The weierstrassian movement patterns of snails

Weierstrassian Levy walks are the archetypical form of random walk that do not satisfy the central limit theorem and are instead characterized by scale invariance. They were originally regarded as a mathematical abstraction but subsequent theoretical studies showed that they can, in principle, at least, be generated by chaos. Recently, Weierstrassian Levy walks have been found to provide accurate representations of the movement patterns of mussels (Mytilus edulis) and mud snails (Hydrobia ulvae) recorded in the laboratory under controlled conditions. Here, we tested whether Weierstrassian Levy walks and chaos are present under natural conditions in intertidal limpets Patella vulgata and P. rustica, and found that both characteristics are pervasive. We thereby show that Weierstrassian Levy walks may be fundamental to how molluscs experience and interact with the world across a wide range of ecological contexts. We also show in an easily accessible way how chaos can produce a wide variety of Weierstrassian Levy walk movement patterns. Our findings support the Levy flight foraging hypothesis that posits that because Levy walks can optimize search efficiencies, natural selection should have led to adaptations for Levy walks.