The Role of Trade-off Shapes in the Evolution and Coexistence of Virulence in Spatial Host-Parasite Interactions: An Approximate Adaptive Dynamical Approach

We propose a new analysis for the evolution of virulence of pathogen in a spatially structured host population where each site of a regular lattice is either occupied by a susceptible or by an infected, or is empty. We assume that reproduction by susceptible individuals occurs locally but infection by a contact of susceptible and infected hosts occurs either locally or globally with a certain proportion. We examine by combining Monte-Carlo simulation and adaptive dynamics approach, how the evolutionarily stable (ESS) virulence depends on the fraction of global infection/transmission and the trade-off between transmission and virulence in the model investigated by Boots and Sasaki (1999). Our analysis developed in this paper can successfully predicted the ESS virulence found in the previous papers, and reveals followings: [1] With a linear trade-off, as is reported by previous studies, there is an ESS virulence when the proportion of global infection is small. We newly find that, if we increase the proportion, the ESS disappears when the proportion exceeds a certain threshold value, and proportions just below the threshold, there are evolutionary bi-stabilities. [2] With a non-linear trade-off, there can be no monomorphic ESS; instead, the evolutionary competition between many parasite genotypes differing in their virulence gives rise to an evolutionarily stable coalition of pathogen strains with markedly different virulence (dimorphic ESS virulence) with a middle proportion of global transmission. These analytical results well illustrate the results by Monte-Carlo simulations. Since coexistence and evolutionary bistability are not impossible in the model we investigate in this paper, these are apparently derived by the effect of spatial structure