title: Hierarchical random walks in trace fossils and the origin of optimal search behavior.
abstract: Efficient searching is crucial for timely location of food and other resources. Recent studies show that diverse living animals use a theoretically optimal scale-free random search for sparse resources known as a Lévy walk, but little is known of the origins and evolution of foraging behavior and the search strategies of extinct organisms. Here, using simulations of self-avoiding trace fossil trails, we show that randomly introduced strophotaxis (U-turns)--initiated by obstructions such as self-trail avoidance or innate cueing--leads to random looping patterns with clustering across increasing scales that is consistent with the presence of Lévy walks. This predicts that optimal Lévy searches may emerge from simple behaviors observed in fossil trails. We then analyzed fossilized trails of benthic marine organisms by using a novel path analysis technique and find the first evidence, to our knowledge, of Lévy-like search strategies in extinct animals. Our results show that simple search behaviors of extinct animals in heterogeneous environments give rise to hierarchically nested Brownian walk clusters that converge to optimal Lévy patterns. Primary productivity collapse and large-scale food scarcity characterizing mass extinctions evident in the fossil record may have triggered adaptation of optimal Lévy-like searches. The findings suggest that Lévy-like behavior has been used by foragers since at least the Eocene but may have a more ancient origin, which might explain recent widespread observations of such patterns among modern taxa.
authors.affiliation: Marine Biological Association of the United Kingdom, Plymouth PL1 2PB, United Kingdom;Ocean and Earth Science, National Oceanography Centre Southampton, University of Southampton, Waterfront Campus, Southampton SO14 3ZH, United Kingdom;Centre for Biological Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, United Kingdom; dws@mba.ac.uk.
authors.forename: David W
authors.initials: DW
authors.lastname: Sims
authors.affiliation: Rothamsted Research, Harpenden, Hertfordshire AL5 2JQ, United Kingdom;
authors.forename: Andrew M
authors.initials: AM
authors.lastname: Reynolds
authors.affiliation: Marine Biological Association of the United Kingdom, Plymouth PL1 2PB, United Kingdom;
authors.forename: Nicolas E
authors.initials: NE
authors.lastname: Humphries
authors.affiliation: Marine Biological Association of the United Kingdom, Plymouth PL1 2PB, United Kingdom;
authors.forename: Emily J
authors.initials: EJ
authors.lastname: Southall
authors.affiliation: Marine Biological Association of the United Kingdom, Plymouth PL1 2PB, United Kingdom;
authors.forename: Victoria J
authors.initials: VJ
authors.lastname: Wearmouth
authors.affiliation: Earth and Climate Cluster, Faculty of Earth and Life Sciences, VU University Amsterdam, 1081 HV, Amsterdam, The Netherlands; and.
authors.forename: Brett
authors.initials: B
authors.lastname: Metcalfe
authors.affiliation: Department of Earth Sciences, The Natural History Museum, London SW7 5BD, United Kingdom.
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Twitchett
mesh_terms: D001070:Appetitive Behavior; D005580:Fossils; D008962:Models, Theoretical
keywords: Brownian motion; climate change; scale invariance; superdiffusion