Taking fear back into the marginal value theorem: the rMVT and optimal boldness

Foragers exploiting heterogeneous habitats make strategic movement decisions to maximize fitness. Charnov's marginal value theorem (MVT) models the sequential visit of habitat patches and their distribution to predict the optimal time allocation strategy. However, it notoriously ignores the effects of predation risk. Brown's giving-up density (GUD) theory is an alternative that includes predation risk. However, it is more abstract and does not have the specificity or graphical appeal of the MVT. Here, we formally introduce the rMVT (r stands for risk), a generalization of the MVT that incorporates predation risks. The rMVT retains the structure and graphical simplicity of the MVT, but implies a shift from residence time to expected dose of risk (micromorts) as the domain over which rate maximization occurs. We show that the rMVT can handle most types of risk, whereas the GUD theory is valid only for specific forms of risk. Applications of the rMVT show that different types of risk can yield opposite responses of optimal strategies to an increase in the risk level, and predict differential behavioral responses observed in experimental vs. natural conditions. The rMVT also predicts the optimal level of risk-taking, or "optimal boldness," and suggests that individuals should generally be bolder in riskier habitats.