A Baseline Model for the Apparent Competition between Many Host Strains: the Evolution of Host Resistance to Microparasites

The purpose of this article is to establish and analyse a baseline model for the apparent competition between many host strains attempting to avoid a uniform microparasitic population. The model is formulated and analysed using invasion criteria in the main text. The results are verified by more formal methods in the appendix. Cases in which the microparasite can invade are distinguished geometrically from those in which it cannot using threshold and strain composition conditions. A major result obtained when the pathogen persists is a competitive exclusion principle for host resistance. For non-lethal infections, the winning strain is that which affords the pathogen maximum threshold density; for possibly lethal infections, a somewhat generalized version of this criterion is presented and discussed. The tension is highlighted between these results and the baseline behaviour of many pathogen strains and a uniform host population—here the winning pathogen strain is that with minimum threshold density.