A Ratio-Dependent Model of Replicator-Genetic Parasite Coevolution Demonstrates Instability of the Parasite-Free State

Abstract

Nearly all organisms on earth are hosts to diverse genetic parasites including viruses and various types of mobile genetic elements. The emergence and persistence of genetic parasites was hypothesized to be an intrinsic feature of biological evolution. Here we examine this proposition by analysis of a ratio-dependent Lotka-Volterra type model of replicator(host)-parasite coevolution where the evolutionary outcome depends on the ratio of the host and parasite numbers. In a large, unbounded domain of the space of the model parameters, which include the replicator carrying capacity, the damage inflicted by the parasite, the replicative advantage of the parasites, and its mortality rate, the parasite-free equilibrium takes the form of a saddle and accordingly is unstable. Therefore, the evolutionary outcome is either the stable coexistence of the replicator and the parasite or extinction of both. Thus, the results of ratio-dependent model analysis are compatible with the hypothesis that genetic parasites are inherent to life.