animal ecology and its connection with reproductive behavior and energy costs. Researchers usually estimate the distance traveled as the sum of the straight-line displacements between sampled positions, but this approach is sensitive to the sampling frequency and does not account for the tortuosity of the animal's movements. By means of the continuous-time movement modeling which takes into account autocorrelation and tortuosity of movement data, we estimated the distance traveled and monthly home range size of 28 wild boar Sus scrofa and modeled their inter-sexual seasonal variability. Males traveled longer distances and used larger home ranges than females, particularly during the rut in autumn-winter, consistently with the different biological cycles of males and females. Males enlarged their home ranges during the rut but traveled constant average distances along the year, whereas females traveled shorter distances in correspondence with the peak of food resources and birth periods but exhibited constant home range size across seasons. The differences between the seasonal variation patterns of distance traveled and home range size, observed in both sexes, revealed the complex relationship between these two aspects of spatial behavior and the great opportunity of including both distance traveled and home range size in behavioral ecology investigations. We provided a detailed analysis of wild boar spatial behavior and its relationships with the reproductive cycles of males and females, promoting a deeper comprehension of their behavioral ecology.

Residency and space use estimation methods based on passive acoustic telemetry data

Acoustic telemetry has helped overcome many of the challenges faced when studying the movement ecology of aquatic species, allowing to obtain unprecedented amounts of data. This has made it into one of the most widely used methods nowadays. Many ways to analyse acoustic telemetry data have been made available and deciding on how to analyse the data requires considering the type of research objectives, relevant properties of the data (e.g., resolution, study design, equipment), habits of the study species, researcher experience, among others. To ease this decision process, here we showcase (1) some of the methods used to estimate pseudo-positions and positions from raw acoustic telemetry data, (2) methods to estimate residency and (3) methods to estimate two-dimensional home and occurrence range using geometric or hull-based methods and density-distribution methods, a network-based approach, and three-dimensional methods. We provide examples of some of these were tested using a sample of real data. With this we intend to provide the necessary background for the selection of the method(s) that better fit specific research objectives when using acoustic telemetry.

Ants combine systematic meandering and correlated random walks when searching for unknown resources

Animal search movements are typically assumed to be mostly random walks, although non-random elements may be widespread. We tracked ants (Temnothorax rugatulus) in a large empty arena, resulting in almost 5 km of trajectories. We tested for meandering by comparing the turn autocorrelations for empirical ant tracks and simulated, realistic Correlated Random Walks. We found that 78% of ants show significant negative autocorrelation around 10 mm (3 body lengths). This means that turns in one direction are likely followed by turns in the opposite direction after this distance. This meandering likely makes the search more efficient, as it allows ants to avoid crossing their own paths while staying close to the nest, avoiding return-travel time. Combining systematic search with stochastic elements may make the strategy less vulnerable to directional inaccuracies. This study is the first to find evidence for efficient search by regular meandering in a freely searching animal.

Increasing Anthropogenic Disturbance Restricts Wildebeest Movement Across East African Grazing Systems

The ability to move is essential for animals to find mates, escape predation, and meet energy and water demands. This is especially important across grazing systems where vegetation productivity can vary drastically between seasons or years. With grasslands undergoing significant changes due to climate change and anthropogenic development, there is an urgent need to determine the relative impacts of these pressures on the movement capacity of native herbivores. To measure these impacts, we fitted 36 white-bearded wildebeest (Connochaetes taurinus) with GPS collars across three study areas in southern Kenya (Amboseli Basin, Athi-Kaputiei Plains, and Mara) to test the relationship between movement (e.g., directional persistence, speed, home range crossing time) and gradients of vegetation productivity (i.e., NDVI) and anthropogenic disturbance. As expected, wildebeest moved the most (21.0 km day–1; CI: 18.7–23.3) across areas where movement was facilitated by low human footprint and necessitated by low vegetation productivity (Amboseli Basin). However, in areas with moderate vegetation productivity (Athi-Kaputiei Plains), wildebeest moved the least (13.3 km day–1; CI: 11.0–15.5). This deviation from expectations was largely explained by impediments to movement associated with a large human footprint. Notably, the movements of wildebeest in this area were also less directed than the other study populations, suggesting that anthropogenic disturbance (i.e., roads, fences, and the expansion of settlements) impacts the ability of wildebeest to move and access available resources. In areas with high vegetation productivity and moderate human footprint (Mara), we observed intermediate levels of daily movement (14.2 km day–1; CI: 12.3–16.1). Wildebeest across each of the study systems used grassland habitats outside of protected areas extensively, highlighting the importance of unprotected landscapes for conserving mobile species. These results provide unique insights into the interactive effects of climate and anthropogenic development on the movements of a dominant herbivore in East Africa and present a cautionary tale for the development of grazing ecosystems elsewhere.

