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.Brownian motion | superdiffusion | scale invariance | climate change

Key Questions in Marine Megafauna Movement Ecology

“…The observed patterns of movement are theoretically optimal for locating the patchy and sparse distributions of prey that occur in the ocean [8]. Although a truncated Lévy walk and other simple null models are convenient for testing commonalities in movement among taxonomically wellseparated species (see also Figure 1), there is a need for future research aimed at understanding the physiological and behavioural mechanisms underpinning common movement patterns [11], their evolutionary origin [21] and the costs and benefits of different patterns (Box 1). As a corollary, addressing this question of commonalities will also shed light on the levels and drivers of variation in vertical and horizontal movements ( Figure 2).…”

Intrinsic Lévy behaviour in organisms – searching for a mechanism

“…This distinct advantage, now shown to be present over a much broader set of conditions than originally theorised [3], implied that the Lévy walk is a search strategy that should be found very widely in organisms [4]. In the years since there have been several influential empirical studies showing that Lévy walks can indeed be detected in the movement patterns of a very broad range of taxa, from jellyfish, insects, fish, reptiles, seabirds, humans [5][6][7][8][9][10], and even in the fossilised trails of extinct invertebrates [11]. The broad optimality and apparent deep evolutionary origin of movement (search) patterns that are well approximated by Lévy walks led to the development of the Lévy flight foraging (LFF) hypothesis [12], which states that "since Lévy flights and walks can optimize search efficiencies, therefore natural selection should have led to adaptations for Lévy flight foraging".…”

“…The idea that organism search strategies naturally evolved to exploit optimal Lévy patterns has gathered pace in recent years [5,7,9,11]. To account for observed Lévy-like behaviour -by which I mean behaviour patterns well approximated by a truncated Lévy distribution -it has been hypothesized that (i) scale-free activities may arise from intrinsic processes [9,11,[13][14][15][16], (ii) that behavioural adaptations to changes in environmental resources may cue the switching between localized Brownian and Lévy random searching [5,7], or (iii) that sensory interactions with heterogeneous environments may give rise to Lévy movement patterns (an emergent phenomena) [17,18].…”

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

“…Numerous recent papers have demonstrated that foraging animals in the wild or under controlled conditions show path lengths consistent with power laws (5)(6)(7)(8)(9)(10)(11), which are proposed to arise from an underlying Lévy walk process. Theoretical models have demonstrated that such a process can be optimal for memoryless agents searching for randomly distributed rewards across space under certain conditions (1,2,12).…”