Identifying stationary phases in multivariate time series for highlighting behavioural modes and home range settlements.

Recent advances in biologging open promising perspectives in the study of animal movements at numerous scales. It is now possible to record time series of animal locations and ancillary data (e.g. activity level derived from on-board accelerometers) over extended areas and long durations with a high spatial and temporal resolution. Such time series are often piecewise stationary, as the animal may alternate between different stationary phases (i.e. characterized by a specific mean and variance of some key parameter for limited periods). Identifying when these phases start and end is a critical first step to understand the dynamics of the underlying movement processes. We introduce a new segmentation-clustering method we called segclust2d (available as a r package at cran.r-project.org/package=segclust2d). It can segment bivariate (or more generally multivariate) time series and possibly cluster the various segments obtained, corresponding to different phases assumed to be stationary. This method is easy to use, as it only requires specifying a minimum segment length (to prevent over-segmentation), based on biological rather than statistical considerations. This method can be applied to bivariate piecewise time series of any nature. We focus here on two types of time series related to animal movement, corresponding to (a) at large scale, series of bivariate coordinates of relocations, to highlight temporary home ranges, and (b) at smaller scale, bivariate series derived from relocations data, such as speed and turning angle, to highlight different behavioural modes such as transit, feeding and resting. Using computer simulations, we show that segclust2d can rival and even outperform previous, more complex methods, which were specifically developed to highlight changes of movement modes or home range shifts (based on hidden Markov and Ornstein-Uhlenbeck modelling), which, contrary to our method, usually require the user to provide relevant initial guesses to be efficient. Furthermore, we demonstrate it on actual examples involving a zebra's small-scale movements and an elephant's large-scale movements, to illustrate how various movement modes and home range shifts, respectively, can be identified.

Optimizing the use of biologgers for movement ecology research.

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

Spatial memory shapes density dependence in population dynamics.

Most population dynamics studies assume that individuals use space uniformly, and thus mix well spatially. In numerous species, however, individuals do not move randomly, but use spatial memory to visit renewable resource patches repeatedly. To understand the extent to which memory-based foraging movement may affect density-dependent population dynamics through its impact on competition, we developed a spatially explicit, individual-based movement model where reproduction and death are functions of foraging efficiency. We compared the dynamics of populations of with- and without-memory individuals. We showed that memory-based movement leads to a higher population size at equilibrium, to a higher depletion of the environment, to a marked discrepancy between the global (i.e. measured at the population level) and local (i.e. measured at the individual level) intensities of competition, and to a nonlinear density dependence. These results call for a deeper investigation of the impact of individual movement strategies and cognitive abilities on population dynamics.

How memory-based movement leads to nonterritorial spatial segregation.

Home ranges (HRs) are a remarkably common form of animal space use, but we still lack an integrated view of the individual-level processes that can lead to their emergence and maintenance, particularly when individuals are in competition for resources. We built a spatially explicit mechanistic movement model to investigate how simple memory-based foraging rules may enable animals to establish HRs and to what extent this increases their foraging efficiency compared to individuals that do not base foraging decisions on memory. We showed that these simple rules enable individuals to perform better than individuals using the most efficient strategy that does not rely on memory and drive them to spatially segregate through avoidance of resource patches used by others. This striking result questions the common assumption that low HR overlaps are indicators of territorial behavior. Indeed, it appears that, by using an information-updating system, individuals can keep their environment relatively predictable without paying the cost of defending an exclusive space. However, memory-based foraging strategies leading to HR emergence seem unable to prevent the disruptive effects of the arrival of new individuals. This calls for further research on the mechanisms that can stabilize HR spatial organization in the long term.

Ultimate failure of the Lévy Foraging Hypothesis: Two-scale searching strategies outperform scale-free ones even when prey are scarce and cryptic.

