Phase Transition in a Non-Markovian Animal Exploration Model with Preferential Returns

Area of Science:

• Ecology
• Theoretical Biology
• Statistical Physics

Background:

• Animal movement is crucial for ecological processes.
• Existing models often simplify complex behaviors like memory and non-stationarity.
• Understanding movement patterns aids in conservation and ecological studies.

Purpose of the Study:

• To develop and validate a non-Markovian, nonstationary model of animal mobility.
• To incorporate exploration and preferential return behaviors into movement ecology.
• To analyze the movement data of Egyptian fruit bats (Rousettus aegyptiacus).

Main Methods:

• Derivation of exact results for site visitation probabilities.
• Development of a Wentzel–Kramers–Brillouin (WKB) approximation for nonstationary problems.
• Application of a generalized model, including a mean-field approach, to empirical data.

Main Results:

• The model accurately describes Egyptian fruit bat movement data, accounting for individual variation.
• A phase transition was identified in the model related to preferential return scaling.
• The probability of visiting sites and mean-field equations were derived.

Conclusions:

• The generalized model effectively captures complex animal movement patterns.
• The observed phase transition suggests a foraging strategy trade-off.
• This work provides a framework for studying memory-based movement in ecology.