Collective Animal Behavior from Bayesian Estimation and Probability Matching

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 based on empirical fits to observations and we lack 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 given by the Bayesian estimation 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

A common rule for decision-making in animal collectives across species

A diversity of decision-making systems has been observed in animal collectives. In some species, choices depend on the differences of the numbers of animals that have chosen each of the available options, while in other species on the relative differences (a behavior known as Weber's law) or follow more complex rules. We here show that this diversity of decision systems corresponds to a single rule of decision-making in collectives. We first obtained a decision rule based on Bayesian estimation that uses the information provided by the behaviors of the other individuals to improve the estimation of the structure of the world. We then tested this rule in decision experiments using zebrafish (Danio rerio), and in existing rich datasets of argentine ants (Linepithema humile) and sticklebacks (Gasterosteus aculeatus), showing that a unified model across species can quantitatively explain the diversity of decision systems. Further, these results show that the different counting systems used by animals, including humans, can emerge from the common principle of using social information to make good decisions

Bayesian decision making in human collectives with binary choices

Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds. In many situations, agents choose between discrete options. We analyze experimental data on binary opinion choices in humans. The data consists of two separate experiments in which humans answer questions with a binary response, where one is correct and the other is incorrect. The questions are answered without and with information on the answers of some previous participants. We find that a Bayesian approach captures the probability of choosing one of the answers. The influence of peers is uncorrelated with the difficulty of the question. The data is inconsistent with Weber's law, which states that the probability of choosing an option depends on the proportion of previous answers choosing that option and not on the total number of those answers. Last, the present Bayesian model fits reasonably well to the data as compared to some other previously proposed functions although the latter sometime perform slightly better than the Bayesian model. The asset of the present model is the simplicity and mechanistic explanation of the behavior.Comment: 8 pages, 6 figures, 1 tabl

A hierarchical Bayesian approach to record linkage and population size problems

We propose and illustrate a hierarchical Bayesian approach for matching statistical records observed on different occasions. We show how this model can be profitably adopted both in record linkage problems and in capture--recapture setups, where the size of a finite population is the real object of interest. There are at least two important differences between the proposed model-based approach and the current practice in record linkage. First, the statistical model is built up on the actually observed categorical variables and no reduction (to 0--1 comparisons) of the available information takes place. Second, the hierarchical structure of the model allows a two-way propagation of the uncertainty between the parameter estimation step and the matching procedure so that no plug-in estimates are used and the correct uncertainty is accounted for both in estimating the population size and in performing the record linkage. We illustrate and motivate our proposal through a real data example and simulations.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS447 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Networks and Transaction Costs

Based on the well-known fact that social networks can provide effective mechanisms that help to increase the trust level between two trade partners, we apply a simple game-theoretical framework to derive transaction costs as a high risk of opportunistic behavior in a repeated trade relation determined by the density and size of trading networks. In the empirical part of the paper we apply a two stage procedure to estimate the impact of social network structures on farm’s transaction costs observed for different input and output markets. At a first stage we estimate a multiple input-multiple output stochastic Ray production function to generate relative shadow prices of three inputs and two outputs traded by farms. At a second stage a structural equation system is derived from the first order conditions of farm’s profit maximization to estimate simultaneously the of commodity specific transaction cost functions for all traded farm inputs and outputs. Estimation results based on a sample of 315 Polish farms imply a significant influence of social network structures on farm’s transaction costs. Moreover, estimated transaction costs correspond to a reasonable amount of farm specific shadow prices.Resource /Energy Economics and Policy,