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

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