| 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.The specific pattern of searching movements used by an organism to locate food relative to the food’s distribution closely determines the number of successful encounters (1–3). The evolution of optimal search patterns is predicted because natural selection favors individuals that are best able to find resources critical to survival (4). It is recognized, however, that the natural environment is too complex for evolution to produce a behavior pattern that is optimal across all scales and contexts (5). Rather, simple rules probably will evolve that, on average, perform well in their natural environment (5). Such rules are exemplified in the different movement modes that tend to characterize behavior across different spatiotemporal scales. For instance, simple deterministic foraging searches, such as Archimedean spirals (6) or area-restricted searching (7), that are driven by sensory and cognitive abilities are efficient where food distributions are known, easily detected, or predictable. However, these patterns are inefficient when food resources are sparsely or patchily distributed and the forager has incomplete information on resource location; under these conditions, probabilistic searches such as Lévy walks become advantageous (1–3).Theory predicts that Lévy walk search strategies should be optimal where food is sparse and distributed unpredictably (1), whereas Brownian walks are sufficiently efficient for locating abundant prey (2). A Lévy walk search pattern comprises displacements (move steps) drawn from a probability distribution with a heavy power-law tail that results in a fractal pattern of “walk clusters” with no characteristic scale, such that P(l) ∼ l−µ, with 1 < µ ≤ 3, where l is the move step length between turns and µ the power-law exponent. Over many iterations, a Lévy walk will be distributed much further from its starting position than a Brownian walk of the same length [hence is termed superdiffusive (8)], because small-step walk clusters are interspersed by long “steps” to new locations, with this pattern repeating across all scales. It has been demonstrated that a Lévy walk with exponent µ ∼2 is optimal when the search targets are not depleted or rejected once visited but instead may be revisited profitably, either because they replenish overtime or because targets are distributed patchily (1, 2). Importantly, Lévy searches with µ ∼2 are optimal for a very broad range of target densities and distributions (9). In the very low-density regime, Lévy strategies remain the optimal solution with the optimal exponent 1 < µopt ≤ 2 dependent on specific environmental properties, such as the degree of spatial landscape heterogeneity or temporal target revisitability (10, 11). Consequently, optimal Lévy searches result in more predictable target encounters during foraging in otherwise unpredictable environments (9). Because Lévy walks can optimize search efficiencies in this way, it is proposed that natural selection should have led to adaptations for Lévy walk foraging [the Lévy flight foraging (LFF) hypothesis] (1–3). The apparent ubiquity of Lévy patterns among extant organisms, including humans (1–3, 12–18), suggests that searches that approximate them have evolved naturally (3). It has been hypothesized that behavioral adaptations to changes in environmental resources cue the switching between localized Brownian and Lévy random searching (2, 3, 13) or that sensory interactions with heterogeneous environments may give rise to Lévy movement patterns (an emergent phenomena) (19); however, the origins of such potential mechanisms remain elusive.The fossilized records of animal movements preserved as trails and burrows (trace fossils) are the only direct record of extinct organisms’ behavior and may provide a means to understand the evolution of search strategies in ancient landscapes, including during dramatic environmental changes (6, 20, 21). At intervals throughout evolutionary history, organisms have faced large-scale collapses of primary productivity due to abiotic environmental changes, such as volcanism and global warming, that often are associated with mass extinctions of species (22, 23). This raises the possibility that random search patterns such as Lévy walks, with characteristic long steps to new locations, might have acted to increase the likelihood of ancient organisms finding scarce resources, as the search time to find distant patches is minimized in this movement strategy compared with Brownian motion (2). Nevertheless, so far, only localized foraging patterns based on simple taxes have been identified in trace fossils (6, 20, 21).An early computer simulation (20) showed that the patterns recorded by many trace fossils could be reconstructed in model foragers by using three simple “rules”: “phobotaxis,” which forbids an individual from crossing its own trail; “thigmotaxis,” which compels an individual to stay close to an existing trail; and “strophotaxis,” which is the propensity for making U-turns and which may be cued innately or triggered by the presence of an obstruction or other discontinuity. These three basic patterns of behavior now underlie most theories of spiral and meandering trace fossils (24). A general characteristic of many fossil trails is that they resemble self-avoiding random walks, as there is minimal recrossing of existing tracks (24). This resemblance is more than superficial, because some trace fossils from deep-water turbidite fan settings are fractal (25, 26), and have fractal dimensions typically estimated to be between 1.5 and 1.6 (25), which span the fractal dimension (1.55) of a self-avoiding random walk. This suggests that trace fossils also may be modeled as Lévy walks, because they share with self-avoiding random walks the same range of fractal dimensions and so exhibit, on average, the same number of subclusters per cluster with change of scale (27). However, to our knowledge, no previous study investigated the possibility of Lévy behavior occurring in ancient organisms. |
