Misconceptions about quantifying animal encounter and interaction processes

Abstract

The ability to quantify when and where animals interact is key to the understanding of a plethora of ecological processes, from the structure of social communities and predator–prey relations to the spreading of pathogens and information. Despite the ubiquity of interaction processes among animals and the revolution in tracking technologies that now allows for the monitoring of multiple individuals simultaneously, a common theoretical framework with which to analyze movement data and extract interaction events is still lacking. Given the wide spectrum of mechanisms that governs how a biological organism detects the proximity of other organisms, most of the proposed theoretical approaches have been tailored to specific species or empirical situations and so far have been lacking a common currency with which to evaluate and compare findings across taxa. Here, we propose such general framework by borrowing techniques from statistical physics, specifically from the theory of reaction diffusion processes. Some of these techniques have already been employed to predict analytically pathogen transmission events between pairs of animals living within home ranges, but have not yet pervaded the movement ecology literature. Using both continuous and discrete variables, we present the mathematical framework and demonstrate its suitability to study interaction processes. By defining interactions whenever a token of information is transferred from one individual to another, we show that the probability of transferring information for the first time is equivalent to the first-passage probability of reacting in a multi-target environment. As interaction events reduce to encounter events when information transfer is perfectly efficient, we compare our formalism to a recently proposed approach to study encounters. Such approach takes the joint occupation probability of two animals over a region of interaction as a measure of the probability of encounter, rather than the first-encounter probability. We show the discrepancy of the two approaches by analytically comparing their predictions with continuous variables, while with discrete space–time variables, we quantify their difference over time. We conclude by pointing to some of the open problems that the reaction diffusion formalism, alternatively, the reaction motion formalism, as it should be more appropriately called, might be able to tackle.