Grognard, F. | bioRxiv Science

bioRxiv2023

Taking fear back into the Marginal Value Theorem: the risk-MVT and optimal boldness

Foragers exploiting heterogeneous habitats must make strategic movement decisions in order to maximize fitness. Foraging theory has produced very general formalizations of the optimal patch-leaving decisions rational individuals should make. One is Charnovs Marginal Value Theorem (MVT), which models the sequential visit of habitat patches and their spatial distribution. The MVT has a simple intuitive graphical interpretation in terms of gain functions and travel times. However, it considers only energy gains, and the effect of predation risk on the time allocation strategy is notoriously lacking. An important development that includes predation risk was Browns economic treatment of optimal patch leaving decisions, the basis of giving-up density (GUD) theory, often cited as an extension of the MVT. However, it is a more abstract result that does not have the specificities or graphical appeal of the MVT. Although both successful, the two theories are cited by distinct communities and are seldom connected in texbooks. Here we formally introduce the risk-MVT (rMVT), a generalization of the MVT that can incorporate most types of predation risks. We show that Browns GUD-theory is equivalent to a rMVT, but applies for one type of predation risk only. The rMVT retains the structure and graphical simplicity of the MVT, but implies a shift from residence time to expected dose of risk (micromort units, as used in decision analysis) as the domain over which rates of gain are computed and maximized. 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 responses of behaviours observed in experimental versus natural conditions. The risk-MVT can also be used to predict the optimal level of risk taking, or "optimal boldness", and suggests that individuals should generally be bolder in riskier habitats.

evolutionary biology↗

bioRxiv2018

How optimal foragers should respond to habitat changes? On the consequences of habitat conversion.

The Marginal Value Theorem (MVT) provides a framework to predict how habitat modifications related to the distribution of resources over patches should impact the realized fitness of individuals and their optimal rate of movement (or patch residence times) across the habitat. Most MVT theory has focused on the consequences of changing the shape of the gain functions in some patches, describing for instance patch enrichment. However an alternative form of habitat modification is habitat conversion, whereby patches are converted from one existing type to another (e.g. closed habitat to open habitat). In such a case the set of gain functions existing in the habitat does not change, only their relative frequencies does. This has received comparatively very little attention in the context of the MVT. Here we analyze mathematically the consequences of habitat conversion under the MVT. We study how realized fitness and the average rate of movement should respond to changes in the frequency distribution of patch-types, and how they should covary. We further compare the response of optimal and non-plastic foragers. We find that the initial pattern of patch-exploitation in a habitat, characterized by the regression slope of patch yields over residence times, can help predict the qualitative responses of fitness and movement rate following habitat conversion. We also find that for some habitat conversion patterns, optimal and non-plastic foragers exhibit qualitatively different responses, and that adaptive foragers can have opposite responses in the early and late phases following habitat conversion. We suggest taking into account behavioral responses may help better understand the ecological consequences of habitat conversion.

ecology↗