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arXiv · 2111.15231

Phase transition in non-Markovian animal exploration model with preferential returns

Ohad Vilk·Daniel Campos·Vicenç Méndez·Emmanuel Lourie·Ran Nathan·Michael Assaf
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Abstract

We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. We derive exact results for the probability of visiting a given number of sites and develop a practical WKB approximation to treat the nonstationary problem. We further show that this model adequately describes empirical movement data of Egyptian fruit bats (Rousettus aegyptiacus) when accounting for inter-individual variation in the population. Finally, we study the probability of visiting any site a given number of times and derive the corresponding mean-field equation. Here, we find a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.

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Ohad Vilk, Daniel Campos, Vicenç Méndez, Emmanuel Lourie, Ran Nathan, Michael Assaf. 2021-11-30. Phase transition in non-Markovian animal exploration model with preferential returns. https://doi.org/10.1103/physrevlett.128.148301

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