Animal movement, search strategies and behavioural ecology: a cross‐disciplinary way forward

A long historical tradition exists among mathematicians, biologists and theoretical ecologists on the topic of quantifying, up-scaling and modelling the statistical properties of animal movement. Nevertheless, new paradigms and technical challenges have recently pervaded the field, attracting renewed interest, as evidenced by the large body of literature on the topic, and by the recent series of international workshops and conferences on the ecology of animal movement(*). As the need of new approaches to study movement and search aspects of behavioural ecology is becoming increasingly evident, we identify those cross-disciplinary concepts and ideas that have been burgeoning over the last few years which have the potential to drive fundamental advances in animal movement research. Three factors can be recognized as the genesis of the exciting scientific advances that have contributed to where movement research is at present. The first one is the extensive use of experimental devices of lighter weight and higher resolution, such as GPS and bio-loggers (e.g. Cooke et al. 2004; Hays et al. 2006; Wilson & McMahon 2006; Wilson et al. 2006), which allow recording of the intimate details of animal lives. New computational tools to analyse and understand such details, gathered from a constantly growing number of species, have become a necessity. The second factor, much related to the first one, is the increased awareness of the need of a unifying theory and an integrative paradigm for organism movement (Nathan et al. 2008). A framework that places animal motion as the central theme would help identify and focus the efforts for developing general empirical and analytical tools to fully understand movement patterns. The third factor is the relatively recent interpretation of animal movement with new tools and concepts borrowed from the field of statistical physics, i.e. Lévy statistics and anomalous diffusion (see the review articles: Montroll & West 1979; Schlesinger, Zaslavsky & Klafter 1993; Klafter & Sokolov 2005), and optimal stochastic search (e.g. Viswanathan et al. 1999; Bartumeus & Levin 2008). All these aspects have contributed to enrich the biological discussion on the classical topics of animal ecology such as dispersal, optimal foraging theory, landscape behavioural ecology, animal decision-making and learning. These recent developments clearly indicate the presence of a productive platform for theoreticians and empiricists to help each other answer fundamental questions in animal ecology. In this Forum, we discuss how we believe cross-disciplinary efforts should be brought to the fore in trying to move the field forward. We do so by considering the statistical modelling of: (i) animal trajectories, (ii) search strategies, and (iii) behavioural ecology. Recorded trajectories are often analysed by considering the collection of fixes as a series of random events (e.g. displacements, turns) whose spatial and temporal distributions are assumed to possess certain statistical regularities. Setting aside technicalities about model selection and validation (Hilborn & Mangel 1997; Burnham & Anderson 2002), characterizing animal movement in statistical terms is challenging because of the difficulty in quantifying the validity of specific assumptions in the adopted modelling framework. In addition, it is rather common that abstract mathematical models, even though detailed, neglect the 'nuisances' of real world data sets. For example, in analysing animal trajectories it is vital to take into account the sampling heterogeneity which can be of a spatial nature (Giuggioli et al. 2006, 2007) such as when observations are limited in space, e.g. by the line of sight of a camera, or of a temporal nature, such as those given by irregular observation frequencies, e.g. by satellite telemetry (Bradshaw, Sims & Hays 2007; Bartumeus et al. 2010). Similarly, boundaries in real experimental systems should be made explicit both in the models and the data analysis. When all these inhomogeneities are properly accounted for, whether within the modelling framework itself or by means of adequate statistical methods, spurious quantifications might be safely avoided. When these complications are taken care of, the use of mathematical models to describe movement data is helpful in identifying the links between the microscopic animal behaviour and the emergent macroscopic patterns. A step forward in tackling this problem has been the use of more sophisticated mathematical frameworks, embracing models with very general statistical properties, and thus amenable to the study and comparative analysis across different taxa. One such model, capable of accurately quantifying the diffusive properties of movement from microscopic rules, is the so-called Continuous Time Random Walk (Montroll & Weiss 1965), which generalizes the standard Brownian Random walk by introducing pausing time and step length distributions. When the animal steps display a certain degree of correlation