# Heterogeneous responsiveness to environmental stimuli

## TL;DR

Animals in the same species show consistent but varied responses to environmental changes, which can be explained by slight differences in individual preferences.

## Contribution

A game-theoretic model explains consistent behavioral differences as a stable strategy mix from minimal individual preference variation.

## Key findings

- Persistent behavioral differences arise from slight individual preference variations.
- A stable mix of strategies can explain coexistence, consistency, and correlation in responsiveness.
- The model provides testable implications for empirical studies on animal behavior.

## Abstract

Individuals of a species cope with environmental variability through behavioral adjustments driven by individuals’ responsiveness to environmental stimuli. Three key empirical observations have been made for many animal species: The coexistence of different degrees of responsiveness within one species; the consistency of an individual’s degree of responsiveness across time; and the correlation of an individual’s degree of responsiveness across contexts. Taking up key elements of existing approaches, we provide one unifying explanation for all three observations, by identifying a unique evolutionarily stable strategy of an appropriately defined game within a stochastic environment that has all three features. Coexistence is explained by a form of negative frequency dependence. Consistency and correlation is explained through potentially small, individual, differences of states animals have and the resulting differential advantages they can get from it. Our results allow us to identify a variety of testable implications.

Animals within the same species often respond differently to environmental changes. Individual behavior, however, is quite consistent across time and contexts. Yet, there seem to be no identifiable characteristics that could explain these differences in behavior. Using a formal game-theoretic model of animal foraging, we show that persistent and consistent differences in behavior can arise as a stable mix of strategies even when there are only the slightest differences in the animals’ personal preferences.