Effects of body size on estimation of mammalian area requirements

Accurately quantifying species' area requirements is a prerequisite for effective area-based conservation. This typically involves collecting tracking data on species of interest and then conducting home-range analyses. Problematically, autocorrelation in tracking data can result in space needs being severely underestimated. Based on the previous work, we hypothesized the magnitude of underestimation varies with body mass, a relationship that could have serious conservation implications. To evaluate this hypothesis for terrestrial mammals, we estimated home-range areas with global positioning system (GPS) locations from 757 individuals across 61 globally distributed mammalian species with body masses ranging from 0.4 to 4000 kg. We then applied block cross-validation to quantify bias in empirical home-range estimates. Area requirements of mammals <10 kg were underestimated by a mean approximately15%, and species weighing approximately100 kg were underestimated by approximately50% on average. Thus, we found area estimation was subject to autocorrelation-induced bias that was worse for large species. Combined with the fact that extinction risk increases as body mass increases, the allometric scaling of bias we observed suggests the most threatened species are also likely to be those with the least accurate home-range estimates. As a correction, we tested whether data thinning or autocorrelation-informed home-range estimation minimized the scaling effect of autocorrelation on area estimates. Data thinning required an approximately93% data loss to achieve statistical independence with 95% confidence and was, therefore, not a viable solution. In contrast, autocorrelation-informed home-range estimation resulted in consistently accurate estimates irrespective of mass. When relating body mass to home range size, we detected that correcting for autocorrelation resulted in a scaling exponent significantly >1, meaning the scaling of the relationship changed substantially at the upper end of the mass spectrum.

How range residency and long-range perception change encounter rates

Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home-range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can lead to systematic, non-negligible biases in encounter-rate predictions.

Scale-insensitive estimation of speed and distance traveled from animal tracking data

BACKGROUND

Speed and distance traveled provide quantifiable links between behavior and energetics, and are among the metrics most routinely estimated from animal tracking data. Researchers typically sum over the straight-line displacements (SLDs) between sampled locations to quantify distance traveled, while speed is estimated by dividing these displacements by time. Problematically, this approach is highly sensitive to the measurement scale, with biases subject to the sampling frequency, the tortuosity of the animal's movement, and the amount of measurement error. Compounding the issue of scale-sensitivity, SLD estimates do not come equipped with confidence intervals to quantify their uncertainty.

METHODS

To overcome the limitations of SLD estimation, we outline a continuous-time speed and distance (CTSD) estimation method. An inherent property of working in continuous-time is the ability to separate the underlying continuous-time movement process from the discrete-time sampling process, making these models less sensitive to the sampling schedule when estimating parameters. The first step of CTSD is to estimate the device's error parameters to calibrate the measurement error. Once the errors have been calibrated, model selection techniques are employed to identify the best fit continuous-time movement model for the data. A simulation-based approach is then employed to sample from the distribution of trajectories conditional on the data, from which the mean speed estimate and its confidence intervals can be extracted.

