Bartumeus F. (2015) Behavioural ecology cannot turn its back on Lévy walk research Comment on "Liberating Lévy walk research from the shackles of optimal foraging" by A.M. Reynolds. Physics of Life Reviews. 14: 84-86.LinkDoi: 10.1016/j.plrev.2015.06.007
[No abstract available]
Campos D., Bartumeus F., Raposo E.P., Méndez V. (2015) First-passage times in multiscale random walks: The impact of movement scales on search efficiency. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 92: 0-0.LinkDoi: 10.1103/PhysRevE.92.052702
An efficient searcher needs to balance properly the trade-off between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multiscale random walks as an approximation to the scale-free case and derive the exact expressions for their mean-first-passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the situation in which both nearby and faraway targets are available to the searcher, so the exploration-exploitation trade-off does not have a trivial solution. For this situation, we prove that the combination of only two movement scales is able to outperform both ballistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about target distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies arise through the informed combination of only two walk scales (related to the exploitative and the explorative scales, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales). © 2015 American Physical Society.
Kolzsch A., Alzate A., Bartumeus F., De Jager M., Weerman E.J., Hengeveld G.M., Naguib M., Nolet B.A., Van De Koppel J. (2015) Experimental evidence for inherent lévy search behaviour in foraging animals. Proceedings of the Royal Society B: Biological Sciences. 282: 0-0.LinkDoi: 10.1098/rspb.2015.0424
Recently, Lévy walks have been put forward as a new paradigm for animal search and many cases have been made for its presence in nature. However, it remains debated whether Lévy walks are an inherent behavioural strategy or emerge from the animal reacting to its habitat. Here, we demonstrate signatures of Lévy behaviour in the search movement of mud snails (Hydrobia ulvae) based on a novel, direct assessment of movement properties in an experimental set-up using different food distributions. Our experimental data uncovered clusters of small movement steps alternating with long moves independent of food encounter and landscape complexity. Moreover, size distributions of these clusters followed truncated power laws. These two findings are characteristic signatures of mechanisms underlying inherent Lévy-like movement. Thus, our study provides clear experimental evidence that such multi-scale movement is an inherent behaviour rather than resulting from the animal interacting with its environment. © 2015 The Author(s) Published by the Royal Society.
Tromer R.M., Barbosa M.B., Bartumeus F., Catalan J., Da Luz M.G.E., Raposo E.P., Viswanathan G.M. (2015) Inferring Lévy walks from curved trajectories: A rescaling method. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 92: 0-0.LinkDoi: 10.1103/PhysRevE.92.022147
An important problem in the study of anomalous diffusion and transport concerns the proper analysis of trajectory data. The analysis and inference of Lévy walk patterns from empirical or simulated trajectories of particles in two and three-dimensional spaces (2D and 3D) is much more difficult than in 1D because path curvature is nonexistent in 1D but quite common in higher dimensions. Recently, a new method for detecting Lévy walks, which considers 1D projections of 2D or 3D trajectory data, has been proposed by Humphries et al. The key new idea is to exploit the fact that the 1D projection of a high-dimensional Lévy walk is itself a Lévy walk. Here, we ask whether or not this projection method is powerful enough to cleanly distinguish 2D Lévy walk with added curvature from a simple Markovian correlated random walk. We study the especially challenging case in which both 2D walks have exactly identical probability density functions (pdf) of step sizes as well as of turning angles between successive steps. Our approach extends the original projection method by introducing a rescaling of the projected data. Upon projection and coarse-graining, the renormalized pdf for the travel distances between successive turnings is seen to possess a fat tail when there is an underlying Lévy process. We exploit this effect to infer a Lévy walk process in the original high-dimensional curved trajectory. In contrast, no fat tail appears when a (Markovian) correlated random walk is analyzed in this way. We show that this procedure works extremely well in clearly identifying a Lévy walk even when there is noise from curvature. The present protocol may be useful in realistic contexts involving ongoing debates on the presence (or not) of Lévy walks related to animal movement on land (2D) and in air and oceans (3D). © 2015 American Physical Society.
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