Alladi Ramakrishnan Hall

Quantifying animal encounter and interactions: Lattice random walk approach

Debraj Das

ICTP, Trieste

We quantify encounters and interactions between moving animals/agents with the help of tools and techniques from statistical physics. We follow the discrete-spacetime approach of lattice random walk to describe the dynamics of individual animals/agents with respective home ranges. Such an approach has a few advantages over its continuous counterpart, in which dealing with spatial heterogeneities or interactions in higher dimensions is nontrivial. To quantify the interactions between individuals, we employ concepts of the theory of reaction-diffusion processes in discrete spacetime. By defining interactions whenever a token of information is transferred from one individual to another, we show that the probability of information transfer for the first time is equivalent to the first-passage probability of reacting in a multi-target environment. We obtain exact analytical expressions for the first-transmission probability, encounter probability, mean transmission time, and mean encounter time. Our work presents the reaction-diffusion theory to the movement ecology community as a hitherto unexplored tool for analyzing movement data and interaction events across diverse taxa.