Comparing the differing effects of host species richness on metrics of disease

Changes in host species richness can alter infection risk and disease levels in multi-host communities. I review theoretical predictions for direct and environmental transmission pathogens about the effects of host additions (or removals) on three commonly used disease metrics: the pathogen community reproduction number $\left(R_0\right)$ and infection prevalence and infected density in a focal host. To extend this prior work and explain why predictions differ between metrics, I analyze Susceptible Infected-Recovered-type models of an environmentally transmitted pathogen and multiple host species that compete for resources. Using local sensitivity analysis, I show how trait-mediated and density-mediated indirect effects drive each metric's response to variation in an added host's ability to transmit a pathogen, the added host's density, and the pathogen transmission mechanism. For each disease metric, the responses are typically predicted by the added host's ability to transmit the pathogen when interspecific competition is weak whereas the responses can be altered by shifts in host densities when interspecific competition is strong. In addition, the three metrics often respond in the same direction. However, the metrics can respond in different directions for three reasons: (1) differences between the ability of exposed individuals to transmit the pathogen over the length of time the individuals are infected (i.e., host competence) and a host population's instantaneous net rate of production of infectious propagules; (2) strong density-mediated feedbacks driven by disease-induced mortality; and (3) host additions or removals cause large changes in focal host density via competition or disease-induced mortality. This study extends and unifies prior theoretical studies, and helps identify the rules governing the context-dependent relationships between host species richness and the three metrics of disease.