The "Lévy Foraging Hypothesis" promotes Lévy walk (LW) as the best strategy to forage for patchily but unpredictably located prey. This strategy mixes extensive and intensive searching phases in a mostly cue-free way through strange, scale-free kinetics. It is however less efficient than a cue-driven two-scale Composite Brownian walk (CBW) when the resources encountered are systematically detected. Nevertheless, it could be assumed that the intrinsic capacity of LW to trigger cue-free intensive searching at random locations might be advantageous when resources are not only scarcely encountered but also so cryptic that the probability to detect those encountered during movement is low. Surprisingly, this situation, which should be quite common in natural environments, has almost never been studied. Only a few studies have considered "saltatory" foragers, which are fully "blind" while moving and thus detect prey only during scanning pauses, but none of them compared the efficiency of LW vs. CBW in this context or in less extreme contexts where the detection probability during movement is not null but very low. In a study based on computer simulations, we filled the bridge between the concepts of "pure continuous" and "pure saltatory" foraging by considering that the probability to detect resources encountered while moving may range from 0 to 1. We showed that regularly stopping to scan the environment can indeed improve efficiency, but only at very low detection probabilities. Furthermore, the LW is then systematically outperformed by a mixed cue-driven/internally-driven CBW. It is thus more likely that evolution tends to favour strategies that rely on environmental feedbacks rather than on strange kinetics.

Of scales and stationarity in animal movements.

With recent technological advances in tracking devices, movements of numerous animal species can be recorded with a high resolution over large spatial and temporal ranges. This opens promising perspectives for understanding how an animal perceives and reacts to the multi-scale structure of its environment. Yet, conceptual issues such as confusion between movement scales and searching modes prevent us from properly inferring the movement processes at different scales. Here, I propose to build on stationarity (i.e. stability of statistical parameters) to develop a consistent theoretical framework in which animal movements are modelled as a generic composite multi-scale multi-mode random walk model. This framework makes it possible to highlight scales that are relevant to the studied animal, the nature of the behavioural processes that operate at each of these different scales, and the way in which the processes involved at any given scale can interact with those operating at smaller or larger scales. This explicitly scale-focused approach should help properly analyse actual movements by relating, for each scale and each mode, the values of the main model parameters (speed, short- and long-term persistences, degree of stochasticity) to the animal's needs and skills and its response to its environment at multiple scales.

Spatial memory and animal movement.

Memory is critical to understanding animal movement but has proven challenging to study. Advances in animal tracking technology, theoretical movement models and cognitive sciences have facilitated research in each of these fields, but also created a need for synthetic examination of the linkages between memory and animal movement. Here, we draw together research from several disciplines to understand the relationship between animal memory and movement processes. First, we frame the problem in terms of the characteristics, costs and benefits of memory as outlined in psychology and neuroscience. Next, we provide an overview of the theories and conceptual frameworks that have emerged from behavioural ecology and animal cognition. Third, we turn to movement ecology and summarise recent, rapid developments in the types and quantities of available movement data, and in the statistical measures applicable to such data. Fourth, we discuss the advantages and interrelationships of diverse modelling approaches that have been used to explore the memory-movement interface. Finally, we outline key research challenges for the memory and movement communities, focusing on data needs and mathematical and computational challenges. We conclude with a roadmap for future work in this area, outlining axes along which focused research should yield rapid progress.

Periodicity analysis of movement recursions.

Many animals adaptively use their environments by adjusting how long and how often they use specific areas of their home range. Whereas questions about residence times have been addressed for a long time, the study of movement recursions has only recently received due interest. A key question concerns the potential periodicity of such recursions, as many potential drivers of movement behaviour such as light, climate or plant-herbivore interactions can be periodic. We propose here to build upon well-established Fourier and wavelet analyses to extract periodic patterns from time-series of presence/absence, arrival or departure from areas of interest, and introduce reliable null models for assessing the statistical significance of the periods detected. We provide an illustrative example which shows how an impala (Aepyceros melampus) expressed periodic use of the main open area of its home range. The significant periods found (12 h using arrival times; 24h, 7 days, and 30 days using presence/absence records) were consistent with a use of this area linked to predation and disturbance, as the area was used more at night, closer to dark moon, and during week-days. Our approach is a further step towards building up a wider analytical framework for the study of movement ecology.

