Evolution of foraging strategies on resource gradients

Question: How are competing foragers expected to distribute their lifetime foraging effort on a gradient of resource types that differ in abundance, quality, foraging costs, and associated mortality risks? Mathematical method: Population dynamics of foragers and resources coupled with adaptive dynamics of foraging strategies based on continuous, function-valued traits. Key assumptions: We start from generalizing the classical patch-based theory of optimal foraging to continuous resource gradients following the traditional assumptions of constant renewal rates of resources, spatially homogeneous mortality risks, and of foragers that are omniscient, free to move without costs, equal, and not experiencing any saturation of intake. We then relax the restrictive assumptions of the classical model, thus accounting for non-linear functional responses of the foragers, heterogeneous mortality risks and resource qualities, energetically costly foraging, genetic covariances constraining foraging, feedbacks between foraging and resource dynamics, and different types of competition between foragers. Results: (1) When expressed as instantaneous rates with the same units (time), mortality risks (d), foraging costs (c), and resource qualities (q) all influence the evolutionarily stable distribution of foraging effort through the dimensionless expression (d + c)/q. (2) Functional responses that imply intake saturation may result in a subset of resources remaining entirely unused. (3) Coupling foraging to resource dynamics results in a rich array of evolutionary outcomes, depending on the type of competition among foragers and the interplay between forager and resource characteristics. (4) Genetic constraints may cause foraging effort to track the resource gradient more coarsely than classical models predict.