Karev, G. P. | bioRxiv Science

bioRxiv2021

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

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.

evolutionary biology↗

bioRxiv2018

Stability of host-parasite systems: you must differ to coevolve

BackgroundGenetic parasites are ubiquitous satellites of cellular life forms most of which host a variety of mobile genetic elements including transposons, plasmids and viruses. Theoretical considerations and computer simulations suggest that emergence of genetic parasites is intrinsic to evolving replicator systems.\n\nResultsUsing methods of bifurcation analysis, we investigated the stability of simple models of replicator-parasite coevolution in a well-mixed environment. It is shown that the simplest imaginable system of this type, one in which the parasite evolves during the replication of the host genome through a minimal mutation that renders the genome of the emerging parasite incapable of producing the replicase but able to recognize and recruit it for its own replication, is unstable. In this model, there are only either trivial or \"semi-trivial\", parasite-free equilibria: an inefficient parasite is outcompeted by the host and dies off whereas an efficient one pushes the host out of existence, which leads to the collapse of the entire system. We show that stable host-parasite coevolution (a non-trivial equilibrium) is possible in a modified model where the parasite is qualitatively distinct from the host replicator in that the replication of the parasite depends solely on the availability of the host but not on the carrying capacity of the environment.\n\nConclusionsWe analytically determine the conditions for stable host-parasite coevolution in simple mathematical models and find that a parasite that initially evolves from the host through the loss of the ability to replicate autonomously must be substantially derived for a stable host-parasite coevolution regime to be established.

evolutionary biology↗