Accounting for central place foraging constraints in habitat selection studies.

Habitat selection studies contrast actual space use with the expected use under the null hypothesis of no selection (hereafter neutral use). Neutral use is most often equated to the relative frequencies with which environmental features occur. This generates a considerable bias when studying habitat selection by foragers that perform numerous trips back and forth to a central place (CP). Indeed, the increased space use close to the CP with respect to distant places reflects a mechanical effect, rather than a true selection for the closest habitats. Yet, correctly estimating habitat selection by CP foragers is of paramount importance for a better understanding of their ecology and to properly plan conservation actions. We show that including the distance to the CP as a covariate in unconditional Resource Selection Functions, as applied in several studies, is ineffective to correct for the bias. This bias can be eliminated only by contrasting the actual use to an appropriate neutral use that considers the CP forager behavior. We also show that the need to specify an appropriate neutral use overall distribution can be bypassed by relying on a conditional approach, where the neutral use is assessed locally regardless of the distance to the CP.

Foraging efficiency in temporally predictable environments: is a long-term temporal memory really advantageous?

Cognitive abilities enabling animals that feed on ephemeral but yearly renewable resources to infer when resources are available may have been favoured by natural selection, but the magnitude of the benefits brought by these abilities remains poorly known. Using computer simulations, we compared the efficiencies of three main types of foragers with different abilities to process temporal information, in spatially and/or temporally homogeneous or heterogeneous environments. One was endowed with a sampling memory, which stores recent experience about the availability of the different food types. The other two were endowed with a chronological or associative memory, which stores long-term temporal information about absolute times of these availabilities or delays between them, respectively. To determine the range of possible efficiencies, we also simulated a forager without temporal cognition but which simply targeted the closest and possibly empty food sources, and a perfectly prescient forager, able to know at any time which food source was effectively providing food. The sampling, associative and chronological foragers were far more efficient than the forager without temporal cognition in temporally predictable environments, and interestingly, their efficiencies increased with the level of temporal heterogeneity. The use of a long-term temporal memory results in a foraging efficiency up to 1.16 times better (chronological memory) or 1.14 times worse (associative memory) than the use of a simple sampling memory. Our results thus show that, for everyday foraging, a long-term temporal memory did not provide a clear benefit over a simple short-term memory that keeps track of the current resource availability. Long-term temporal memories may therefore have emerged in contexts where short-term temporal cognition is useless, i.e. when the anticipation of future environmental changes is strongly needed.

Marine turtles use geomagnetic cues during open-sea homing.

Marine turtles are renowned long-distance navigators, able to reach remote targets in the oceanic environment; yet the sensory cues and navigational mechanisms they employ remain unclear [1, 3]. Recent arena experiments indicated an involvement of magnetic cues in juvenile turtles' homing ability after simulated displacements [4, 5], but the actual role of geomagnetic information in guiding turtles navigating in their natural environment has remained beyond the reach of experimental investigations. In the present experiment, twenty satellite-tracked green turtles (Chelonia mydas) were transported to four open-sea release sites 100-120 km from their nesting beach on Mayotte island in the Mozambique Channel; 13 of them had magnets attached to their head either during the outward journey or during the homing trip. All but one turtle safely returned to Mayotte to complete their egg-laying cycle, albeit with indirect routes, and showed a general inability to take into account the deflecting action of ocean currents as estimated through remote-sensing oceanographic measurements [7]. Magnetically treated turtles displayed a significant lengthening of their homing paths with respect to controls, either when treated during transportation or when treated during homing. These findings represent the first field evidence for the involvement of geomagnetic cues in sea-turtle navigation.

