Recent advances in spatial ecology have improved our understanding of the role of large-scale animal movements. However, an unsolved problem concerns the inherent stochasticity involved in many animal search displacements and its possible adaptive value. When animals have no information about where targets (i.e., resource patches, mates, etc.) are located, different random search strategies may provide different chances to find them. Assuming random-walk models as a necessary tool to understand how animals face such environmental uncertainty, we analyze the statistical differences between two random-walk models commonly used to fit animal movement data, the Lévy walks and the correlated random walks, and we quantify their efficiencies (i.e., the number of targets found in relation to total displacement) within a random search context. Correlated random-walk properties (i.e., scale-finite correlations) may be interpreted as the by-product of locally scanning mechanisms. Lévy walks, instead, have fundamental properties (i.e., super-diffusivity and scale invariance) that allow a higher efficiency in random search scenarios. Specific biological mechanisms related to how animals punctuate their movement with sudden reorientations in a random search would be sufficient to sustain Lévy walk properties. Furthermore, we investigate a new model (the Lévy-modulated correlated random walk) that combines the properties of correlated and Lévy walks. This model shows that Lévy walk properties are robust to any behavioral mechanism providing short-range correlations in the walk. We propose that some animals may have evolved the ability of performing Lévy walks as adaptive strategies in order to face search uncertainties.

T cell migration is essential for T cell responses, allowing for detection of cognate antigen at the surface of an Antigen-Presenting Cell (APC) and for interactions with other cells involved in the immune response. Although appearing random, growing evidence supports that T cell motility patterns are strategic and governed by mechanisms that are optimized for both activation-stage and environment-specific attributes. In this Opinion Article, we will discuss how to understand the combined effects of T cell- intrinsic and -extrinsic forces upon these motility patterns when viewed in highly complex tissues filled with other cells involved in parallel motility. In particular, we will examine how insights from ‘search theory’ describe T cell movement across exploitation-exploration gradients, in the context of activation versus effector function and in the context of lymph nodes versus peripheral tissues.

The searching trajectories of different animals can be described with a broad class of flight length (l j) distributions with P(lj) ‫؍‬ lj ؊ . Theoretical studies have shown that changes in these distributions (i.e., different values) are key to optimizing the long-term encounter statistics under certain searcher-resource scenarios. In particular, they predict the advantage of Lé vy searching ( Ϸ 2) over Brownian motion ( > 3) for low-prey-density scenarios. Here, we present experimental evidence of predicted optimal changes in the flight-time distribution of a predator's walk in response to gradual density changes of its moving prey. Flight times of the dinoflagellate Oxyrrhis marina switched from an exponential to an inverse square power-law distribution when the prey (Rhodomonas sp.) decreased in abundance. Concomitantly, amplitude and frequency of the short-term helical path increased. The specific biological mechanisms involved in these searching behavioral changes are discussed. We suggest that, in a threedimensional environment, a stronger helical component combined with a Lé vy walk searching strategy enhances predator's encounter rates. Our results support the idea of universality of the statistical laws in optimal searching processes despite variations in the biological details of the organisms. R andom walks based on Lévy flight distributions P(l j ) ϭ l j Ϫ in concrete ''Lévy walks'' with Ϸ 2, are the optimal searching strategy for scarce fixed targets that are randomly located (1). A Lévy walk could be more efficient than the usual Gaussian (i.e., Brownian) motion as suggested by early works on microzooplankton (2-4), although Brownian motion is generally assumed in reaction-diffusion predator-prey models. Recently, ecological examples of Lévy walks have been provided for a wide range of animal species (5-10). However, the theoretical study of more complex scenarios has shown that the advantage of Lévy searching over other types of motion is restricted to a set of prey densities, and mobility and size of the predator relative to the prey (11-13). Therefore, natural selection should favor flexible behaviors, combining different searching strategies (i.e., searching statistics) under different conditions. Here, we present experimental evidence that changes occur in both the short-and long-term searching statistics of a predator (Oxyrrhis marina), coinciding with density changes of its moving prey (Rhodomonas sp.). The specific biological mechanisms involved are also identified.The marine heterotrophic dinoflagellate O. marina has two flagella, one transversal and one longitudinal, providing three types of movement: rotation, translation, and sudden directional changes (14, 15). The flagellar apparatus of O. marina has been well studied at both the cellular (15) and the ultrastructural (16) level. Continuous flagellar movements are responsible for simultaneous rotation and translation of organisms, giving rise to a helical path during movement. Normal helical motion is interrupted by sudden (60-100 ms)...

