Frank, S. A. 1994. Coevolutionary genetics of hosts and parasites with quantitative inheritance. Evolutionary Ecology 8:74-94.
A model of host-parasite coevolution is analyzed. A host resistance trait and a parasite virulence trait interact to determine the outcome of a parasitic attack, where each trait is determined by quantitative genetic variation. The resistance and virulence traits are assumed to have a fitness cost. Each host and parasite genotype is treated as a separate species in a multidimensional Lotka-Volterra system in which the numerical abundance of each genotype is free to change. Thus the epidemiological effects of fluctuating population sizes are analyzed jointly with changes in genotype frequencies. Population sizes fluctuate increasingly as the parasites' reproductive capacity increases and as resistance and virulence benefits per unit cost decline. The patterns of genetic variability depend mainly on the stability of population sizes and on the shape of the relationship between the costs and benefits of a trait.