in time, other types of mathematical frameworks become useful (see Giuggioli, Sevilla & Kenkre 2009 for an application to animal movement). These are mathematical models that generalize the classical correlated random walk (Goldstein 1951) when directional persistence does not necessarily decay exponentially in time. Another example of a more refined approach is the use of likelihood and Bayesian models (Morales et al. 2004), which has been shown to be practically useful in identifying behavioural modes within single trajectories. It is evident that combining the strengths of these recent modelling efforts with other sorts of available information (e.g. landscape patterns provided by GIS, local environmental cues, physiological information) will be useful to pursue in the future (Dalziel, Morales & Fryxell 2008; Bartumeus 2009). Anomalous diffusion and Lévy walks (see Metzler & Klafter 2000 for review) have played a crucial role in giving a spatio-temporal dimension to the study of animal foraging and search processes. Indeed, animal search strategies have received renewed interest in recent years since the possibility of optimal stochastic searching by animals was first suggested (Shlesinger & Klafter 1986). The Lévy walk/search model (Viswanathan et al. 1999; Lomholt et al. 2008; Bartumeus 2009; Reynolds & Rhodes 2009) is one important example and has been used to characterize movement patterns in many different species (Boyer et al. 2006; Reynolds et al. 2007; Sims et al. 2008). However, although more caution in the quantification of statistical search patterns (Edwards et al. 2007) and in their biological interpretation is needed (Boyer et al. 2006; Benhamou 2007; Bartumeus & Levin 2008), it is important to continue studies to identify clear Lévy patterns in free-ranging animals particularly for testing hypotheses in relation to the actual foraging success. For a range of taxa there exist in fact a variety of feeding sensors that nowadays make possible to directly record when an animal achieves foraging success (see, e.g. Fossette et al. 2008; Soto et al. 2008). Beyond the heavily improved statistical analyses to test Lévy walks in empirical data sets (Reynolds et al. 2007; Sims, Righton & Pitchford 2007; Edwards 2008; White, Enquist & Green 2008), theoretical work should be put forward to clarify the necessary and sufficient conditions for Lévy walking to become an optimal search strategy, in particular in relation to the assumptions of strongly heterogeneous target fields and high uncertainty in target locations. From a biological perspective, the activation of scale-free reorientation mechanisms as a response to uncertainty has been suggested to underlie Lévy patterns in some 'simple' animals (Bartumeus 2007; Bartumeus & Levin 2008). Despite interesting extensions of the optimal search results as the animal step lengths are linearly weighted by energy constraints (Faustino et al. 2007), a thorough evaluation of energetic budgets, not just encounter costs, such as motor processes and navigational constraints during search/foraging tasks is still lacking. It is necessary to better integrate the concepts of search and uncertainty in foraging theory in order to answer questions rigorously about the efficiency of animal foraging strategies. Interestingly, the study of spatially extended experimental setups (in the laboratory and in the field) to observe probabilistic learning and human decision-making processes during search tasks (Smith et al. 2008) could further inspire the behaviourists to use similar designs in animal foraging studies. Indeed, the study of search task performance where the amount and quality of search cues can be controlled seems a promising way to gain insight about how organisms deal with environmental uncertainties. One clear challenge in understanding animal movement is to explain how behavioural components are affected by the resource or resource cue detection in complex environments. Methods to interpret behavioural changes in movement trajectories (e.g. Dalziel et al. 2008; Gurarie, Andrews & Laidre 2009), or to identify the role of resource distributions on animal movement patterns (Boyer et al. 2006) have proved a valuable improvement. From a mere experimental perspective, and to help uncover possible mechanisms that might be common across species, general criteria to study the role of chance in behavioural/foraging ecology should be developed. State-of-the-art experiments assessing how animals integrate statistical information regarding resource distributions lack a true spatial dimension: time-resource patterns are used as a surrogate of spatial information (Dall et al. 1997). A reasonable recommendation would be to seek a fertile middle ground between measuring behaviour in the natural environment and in controlled experiments reminiscent of classical behavioural ecology. Such ground could be well represented by spatially extended systems with tight control over the spatio-temporal stochastic nature of the environmental cues that trigger the animal behavioural response (e.g. search