The evolutionary maintenance of Lévy flight foraging

Lévy flight is a type of random walk that characterizes the behaviour of many natural phenomena studied across a multiplicity of academic disciplines; within biology specifically, the behaviour of fish, birds, insects, mollusks, bacteria, plants, slime molds, t-cells, and human populations. The Lévy flight foraging hypothesis states that because Lévy flights can maximize an organism’s search efficiency, natural selection should result in Lévy-like behaviour. Empirical and theoretical research has provided ample evidence of Lévy walks in both extinct and extant species, and its efficiency across models with a diversity of resource distributions. However, no model has addressed the maintenance of Lévy flight foraging through evolutionary processes, and existing models lack ecological breadth. We use numerical simulations, including lineage-based models of evolution with a distribution of move lengths as a variable and heritable trait, to test the Lévy flight foraging hypothesis. We include biological and ecological contexts such as population size, searching costs, lifespan, resource distribution, speed, and consider both energy accumulated at the end of a lifespan and averaged over a lifespan. We demonstrate that selection often results in Lévy-like behaviour, although conditional; smaller populations, longer searches, and low searching costs increase the fitness of Lévy-like behaviour relative to Brownian behaviour. Interestingly, our results also evidence a bet-hedging strategy; Lévy-like behaviour reduces fitness variance, thus maximizing geometric mean fitness over multiple generations.
Author summary In heterotrophs, incuding animals, survival depends on the net energy gained through foraging. The expectation, then, is that natural selection results in adaptations for efficient foraging that optimize the balance of searching costs and rewards. Lévy flight foraging has been proposed as an optimal foraging solution. The hypothesis states, if no information about resource locations are available, and the locations are re-visitable, then selection will result in adaptations for Lévy flight foraging, a type of random walk. It has been argued that Levy-like foraging behaviour may simply reflect how resources are distributed, but empirical and theoretical research suggests that this behaviour is intrinsic or innate. However, this research does not address evolutionary mechanisms, and lacks ecological breadth. We extend the current theoretical framework by including evolutionary ecological contexts. We treat an organism’s random walk as a heritable trait, and explore ecological contexts such as population size, lifespan, carrying capacity, searching costs, reproductive strategies, and different distributions of food. Our evolutionary simulations overwhelmingly resulted in selection for Lévy-like foraging, regardless of the distribution of food, and evidences Lévy flight foraging as a bet-hedging strategy. Thus, here we provide some of the first evidence for the evolutionary maintenance of Lévy flight foraging.