Animal Search Strategies: A Quantitative Random-Walk Analysis

Abstract

Recent advances in spatial ecology have improved our understanding of the role of large-scale animal movements. However, an unsolved problem concerns the inherent stochasticity involved in many animal search displacements and its possible adaptive value. When animals have no information about where targets (i.e., resource patches, mates, etc.) are located, different random search strategies may provide different chances to find them. Assuming random-walk models as a necessary tool to understand how animals face such environmental uncertainty, we analyze the statistical differences between two random-walk models commonly used to fit animal movement data, the Lévy walks and the correlated random walks, and we quantify their efficiencies (i.e., the number of targets found in relation to total displacement) within a random search context. Correlated random-walk properties (i.e., scale-finite correlations) may be interpreted as the by-product of locally scanning mechanisms. Lévy walks, instead, have fundamental properties (i.e., super-diffusivity and scale invariance) that allow a higher efficiency in random search scenarios. Specific biological mechanisms related to how animals punctuate their movement with sudden reorientations in a random search would be sufficient to sustain Lévy walk properties. Furthermore, we investigate a new model (the Lévy-modulated correlated random walk) that combines the properties of correlated and Lévy walks. This model shows that Lévy walk properties are robust to any behavioral mechanism providing short-range correlations in the walk. We propose that some animals may have evolved the ability of performing Lévy walks as adaptive strategies in order to face search uncertainties.

Environmental context explains Lévy and Brownian movement patterns of marine predators

“…3a). This indicates that the frequency of observed movement patterns approximated by a Lévy distribution in less productive areas and by an exponential (Brownian) distribution in more productive waters did not deviate significantly from theoretical predictions of the LFF hypothesis 1,4 . For bigeye and yellowfin tuna in the central eastern Pacific moving between warm stratified waters and cooler, more productive convergence-front waters (Supplementary Information, sections 2.2 and 2.3) there were 21 sections for analysis.…”

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An optimal search theory, the so-called Lévy-flight foraging hypothesis 1 , predicts that predators should adopt search strategies known as Lévy flights where prey is sparse and distributed unpredictably, but that Brownian movement is sufficiently efficient for locating abundant prey [2][3][4] . Empirical studies have generated controversy because the accuracy of statistical methods that have been used to identify Lévy behaviour has recently been questioned 5,6 .

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Bio-inspired multi-agent data harvesting in a proactive urban monitoring environment

“…Such a distribution is said to have a "heavy" tail because large-length values are more prevalent than would be present within other random distributions, such as Poisson or Gaussian. Viswanathan et al, [65,4] demonstrated that a = 2 constitutes an optimal Lévy-flight search strategy for locating targets that are distributed randomly and sparsely. Under such conditions, the a = 2 Lévy search strategy minimizes the mean distance traveled and presumably the mean energy expended before encountering a target.…”

Parameter identification of BIPT system using chaotic-enhanced fruit fly optimization algorithm

“…More recently, a new kind of Drosophila (fruit fly) inspired swarm intelligence technique has been developed, called fruit fly optimization algorithm (FOA) [17]. The main inspiration of FOA is that the fruit fly itself is superior to other species in sensing and perception, especially in osphresis and vision [18,19]. Since FOA is simple and elegant in concept, easy to implement and has few parameters, it has been applied in many areas [20][21][22][23][24].…”