movement, decision-making). With experiments conducted at intermediate spatial scales there should be a sufficient control for repetitive observations and, at the same time, a large enough stochastic variation to bring ecological realism. Uncertainty during environment-organism interactions arises as a function of both environmental complexity and an animal's cognitive capacity, i.e. its ability to process and integrate external sensory information with internal processes related, for example, to memory and motivation (in the context of ants, see, e.g. Franks & Richardson 2006; Richardson et al. 2007). In this context, an emergent interest in animal ecology lies with trying to link the neuroscience of decision-making processes, ultimately triggered by organism–environment information fluxes, with the statistics of animal movement. Recent neurophysiological studies have shed light on how neuronal networks in the mammalian brain encode information about an animal's spatial location (see Moser, Kropff & Moser 2008 for review) and underlie memory- or reward-based decisions (Jones & Wilson 2005). These spatially extended experiments might become particularly useful, for example, in trying to discern if the timing of reorientations emerges as a response to spatial environmental uncertainty, or if it is related to the information processing of external cues reflected by distinct neurophysiological signatures. More generally, recording of neuronal activity in animals performing complex tasks in spatially extended environments could help in resolving long-standing questions at the interface of neuroscience and behavioural and movement ecology. Other effects, when analysing movement trajectories, such as the presence of predators, and the social or competitive interactions between conspecifics, are often neglected for the sake of simplicity and/or the lack of data. It is imperative however to introduce these two realistic complexities into the studied systems, both at the theoretical as well as at the experimental level. Along with these improvements we also believe it is crucial to extend the idea of uncertainty to other movement contexts such as dispersal or migration in young inexperienced individuals. Despite the inherent simplicity, elementary mathematical models and controlled experimental setups help generate hypotheses about fundamental biological processes and become valuable in comparative studies between different species and taxa. However, they should only be considered as 'null models' upon which further ecological complexity may be built. Seeking to examine even further the goodness of a fundamental hypothesis, theoreticians should not shy away from confronting their predictions with experimental observations while empiricists should try to test the validity of theoretical constructs. Mathematical movement models could gain in realism moving from quantitative description to mechanistic based understanding, whereas carefully designed experiments could reveal insights that unequivocally either discard or embrace a modelling study. The themes of research presented here point to very fertile grounds for theoreticians and empiricists to help each other advance the field of animal ecology. Nurturing established cross-disciplinary collaborations and fostering new ones is an efficient vehicle to achieve leaps rather than steps forward. Our hope is that in the future, highly cross-disciplinary endeavours in animal ecology will represent a norm rather than an exception. Acknowledgements are due to all the delegates of the workshop on 'Animal Movement and Search Strategies: from Empirical Data to Modelling', held from 23 to 25 July 2009 at the University of Bristol, UK, and hosted by the Bristol Centre for Complexity Sciences and the Bristol Centre for Applied Nonlinear Mathematics. Part of the discussion presented here has emerged during that meeting. We also wish to thank D. Boyer, N.R. Franks, M.W. Jones, Y. Klafter, J.M. Morales and R. Nathan for commenting on drafts of the manuscript, and two anonymous referees for their suggestions. L.G. acknowledges funding from EPSRC grant EP/E501214/1. Special Topic: Movement Ecology. Ecological Society of America International Meeting. San José, California, USA, 5–10 August 2007; Modelling anomalous diffusion and relaxation: from single molecules to the flight of albatross. Institute for Advanced Studies and the Hebrew University of Jerusalem. Jerusalem, Israel, 23–28 March 2008; New frontiers in biologging science. Pacific Grove, California (USA), 1–5 September 2008; Movebank workshop on raptor migration. Acopian Center for Conservation Science, Hawk Mountain Sanctuary, Pennsylvania, USA, 17–20 January, 2009; Animal migration: linking models and data beyond taxonomic limits, Lorentz center, Leiden, The Netherlands, 2–6 March; Path Analysis and Modelling movement behaviour, University of Essex, 17–18 June 2009; Animal Movement and Search Strategies: From Empirical Data to Modelling. University of Bristol, 23–25 July 2009; Movebank workshop on Global Waterbird Tracking, 19–23 September 2009.