RESULTS

Using simulated data, we demonstrate how CTSD provides accurate, scale-insensitive estimates with reliable confidence intervals. When applied to empirical GPS data, we found that SLD estimates varied substantially with sampling frequency, whereas CTSD provided relatively consistent estimates, with often dramatic improvements over SLD.

CONCLUSIONS

The methods described in this study allow for the computationally efficient, scale-insensitive estimation of speed and distance traveled, without biases due to the sampling frequency, the tortuosity of the animal's movement, or the amount of measurement error. In addition to being robust to the sampling schedule, the point estimates come equipped with confidence intervals, permitting formal statistical inference. All the methods developed in this study are now freely available in the ctmmR package or the ctmmweb point-and-click web based graphical user interface.

Population structure and spatial ecology of Kordofan giraffe in Garamba National Park, Democratic Republic of Congo

Population numbers of Kordofan giraffe (Giraffa camelopardalis antiquorum) have declined throughout its range by more than 85% in the last three decades, including in the isolated easternmost population found in the Garamba National Park (NP) in the Democratic Republic of Congo.We provide new data on the conservation status and ecology of Kordofan giraffe in Garamba NP, specifically on the current population dynamics, distribution patterns, and spatial ecology for informed conservation management decisions.Data were gathered between September 26, 2016, and August 17, 2017, through direct observation and from eight GPS satellite collars deployed in early 2016. Movements, distribution patterns, and autocorrelated kernel density home ranges were estimated using the Continuous-Time Movement Modeling (CTMM) framework. We then compared results with home ranges calculated using the kernel density estimation (95% KDE) method.The Garamba NP population was estimated to be 45 giraffe with a female-dominated sex ratio (35% males; 65% females), and adult-dominated age class ratio (11.2% juveniles; 17.7% subadults; 71.1% adults). The giraffe's distribution was limited to the south-central sector of the Park, and giraffe were divided over different areas with some degree of connectivity. The average giraffe home range size was 934.3 km2 using AKDE and 268.8 km2 using KDE. Both methods have shown surprisingly large home ranges despite of the relatively high humidity of Garamba NP.Based on the outcomes of this research, urgent conservation action is needed to protect Garamba's remaining giraffe population.

Disentangling social interactions and environmental drivers in multi-individual wildlife tracking data

While many animal species exhibit strong conspecific interactions, movement analyses of wildlife tracking datasets still largely focus on single individuals. Multi-individual wildlife tracking studies provide new opportunities to explore how individuals move relative to one another, but such datasets are frequently too sparse for the detailed, acceleration-based analytical methods typically employed in collective motion studies. Here, we address the methodological gap between wildlife tracking data and collective motion by developing a general method for quantifying movement correlation from sparsely sampled data. Unlike most existing techniques for studying the non-independence of individual movements with wildlife tracking data, our approach is derived from an analytically tractable stochastic model of correlated movement. Our approach partitions correlation into a deterministic tendency to move in the same direction termed 'drift correlation' and a stochastic component called 'diffusive correlation'. These components suggest the mechanisms that coordinate movements, with drift correlation indicating external influences, and diffusive correlation pointing to social interactions. We use two case studies to highlight the ability of our approach both to quantify correlated movements in tracking data and to suggest the mechanisms that generate the correlation. First, we use an abrupt change in movement correlation to pinpoint the onset of spring migration in barren-ground caribou. Second, we show how spatial proximity mediates intermittently correlated movements among khulans in the Gobi desert. We conclude by discussing the linkages of our approach to the theory of collective motion.This article is part of the theme issue 'Collective movement ecology'.

