Why Lévy Foraging does not need to be ‘unshackled’ from Optimal Foraging Theory

Abstract

The comprehensive review of Lévy patterns observed in the moves and pauses of a vast array of organisms by Reynolds [1] makes clear a need to attempt to unify phenomena to understand how organism movement may have evolved. However, I would contend that the research on Lévy 'movement patterns' we detect in time series of animal movements has to a large extent been misunderstood. The statistical techniques, such as Maximum Likelihood Estimation, used to detect these patterns look only at the statistical distribution of move step-lengths and not at the actual pattern, or structure, of the movement path. The path structure is lost altogether when move steplengths are sorted prior to analysis. Likewise, the simulated movement paths, with step-lengths drawn from a truncated power law distribution in order to test characteristics of the path, such as foraging efficiency, in no way match the actual paths, or trajectories, of real animals. These statistical distributions are, therefore, null models of searching or foraging activity. What has proved surprising about these step-length distributions is the extent to which they improve the efficiency of random searches over simple Brownian motion. It has been shown unequivocally that a power law distribution of move step lengths is more efficient, in terms of prey items located per unit distance travelled, than any other distribution of move step-lengths so far tested (up to 3 times better than Brownian), and over a range of prey field densities spanning more than 4 orders of magnitude [2].

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

“…Additionally, we extended our model to show that for foragers in the wild with noisy temporal perception, the exponent of the best fit power law is governed by the nonlinearity of time perception and the amount of competition faced from other foragers. Thus, we contribute to the ongoing discussion regarding the mechanistic origins of power law path lengths in foragers (47)(48)(49)(50)(51)(52)(53)(54)(55)(56)(57)(58) by arguing that search patterns are unlikely to be purely random when cognitive modeling is advantageous and that approximate power law path lengths emerge due to the temporal discounting of farther away rewards. A deeper understanding of the neurobiological basis of spatial search (59)(60)(61)(62)(63) may further enrich this model and provide greater insight into the movements of wild animals and humans.…”

Current status and future directions of Lévy walk research

“…These and other advances will appear in print in due course. In the meantime, the interested reader can find out more in a recent technical review ( Reynolds, 2015a ) and in the associated commentaries ( Bartumeus, 2015 ; Boyer, 2015 ; Cheng, 2015 ; da Luz et al, 2015 ; Focardi, 2015 ; Humphries, 2015 ; MacIntosh, 2015 ; Miramontes, 2015 ; Sims, 2015 ; Reynolds, 2015b ), which for the most part were written by the delegates of the Workshop. For researchers, open questions abound.…”

Venturing beyond the Lévy flight foraging hypothesis: Reply to comments on “Liberating Lévy walk research from the shackles of optimal foraging”

“…Instead they typically result in the kind of Lévy walks that optimize or near optimize search efficiencies under the rather exacting conditions given in da Luz et al [4] and in the literature they cite [10]. The picture, as Bartumeus [1], Cheng [3] and Focardi [6] point out, seems to be pluralist and multi-faceted embracing both "adaptation" and "emergent" programs. This in no way detracts from the Lévy flight foraging hypothesis which da Luz et al were so instrumental in founding and which has spawned a new field of ecological research.…”

“…Similarly, power spectra analyses indicate that the overall movement patterns of E. coli also resemble Lévy walks [13]. Humphries [6] notes that most kinds of Lévy walk can outperform Brownian walks when randomly searching and that this provides useful insights when attempting to understand movement pattern data. I hold the same DOI of original article: http://dx.…”

“…Once generated they may be maintained by selection or as Focardi [5] remarked be like the "spandrels of St Mark" without biological relevance. Humphries [6] goes on to state that it has been shown "unequivocally" that Lévy walks outperform Brownian walks. I think that this is too strongly put because Lévy searching is advantageous only when certain conditions are satisfied (e.g., searching begins close a target, directionality is lost after target encounters, foragers do not adapt to conditions found along the search, energetic costs of turning are minimal, motion does not degrade perception, searching efficiency does not trade-off with safety from predation) [14][15][16].…”