Population Dynamics and the Evolution of Virulence in Epidemiological Models with Discrete Host Generations

Abstract

Chaos is the likely outcome of the interaction between a parasite and a host with discrete generations, if the parasite's virulence is high and if transmission from one generation to the next is held constant. We studied two alternative routes of transmission—vertical transmission from infecteds to their offspring, and transmission via long-lasting spores produced in those individuals that were killed by the infection—to investigate the influence of the transmission route on the system's evolution and population dynamics. The major results are: (1) vertical transmission often leads to low virulence, thus confirming most epidemiological models. However, if hosts can become super-infected, the evolutionary dynamics of virulence can have several equilibrium points, including 100% disease-induced mortality; (2) when parasites are transmitted with long-lasting spores, the evolutionary dynamics of virulence can become unstable, leading to the repeated bifurcation of two sub-populations with high and low virulence or to punctuated equilibria with sudden changes in the average level of virulence; (3) in general, the evolution of virulence moves the system to an area where the population dynamics are stable. When evolution leads to chaos, the system most often becomes extinct. Only for a restricted parameter space in the system where transmission from one generation to the next is via long-lasting spores do the dynamics become chaotic without extinction of the system.