Correcting for missing and irregular data in home-range estimation

Home-range estimation is an important application of animal tracking data that is frequently complicated by autocorrelation, sampling irregularity, and small effective sample sizes. We introduce a novel, optimal weighting method that accounts for temporal sampling bias in autocorrelated tracking data. This method corrects for irregular and missing data, such that oversampled times are downweighted and undersampled times are upweighted to minimize error in the home-range estimate. We also introduce computationally efficient algorithms that make this method feasible with large data sets. Generally speaking, there are three situations where weight optimization improves the accuracy of home-range estimates: with marine data, where the sampling schedule is highly irregular, with duty cycled data, where the sampling schedule changes during the observation period, and when a small number of home-range crossings are observed, making the beginning and end times more independent and informative than the intermediate times. Using both simulated data and empirical examples including reef manta ray, Mongolian gazelle, and African buffalo, optimal weighting is shown to reduce the error and increase the spatial resolution of home-range estimates. With a conveniently packaged and computationally efficient software implementation, this method broadens the array of data sets with which accurate space-use assessments can be made.

An ecophysiologically informed model of seed dispersal by orangutans: linking animal movement with gut passage across time and space

Fauna-mediated ecosystem service provision (e.g. seed dispersal) can be difficult to quantify and predict because it is underpinned by the shifting niches of multiple interacting organisms. Such interactions are especially complex in tropical ecosystems, including endangered peat forests of Central Borneo, a biodiversity hot spot and home to the critically endangered orangutan (Pongo pygmaeus wurmbii). We combined studies of the digestive physiology of captive orangutans in Australia with detailed field studies of wild orangutans in the Natural Laboratory of Peat-Swamp Forest of Sabangau, Central Kalimantan, Indonesia. By measuring the gut transit time (TT) of indigestible seed mimics (beads) in captivity and applying this as a temporal constraint to movement data of wild orangutans, we developed a mechanistic, time-explicit spatial model to project the seed dispersal patterns by these large-bodied, arboreal frugivores. We followed seven orangutans and established home range kernels using Time Local Convex Hull (T-LoCoH) modelling. This allowed us to model individual orangutan movements and to adjust these models according to gut transit times to estimate seed dispersal kernels. Female movements were conservative (core ranges of 55 and 52 ha in the wet and dry seasons, respectively) and revisitation rates to the same location of n = 4 in each 24-h block. Male movements were more unpredictable, yielding fragmented core ranges and revisitation rates to the same location of only 1.2 times each 24 h; males also demonstrated large disjunctions where they moved rapidly over long distances and were frequently lost from view. Seed dispersal kernels were nested predictably within the core ranges of females, but not males. We used the T-LoCoH approach to analyse movement ecology, which offered a powerful tool to predict the primary deposition of seeds by orangutans, thereby providing a reliable method for making a priori predictions of seed dispersal dynamics by other frugivores in novel ecosystems.

Estimation of baboon daily travel distances by means of point sampling - the magnitude of underestimation

Daily travel distance (DTD), the distance an animal moves over the course of the day, is an important metric in movement ecology. It provides data with which to test hypotheses related to energetics and behaviour, e.g. impact of group size or food distribution on DTDs. The automated tracking of movements by applying GPS technology has become widely available and easy to implement. However, due to battery duration constraints, it is necessary to select a tracking-time resolution, which inevitably introduces an underestimation of the true underlying path distance. Here we give a quantification of this inherent systematic underestimation of DTDs for a terrestrial primate, the Guinea baboon. We show that sampling protocols with interval lengths from 1 to 120 min underestimate DTDs on average by 7 to 35 %. For longer time intervals (i.e. 60, 90, 120 min), the relative increase of deviation from the “true” trajectory is less pronounced than for shorter intervals. Our study provides first hints on the magnitude of error, which can be applied as a corrective when estimating absolute DTDs in calculations on travelling costs in terrestrial primates.

Correlated velocity models as a fundamental unit of animal movement: synthesis and applications

BACKGROUND

Continuous time movement models resolve many of the problems with scaling, sampling, and interpretation that affect discrete movement models. They can, however, be challenging to estimate, have been presented in inconsistent ways, and are not widely used.

METHODS

We review the literature on integrated Ornstein-Uhlenbeck velocity models and propose four fundamental correlated velocity movement models (CVM's): random, advective, rotational, and rotational-advective. The models are defined in terms of biologically meaningful speeds and time scales of autocorrelation. We summarize several approaches to estimating the models, and apply these tools for the higher order task of behavioral partitioning via change point analysis.