During immune surveillance, T cells survey the surface of antigen-presenting cells. In searching for peptide-loaded major histocompatibility complexes (pMHCs), they must solve a classic trade-off between speed and sensitivity. It has long been supposed that microvilli on T cells act as sensory organs to enable search, but their strategy has been unknown. We used lattice light-sheet and quantum dot-enabled synaptic contact mapping microscopy to show that anomalous diffusion and fractal organization of microvilli survey the majority of opposing surfaces within 1 minute. Individual dwell times were long enough to discriminate pMHC half-lives and T cell receptor (TCR) accumulation selectively stabilized microvilli. Stabilization was independent of tyrosine kinase signaling and the actin cytoskeleton, suggesting selection for avid TCR microclusters. This work defines the efficient cellular search process against which ligand detection takes place.

The movement ecology framework depicts animal movement as the result of the combined effects of internal and external constraints on animal navigation and motion capacities. Nevertheless, there are still fundamental problems to understand how these modulations take place and how they might be translated into observed statistical properties of animal trajectories. Of particular interest, here, is the general idea of intermittence in animal movement. Intermittent locomotion assumes that animal movement is, in essence, discrete. The existence of abrupt interruptions in an otherwise continuous flow of movement allows for the possibility of reorientations, that is, to break down previous directional memories of the trajectory. In this study, we explore the potential links between intermittent locomotion, reorientation behavior, and search efficiency. By means of simulations we show that the incorporation of Lé vy intermittence in an otherwise nonintermittent search strongly modifies encounter rates. The result is robust to different types of landscapes (i.e., target density and spatial distribution), and spatial dimensions (i.e., 2D, 3D). We propose that Lé vy intermittence may come from reorientation mechanisms capable of organizing directional persistence on time (i.e., fractal reorientation clocks), and we rationalize that the explicit distinction between scanning and reorientation mechanisms is essential to make accurate statistical inferences from animal search behavior. Finally, we provide a statistical tool to judge the existence of episodic and strong reorientation behaviors capable of modifying relevant properties of stochastic searches, ultimately controlling the chances of finding unknown located items.animal movement ͉ intermittent locomotion ͉ Lé vy walks ͉ random walks ͉ search strategies T he movement ecology framework explicitly recognizes animal movement as the result of a constant ''dialogue'' between environment (external factors) and animal internal states. This dialogue affects organisms' motion and/or navigation capacities to finally produce the actual movement (1). Beyond phenomenological descriptions of movement, the random paradigm (1) should seek to understand how interactions between the four components of the movement ecology framework (i.e., internal states, external forces, motion, and navigation capacities) might be translated into observed statistical patterns of movement (2, 3). In the present work, we suggest that a major advance in bridging the gap between animal behavior (mechanistic approach) and the statistical properties of search strategies involves a statistical reinterpretation of the idea of intermittent locomotion (4-6).The biological principle of intermittent locomotion assumes that animal behavior unavoidably produces observable punctuations in the movement (e.g., stops, strong changes in speed). Thus, the forces generating movement operate discontinuously, producing pauses and speeding patterns on the move. Intermittent locomotion (also known as stop-and-go movement, pau...

An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized searcher-target model (e.g., predator-prey, mating partner, pollinator-flower), we find that Lévy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statistical patterns of movement suggests that, beyond movement quantification, statistical physics may prove to be an adequate framework to understand animal behavior across scales from an ecological and evolutionary perspective. Recently developed random search theory has served to critically re-evaluate classic ecological questions on animal foraging. For instance, during the last few years, there has been a growing debate on whether search behavior can include traits that improve success by optimizing random (stochastic) searches. Here, we stress the need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching. By sketching the assumptions of optimal foraging theory (OFT) and by summarizing recent results on random search strategies, we pinpoint ways to extend classic OFT, and integrate the study of search strategies and its main results into the more general theory of optimal foraging.

The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems, fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms in animal foraging processes. In particular, it has been shown that Lévy processes can optimize the success of random encounters in a wide range of search scenarios, representing robust solutions to the general search problem. These results set the scene for an evolutionary explanation for the widespread observed scale-invariant properties of animal movements. Here, it is suggested that scale-free reorientations of the movement could be the basis for a stochastic organization of the search whenever strongly reduced perceptual capacities come into play. Such a proposal represents two new evolutionary insights. First, adaptive mechanisms are explicitly proposed to work on the basis of stochastic laws. And second, though acting at the individual-level, these adaptive mechanisms could have straightforward effects at higher levels of ecosystem organization and dynamics (e.g. macroscopic diffusive properties of motion, population-level encounter rates). Thus, I suggest that for the case of animal movement, fractality may not be representing an emergent property but instead adaptive random search strategies. So far, in the context of animal movement, scale-invariance, intermittence, and chance have been studied in isolation but not synthesized into a coherent ecological and evolutionary framework. Further research is needed to track the possible evolutionary footprint of Lévy processes in animal movement.