Coevolution of host resistance and pathogen exploitation in a propagule-mediated infection model

Host populations often face infection risk from pathogens that can persist in the environment as free-living propagules. We develop a population-level model to understand how host resistance - defined as reduced susceptibility to infection - evolves in response to the exploitation strategy of a pathogen where transmission occurs exclusively via environmental propagules. Using an adaptive dynamics framework, we analyze how the coevolution of host resistance and pathogen exploitation strategy unfolds under the following fitness costs: reduced survival associated with investment in resistance reflected by additional background mortality for the host; and reduced average lifespan represented by increased infected host mortality for the pathogen. Calculating individual host and pathogen invasion fitness expressions using standard invasion analysis, we track how stable levels of investment in host resistance vary across different infection scenarios. We found that costly resistance is disfavoured when pathogen encounters are excessively high, with maximal resistance selected at intermediate levels of transmission. Coevolutionary feedbacks between host resistance and pathogen exploitation can lead to diverse outcomes, including stable evolutionarily singular strategies and, under weakly accelerating costs, evolutionary branching that generates coexistence in the resistance trait. We further quantify how coevolution shapes the equilibrium density of free propagules, revealing conditions under which coevolution suppresses or amplifies pathogen prevalence in comparison to non-evolving scenarios. Overall, our model framework built on survival-based costs offers testable predictions for environmentally transmitted host-pathogen systems.