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. However, there remains debate over whether Lévy-like behaviour is the result of selection for behavioural adaptations or is an emergent phenomenon due to the encounters within an environment’s distribution of resources. We ask two primary questions: 1) will Lévy-like behaviour evolve regardless of the distribution of resources? and 2) how will varying different ecological contexts affect the results of selection? We simulated populations of digital organisms which traversed environments with resources distributed according to Lévy dust and random uniform patterns. We treated an organism’s random walk as a heritable trait, and explored ecological contexts such as population size, lifespan, carrying capacity, searching costs, reproductive strategies, and competition.
Results/Conclusions
Our results overwhelmingly resulted in selection for Lévy-like foraging. More specifically, selection often resulted in search patterns with a power-law exponent of u≈2 even though resources were distributed by power-laws with 1 ≤ u ≤ 3, and regardless of most ecological contexts. However, there were subsets of parameters which resulted in selection for Brownian-like behaviour; larger populations, shorter lifespans, higher searching costs, and increasingly homogeneous distributions increased the fitness of Brownian-like behaviour relative to Lévy-like behaviour. Importantly, although the average fitness of Brownian-like behaviour was lower, the fitness variance was much larger, and this was sometimes a sufficient condition to select for Brownian-like searching patterns. The results of our model suggests two main conclusions: 1) that the Lévy flight foraging hypothesis is a sufficient explanation for Lévy-like behaviour and 2) because Lévy-like behaviour reduces fitness variance, and since its fitness is realized over longer timespans, it is arguably a bet-hedging strategy.
