Abstract
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.
Highlights
A Levy flight can be described as a random walk with move lengths pulled from a heavy-tailed distribution, P(l) * l−u with power-law exponent 1 < u < 3 [1,2,3,4] (Fig 1)
The Levy flight foraging hypothesis states that natural selection should result in Levy flight foraging
Building upon existing theoretical models, we treated a distribution of move lengths as a variable and heritable trait, and added ecological contexts such as population size, searching costs, speed of movement, lifespans, reproductive strategies, and different resource distributions
Summary
A Levy flight can be described as a random walk with move lengths pulled from a heavy-tailed distribution, P(l) * l−u with power-law exponent 1 < u < 3 [1,2,3,4] (Fig 1). Levy flights have been shown to be an efficient searching strategy for foragers [2,3,4]. Efficiency of the search for food is given by the balance between cost and reward, and is key to survival [23,24,25,26]. If the distribution of resources is unknown, the resources are sparse, randomly distributed and revisitable, and the searcher has no memory, the Levy flight foraging hypothesis states that a Levy flight with power-law exponent u ’ 2 is an optimal or near-optimal searching strategy. There is ample evidence demonstrating the prevalence of ‘Levy-like’
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