The mean and variance of infection load reveal unseen host evolution

Abstract

Some hosts are more heavily infected than others, but this fact has been relatively neglected in the microparasite literature compared to the macroparasite literature. We develop a model that allows host population mean and variance of microparasite load to fluctuate dynamically over time, dependent on underlying processes. Our model uses empirically reasonable, non-linear functional forms, e.g., for the probability of infected hosts surviving as a function of load. Despite non-linearities, we derive an approximation that assumes a lognormal distribution of load, improving computational and analytical tractability. We show negative feedbacks between load mean and variance at equilibrium. These feedbacks determine how a change in the host-microparasite system shifts mean and variance in load, directly as well as indirectly. We parameterize this model with empirically supported parameter values for a focal frog-fungal pathogen system. We illustrate system changes through evolution of host defenses against microparasites that may drive evolutionary recovery from disease-induced declines. We find that different forms of host defenses have different implications for load, e.g., constitutive resistance has little impact on the standard deviation while inducible resistance decreases it, with different outcomes for host fitness, pathogen fitness, and our ability to infer underlying dynamics from population-level data.