RESULTS

An array of simulation illustrate the precision and accuracy of the estimation tools. An analysis of a swimming track of a bowhead whale (Balaena mysticetus) illustrates their robustness to irregular and sparse sampling and identifies switches between slower and faster, and directed vs. random movements. An analysis of a short flight of a lesser kestrel (Falco naumanni) identifies exact moments when switches occur between loopy, thermal soaring and directed flapping or gliding flights.

CONCLUSIONS

We provide tools to estimate parameters and perform change point analyses in continuous time movement models as an R package (smoove). These resources, together with the synthesis, should facilitate the wider application and development of correlated velocity models among movement ecologists.

Space Use and Movement of a Neotropical Top Predator: The Endangered Jaguar

Accurately estimating home range and understanding movement behavior can provide important information on ecological processes. Advances in data collection and analysis have improved our ability to estimate home range and movement parameters, both of which have the potential to impact species conservation. Fitting continuous-time movement model to data and incorporating the autocorrelated kernel density estimator (AKDE), we investigated range residency of forty-four jaguars fit with GPS collars across five biomes in Brazil and Argentina. We assessed home range and movement parameters of range resident animals and compared AKDE estimates with kernel density estimates (KDE). We accounted for differential space use and movement among individuals, sex, region, and habitat quality. Thirty-three (80%) of collared jaguars were range resident. Home range estimates using AKDE were 1.02 to 4.80 times larger than KDE estimates that did not consider autocorrelation. Males exhibited larger home ranges, more directional movement paths, and a trend towards larger distances traveled per day. Jaguars with the largest home ranges occupied the Atlantic Forest, a biome with high levels of deforestation and high human population density. Our results fill a gap in the knowledge of the species' ecology with an aim towards better conservation of this endangered/critically endangered carnivore-the top predator in the Neotropics.

Flexible characterization of animal movement pattern using net squared displacement and a latent state model

BACKGROUND

Characterizing the movement patterns of animals is an important step in understanding their ecology. Various methods have been developed for classifying animal movement at both coarse (e.g., migratory vs. sedentary behavior) and fine (e.g., resting vs. foraging) scales. A popular approach for classifying movements at coarse resolutions involves fitting time series of net-squared displacement (NSD) to models representing different conceptualizations of coarse movement strategies (i.e., migration, nomadism, sedentarism, etc.). However, the performance of this method in classifying actual (as opposed to simulated) animal movements has been mixed. Here, we develop a more flexible method that uses the same NSD input, but relies on an underlying discrete latent state model. Using simulated data, we first assess how well patterns in the number of transitions between modes of movement and the duration of time spent in a mode classify movement strategies. We then apply our approach to elucidate variability in the movement strategies of eight giant tortoises (Chelonoidis sp.) using a multi-year (2009-2014) GPS dataset from three different Galapagos Islands.

RESULTS

With respect to patterns of time spent and the number of transitions between modes, our approach out-performed previous efforts to distinguish among migration, dispersal, and sedentary behavior. We documented marked inter-individual variation in giant tortoise movement strategies, with behaviors indicating migration, dispersal, nomadism and sedentarism, as well as hybrid behaviors such as "exploratory residence".

CONCLUSIONS

Distilling complex animal movement into discrete modes remains a fundamental challenge in movement ecology, a problem made more complex by the ever-longer duration, ever-finer resolution, and gap-ridden trajectories recorded by GPS devices. By clustering into modes, we derived information on the time spent within one mode and the number of transitions between modes which enabled finer differentiation of movement strategies over previous methods. Ultimately, the techniques developed here address limitations of previous approaches and provide greater insights with respect to characterization of movement strategies across scales by more fully utilizing long-term GPS telemetry datasets.

Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns

Increased availability of high-resolution movement data has led to the development of numerous methods for studying changes in animal movement behavior. Path segmentation methods provide basics for detecting movement changes and the behavioral mechanisms driving them. However, available path segmentation methods differ vastly with respect to underlying statistical assumptions and output produced. Consequently, it is currently difficult for researchers new to path segmentation to gain an overview of the different methods, and choose one that is appropriate for their data and research questions. Here, we provide an overview of different methods for segmenting movement paths according to potential changes in underlying behavior. To structure our overview, we outline three broad types of research questions that are commonly addressed through path segmentation: 1) the quantitative description of movement patterns, 2) the detection of significant change-points, and 3) the identification of underlying processes or 'hidden states'. We discuss advantages and limitations of different approaches for addressing these research questions using path-level movement data, and present general guidelines for choosing methods based on data characteristics and questions. Our overview illustrates the large diversity of available path segmentation approaches, highlights the need for studies that compare the utility of different methods, and identifies opportunities for future developments in path-level data analysis.

Uncovering periodic patterns of space use in animal tracking data with periodograms, including a new algorithm for the Lomb-Scargle periodogram and improved randomization tests

BACKGROUND

Periodicity in activity level (rest/activity cycles) is ubiquitous in nature, but whether and how these periodicities translate into periodic patterns of space use by animals is much less documented. Here we introduce an analytical protocol based on the Lomb-Scargle periodogram (LSP) to facilitate exploration of animal tracking datasets for periodic patterns. The LSP accommodates missing observations and variation in the sampling intervals of the location time series.

RESULTS

We describe a new, fast algorithm to compute the LSP. The gain in speed compared to other R implementations of the LSP makes it tractable to analyze long datasets (>10(6) records). We also give a detailed primer on periodicity analysis, focusing on the specificities of movement data. In particular, we warn against the risk of flawed inference when the sampling schedule creates artefactual periodicities and we introduce a new statistical test of periodicity that accommodates temporally autocorrelated background noise. Applying our LSP-based analytical protocol to tracking data from three species revealed that an ungulate exhibited periodicity in its movement speed but not in its locations, that a central place-foraging seabird tracked moon phase, and that the movements of a range-resident canid included a daily patrolling component that was initially masked by the stochasticity of the movements.

CONCLUSION

The new, fast algorithm tailored for movement data analysis and now available in the R-package ctmm makes the LSP a convenient exploratory tool to detect periodic patterns in animal movement data.

Rigorous home range estimation with movement data: a new autocorrelated kernel density estimator

Quantifying animals' home ranges is a key problem in ecology and has important conservation and wildlife management applications. Kernel density estimation (KDE) is a workhorse technique for range delineation problems that is both statistically efficient and nonparametric. KDE assumes that the data are independent and identically distributed (IID). However, animal tracking data, which are routinely used as inputs to KDEs, are inherently autocorrelated and violate this key assumption. As we demonstrate, using realistically autocorrelated data in conventional KDEs results in grossly underestimated home ranges. We further show that the performance of conventional KDEs actually degrades as data quality improves, because autocorrelation strength increases as movement paths become more finely resolved. To remedy these flaws with the traditional KDE method, we derive an autocorrelated KDE (AKDE) from first principles to use autocorrelated data, making it perfectly suited for movement data sets. We illustrate the vastly improved performance of AKDE using analytical arguments, relocation data from Mongolian gazelles, and simulations based upon the gazelle's observed movement process. By yielding better minimum area estimates for threatened wildlife populations, we believe that future widespread use of AKDE will have significant impact on ecology and conservation biology.

Maximum-entropy description of animal movement

We introduce a class of maximum-entropy states that naturally includes within it all of the major continuous-time stochastic processes that have been applied to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion, integrated Ornstein-Uhlenbeck motion, a recently discovered hybrid of the previous models, and a new model that describes central-place foraging. We are also able to predict a further hierarchy of new models that will emerge as data quality improves to better resolve the underlying continuity of animal movement. Finally, we also show that Langevin equations must obey a fluctuation-dissipation theorem to generate processes that fall from this class of maximum-entropy distributions when the constraints are purely kinematic.