A new theoretical treatment of pathogen and host evolution
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Evolutionary processes are inherently stochastic, since we can never know with certainty exactly how many descendants an individual will leave, or what the phenotypes of those descendants will be. Despite this, models of pathogen evolution have nearly all been deterministic, treating values such as transmission and virulence as parameters that can be known ahead of time. I present a broadly applicable analytic approach for modeling pathogen evolution in which vital parameters such as transmission and virulence are treated as random variables, rather than as fixed values. Starting from a general stochastic model of evolution, I derive specific equations for the evolution of transmission and virulence. I show that adding stochasticity introduces new directional components to pathogen evolution. In particular, two kinds of covariation between traits emerge as important: covariance across the population (what is usually measured), and covariance between random variables within an individual. I show that these different kinds of trait covariation can be of opposite sign and contribute to evolution in very different ways. I then apply these to a particular special case; the SIR model of pathogen dynamics. In host-parasite coevolution, the parasite is selected to increase its infectivity while host is selected to resists the parasite infection. It is widely held that parasite-mediated sexual selection can further amplify the selective pressure on the host to overcome parasite infection. I focus on certain types of parasites, those that can impair the activity of the host immune function and I show that the effect of sexual selection can actually reduce the selective pressure on the host immune response to adapt to the parasite infection. I design a simple mathematical model for a population of sexually reproducing organism in which individuals are choosy, preferring traits that are correlated with immune system activity. I introduce to this population a parasite that can suppress activation of the host's immune response. The derived results show that even though the host immune system is likely to ultimately evolve and adapt to the parasite infection, when sexual selection is part of this process, it can slow down this evolution on the host and give the parasite more time to get established.