Evolutionary applications of risk sensitivity models to socially stratified species: Comparison of sigmoid, concave, and linear functions

Abstract

Risk sensitivity is important for modeling behavior since organisms live in a stochastic world and must respond to risk by either avoiding it to the extent possible or taking chances. Researchers have proposed various models of risk-sensitive behavior including concave utility functions and step functions. These formulations either do not model attraction to risk, or they are overly simple or discontinuous models of more complex behavior. I propose a sigmoid formulation to overcome these limitations. I then compare different models using data from Andean pastoralists, Aché foragers, and Sulawesi Crested Black Macaques. The analyses indicate that the sigmoid utility function provides a useful model in situations where class-like status differences exist. Otherwise, more traditional concave or linear functions can model utility, although the sigmoid formulation can subsume both linear and concave functions. Importantly, the models considered contain variables that have an impact on reproductive fitness, indicating that there could be an evolutionary basis for systematic risk sensitivity.