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

TL;DR

This paper introduces a non-Markovian animal movement model with memory and exploration, revealing a phase transition in visitation patterns that explains foraging behavior, supported by empirical data from Egyptian fruit bats.

Contribution

The study develops an exact analytical framework for a non-Markovian animal exploration model with preferential returns, including a WKB approximation and empirical validation.

Findings

Identifies a phase transition at linear preferential returns.

Model accurately fits movement data of Egyptian fruit bats.

Reveals a trade-off between extensive and intensive foraging modes.

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.