Behavioural inference from signal processing using animal-borne multi-sensor loggers: a novel solution to extend the knowledge of sea turtle ecology.

The identification of sea turtle behaviours is a prerequisite to predicting the activities and time-budget of these animals in their natural habitat over the long term. However, this is hampered by a lack of reliable methods that enable the detection and monitoring of certain key behaviours such as feeding. This study proposes a combined approach that automatically identifies the different behaviours of free-ranging sea turtles through the use of animal-borne multi-sensor recorders (accelerometer, gyroscope and time-depth recorder), validated by animal-borne video-recorder data. We show here that the combination of supervised learning algorithms and multi-signal analysis tools can provide accurate inferences of the behaviours expressed, including feeding and scratching behaviours that are of crucial ecological interest for sea turtles. Our procedure uses multi-sensor miniaturized loggers that can be deployed on free-ranging animals with minimal disturbance. It provides an easily adaptable and replicable approach for the long-term automatic identification of the different activities and determination of time-budgets in sea turtles. This approach should also be applicable to a broad range of other species and could significantly contribute to the conservation of endangered species by providing detailed knowledge of key animal activities such as feeding, travelling and resting.

Animal movements in heterogeneous landscapes: identifying profitable places and homogeneous movement bouts.

Because of the heterogeneity of natural landscapes, animals have to move through various types of areas that are more or less suitable with respect to their current needs. The locations of the profitable places actually used, which may be only a subset of the whole set of suitable areas available, are usually unknown, but can be inferred from movement analysis by assuming that these places correspond to the limited areas where the animals spend more time than elsewhere. Identifying these intensively used areas makes it possible, through subsequent analyses, to address both how they are distributed with respect to key habitat features, and the underlying behavioral mechanisms used to find these areas and capitalize on such habitats. We critically reviewed the few previously published methods to detect changes in movement behavior likely to occur when an animal enters a profitable place. As all of them appeared to be too narrowly tuned to specific situations, we designed a new, easy-to-use method based on the time spent in the vicinity of successive path locations. We used computer simulations to show that our method is both quite general and robust to noisy data.

Random walk models in biology.

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.

Flexible migratory choices of Cory's shearwaters are not driven by shifts in prevailing air currents.

Wind conditions strongly affect migratory costs and shape flyways and detours for many birds, especially soaring birds. However, whether winds also influence individual variability in migratory choices is an unexplored question. Cory's shearwaters (Calonectris borealis) exhibit migratory flexibility, changing non-breeding destination across the Atlantic Ocean within and between years. Here, we investigated how wind dynamics affect the spatiotemporal migratory behaviour and whether they influence individual choices of non-breeding destination. We analysed 168 GLS tracks of migratory Cory's shearwaters over five years in relation to concurrent wind data. We found no evidence for an association of the use of specific paths or destinations with particular wind conditions. Our results suggest that shearwaters deliberately choose their non-breeding destination, even when the choice entails longer distances and higher energetic costs for displacement due to unfavourable wind conditions en route. Favourable winds trigger migration only when directed towards specific areas but not to others. Despite their dependence on wind for dynamic soaring, Cory's shearwaters show a high individuality in migratory behaviour that cannot be explained by individual birds encountering different meteorological conditions at departure or during migratory movements.

How many animals really do the Lévy walk?

Lévy walks (LW) are superdiffusive and scale-free random walks that have recently emerged as a new conceptual tool for modeling animal search paths. They have been claimed to be more efficient than the "classical" random walks, and they also seem able to account for the actual search patterns of various species. This suggests that many animals may move using a LW process. LW patterns look like the actual search patterns displayed by animals foraging in a patchy environment, where extensive and intensive searching modes alternate, and which can be generated by a mixture of classical random walks. In this context, even elementary composite Brownian walks are more efficient than LW but may be confounded with them because they present apparent move-length-heavy tail distributions and superdiffusivity. The move-length "survival" distribution (i.e., the cumulative number of moves greater than any given threshold) appears to be a better means to highlight a LW pattern. Even once such a pattern has been clearly identified, it remains to determine how it was actually generated, because a LW pattern is not necessarily produced by a LW process but may emerge from the way the animal interacted with the environment structure through more classical movement processes. In any case, emergent movement patterns should not be confused with the processes that gave rise to them.

