Collective Animal Behavior from Bayesian Estimation and Probability Matching

Abstract

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to observations, with less emphasis in obtaining first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching. In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability equal to the Bayesian-estimated probability that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior.

Author Summary

Animals need to act on uncertain data and with limited cognitive abilities to survive. It is well known that our sensory and sensorimotor processing uses probabilistic estimation as a means to counteract these limitations. Indeed, the way animals learn, forage or select mates is well explained by probabilistic estimation. Social animals have an interesting new opportunity since the behavior of other members of the group provides a continuous flow of indirect information about the environment. This information can be used to improve their estimations of environmental factors. Here we show that this simple idea can derive basic interaction rules that animals use for decisions in social contexts. In particular, we show that the patterns of choice of Gasterosteus aculeatus correspond very well to probabilistic estimation using the social information. The link found between estimation and collective behavior should help to design experiments of collective behavior testing for the importance of estimation as a basic property of how brains work.