Community dynamics, trade-offs, invasion criteria and the evolution of host resistance to microparasites

This article discusses the community dynamics of the evolution of host resistance to microparasites. We present exact results for a model with an arbitrary number of host strains. We show that these results are identical to those inferred on the basis of invadability criteria. The long-term behaviour of the model allows monomorphism or dimorphism (but no higher polymorphisms). We invoke trade-offs between pathogen transmissibility and either host intrinsic growth rate or resistance to crowding. In the first case, convexity leads to an ESS, concavity to branching points and repellers. In the second, these roles are interchanged. We present results for fixed strain distributions and establish parallels with results using an adaptive dynamics perspective. We also establish differences. For example, if an ESS is "deleted" from the strain distribution, then adjacent-strain dimorphism is possible. The invadability criteria which we obtain can be expressed in terms of geometrical properties of the trade-offs namely, the slopes of chords and tangent to the associated function. We speculate that this result may have wider applicability than provided by the context of the present work.