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Background  Genetic 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.    Results  Using methods of bifurcation analysis, we investigated the stability of simple models of replicator-parasite coevolution in a well-mixed environment. We first analyze what appears to be 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. This model has only 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, leading 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.    Conclusions  We analytically determine the conditions for stable coevolution of genetic parasites and their hosts coevolution in simple mathematical models. It is shown that the evolutionary dynamics of a parasite that initially evolves from the host through the loss of the ability to replicate autonomously must substantially differ from that of the host, for a stable host-parasite coevolution regime to be established.    Electronic supplementary material  The online version of this article (10.1186/s13062-018-0230-9) contains supplementary material, which is available to authorized users.

Stable coevolutionary regimes for genetic parasites and their hosts: you must differ to coevolve