Optimal foraging strategies: Lévy walks balance searching and patch exploitation under a very broad range of conditions

While evidence for optimal random search patterns, known as Lévy walks, in empirical movement data is mounting for a growing list of taxa spanning motile cells to humans, there is still much debate concerning the theoretical generality of Lévy walk optimisation. Here, using a new and robust simulation environment, we investigate in the most detailed study to date (24×10(6) simulations) the foraging and search efficiencies of 2-D Lévy walks with a range of exponents, target resource distributions and several competing models. We find strong and comprehensive support for the predictions of the Lévy flight foraging hypothesis and in particular for the optimality of inverse square distributions of move step-lengths across a much broader range of resource densities and distributions than previously realised. Further support for the evolutionary advantage of Lévy walk movement patterns is provided by an investigation into the 'feast and famine' effect, with Lévy foragers in heterogeneous environments experiencing fewer long 'famines' than other types of searchers. Therefore overall, optimal Lévy foraging results in more predictable resources in unpredictable environments.

Within-Otolith Variability in Chemical Fingerprints: Implications for Sampling Designs and Possible Environmental Interpretation

Largely used as a natural biological tag in studies of dispersal/connectivity of fish, otolith elemental fingerprinting is usually analyzed by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). LA-ICP-MS produces an elemental fingerprint at a discrete time-point in the life of a fish and can generate data on within-otolith variability of that fingerprint. The presence of within-otolith variability has been previously acknowledged but not incorporated into experimental designs on the presumed, but untested, grounds of both its negligibility compared to among-otolith variability and of spatial autocorrelation among multiple ablations within an otolith. Here, using a hierarchical sampling design of spatial variation at multiple scales in otolith chemical fingerprints for two Mediterranean coastal fishes, we explore: 1) whether multiple ablations within an otolith can be used as independent replicates for significance tests among otoliths, and 2) the implications of incorporating within-otolith variability when assessing spatial variability in otolith chemistry at a hierarchy of spatial scales (different fish, from different sites, at different locations on the Apulian Adriatic coast). We find that multiple ablations along the same daily rings do not necessarily exhibit spatial dependency within the otolith and can be used to estimate residual variability in a hierarchical sampling design. Inclusion of within-otolith measurements reveals that individuals at the same site can show significant variability in elemental uptake. Within-otolith variability examined across the spatial hierarchy identifies differences between the two fish species investigated, and this finding leads to discussion of the potential for within-otolith variability to be used as a marker for fish exposure to stressful conditions. We also demonstrate that a 'cost'-optimal allocation of sampling effort should typically include some level of within-otolith replication in the experimental design. Our findings provide novel evidence to aid the design of future sampling programs and improve our general understanding of the mechanisms regulating elemental fingerprints.

Hierarchical random walks in trace fossils and the origin of optimal search behavior

Efficient searching is crucial for timely location of food and other resources. Recent studies show diverse living animals employ a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behaviour and the search strategies of extinct organisms. Here we show using simulations of self-avoiding trace fossil trails that randomly introduced strophotaxis (U-turns) – initiated by obstructions such as ¬¬¬self-trail avoidance or innate cueing – leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts optimal Lévy searches can emerge from simple behaviours observed in fossil trails. We then analysed fossilized trails of benthic marine organisms using a novel path analysis technique and find the first evidence of Lévy-like search strategies in extinct animals. Our results show that simple search behaviours of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterising mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest Lévy-like behaviour has been employed by foragers since at least the Eocene but may have a more ancient origin, which could explain recent widespread observations of such patterns among modern taxa.