Detecting an orientation component in animal paths when the preferred direction is individual-dependent.

An orientation component leads to directionally biased paths, with major consequences in animal population redistribution. Classical orientation analyses, which focus on the overall direction of motion, are useless for detecting such a component when the preferred direction is not common to the whole population, but differs from one path to another. In-depth path analyses are required in this case. They consist of determining whether paths are more suitably represented as biased or unbiased random walks. The answer is not easy because most animals' paths show some forward persistence propensity that acts as a purely local directional bias and, hence, blurs the possible occurrence of an additional, consistent bias in a preferred direction. I highlight the key differences between biased and unbiased random walks and the different ways orientation mechanisms can generate a consistent directional bias. I then examine the strength and weakness of the available methods likely to detect it. Finally, I introduce a new procedure based on the backward evolution of the beeline distance, from the end of the path, which might correspond to a goal toward which the animal orients itself, to each of the animal's preceding locations. This new procedure proves to be very efficient, as it requires only a small sample of short paths for detecting a possible orientation component.

What do European badgers (Meles meles) know about the spatial organisation of neighbouring groups?

European badgers (Meles meles) live in groups. Although they can distinguish between a member of their own group, a member of a neighbouring group and a stranger, their ability to understand that neighbouring individuals belong to different groups inhabiting different places, and possibly to build up some representation of the spatial organisation of neighbouring groups remains to be shown. In this study, we conducted a pilot homing experiment to test such ability. Radio-collared badgers were displaced to the home ranges of neighbouring groups and their homing performances were compared to those of badgers displaced either to the periphery of their own group's home range or beyond the neighbouring home ranges. When released in their own home range, badgers homed rapidly and efficiently, whereas when released beyond the neighbouring groups' home ranges (whatever the distance) they did not home. In contrast, badgers released in the home range of a neighbouring group performed some random search there, before returning to their setts quite efficiently. These results suggest that badgers may consider their neighbours as members of different groups inhabiting different places close to their own home range, but their ability to build up some spatial representation of neighbourhood relationships could not be demonstrated.

Coping with spatial heterogeneity and temporal variability in resources and risks: adaptive movement behaviour by a large grazing herbivore.

Movement is a key mean for mobile species to cope with heterogeneous environments. While in herbivorous mammals large-scale migration has been widely investigated, fine-scale movement responses to local variations in resources and predation risk remain much less studied, especially in savannah environments. We developed a novel approach based on complementary movement metrics (residence time, frequency of visits and regularity of visits) to relate movement patterns of a savannah grazer, the blue wildebeest Connochaetes taurinus, to fine-scale variations in food availability, predation risk and water availability in the Kruger National Park, South Africa. Wildebeests spent more time in grazing lawns where the grass is of higher quality but shorter than in seep zones, where the grass is of lower quality but more abundant. Although the daily distances moved were longer during the wet season compared to the dry season, the daily net displacement was lower, and the residence time higher, indicating a more frequent occurrence of area-concentred searching. In contrast, during the late dry season the foraging sessions were more fragmented and wildebeests moved more frequently between foraging areas. Surprisingly, predation risk appeared to be the second factor, after water availability, influencing movement during the dry season, when resources are limiting and thus expected to influence movement more. Our approach, using complementary analyses of different movement metrics, provided an integrated view of changes in individual movement with varying environmental conditions and predation risk. It makes it possible to highlight the adaptive behavioral decisions made by wildebeest to cope with unpredictable environmental variations and provides insights for population conservation.