Lévy flight random searches in biological phenomena

Abstract

There has been growing interest in the study of L evy ights observed in the movements of biological organisms performing random walks while searching for other organisms. Here, we approach the problem of what is the best statistical strategy for optimizing the encounter rate between “searcher” and “target” organisms—either of the same or of di9erent species—in terms of a limiting generalized searcher–target model (e.g., predator-prey, mating partner, pollinator– ower). In this context, we discuss known results showingthat for =xed targets an inverse square density distribution of step lengths can optimize the encounter rate. For moving targets, we review how the encounter rate depends on whether organisms move in L evy or Brownian random walks. We discuss recent =ndings indicating that L evy walks confer a signi=cant advantage for increasing encounter rates only when the searcher is larger or moves rapidly relative to the target, and when the target density is low.