Evolutionary branching of host resistance induced by density-dependent mortality

This study explores the evolutionary dynamics of host resistance in a susceptible-infected model with density-dependent mortality. We assume that the resistant ability of susceptible host will adaptively evolve, a different type of host differs in its susceptibility to infection, but the resistance to a pathogen involves a cost such that a less susceptible host results in a lower birth rate. By using the methods of adaptive dynamics and critical function analysis, we find that the evolutionary outcome relies mainly on the trade-off relationship between host resistance and its fertility. Firstly, we show that if the trade-off curve is globally con-cave, then a continuously stable strategy is predicted. In contrast, if the trade-off curve is weakly convex in the vicinity of singular strategy, then the evolutionary branching of host resistance is possible. Moreover, the bifurcation analysis shows that independent of the trade-off curve, the values of continuously stable strategy and evolutionary branching point will always increase as the demographic parameters increase. Secondly, after evolutionary branching in the host resistance has occurred, we examine the coevolutionary dynamics of the dimorphic host population and find that for a type of concave-convex-concave trade-off curve, the final evolutionary outcome may contain a relatively higher susceptible host and a relatively higher resistant host, which can continuously stably coexist on a long-term evo-lutionary timescale. Numerical simulation further shows that eventually the equilibrium population densities of the dimorphic susceptible host might be very close to each other. Finally, we find that for a type of sigmoidal trade-off curve, due to the high cost in terms of the birth rate, always the branch with higher resistance will go extinct, the eventual evolutionary outcome includes a monomorphic host with relatively lower resistance. Particularly, in this case we find that the evolution of costly host resistance may reduce the equilibrium population density of susceptible host, instead it may increase the equilibrium population density of infected host.