The coevolution of hosts and symbionts based on virulence and mode of transmission is a complex and diverse biological phenomenon. We introduced a conceptual model to study the stable coexistence and coevolution of an obligate symbiont (mutualist or parasite) with mixed-mode transmission and its host. Using an age-structured Leslie model for the host, we demonstrated how the obligate symbiont could modify the host's life history traits (survival and fecundity) and the long-term growth rate of the infected lineage. When the symbiont is vertically transmitted, we found that the host and its symbiont could maximize the infected lineage's evolutionary success (multi-level selection). Our model showed that symbionts' effect on host longevity and reproduction might differ, even be opposing, and their net effect might often be counterintuitive. The evolutionary stability of the ecologically stable coexistence was analyzed in the framework of coevolutionary dynamics. Moreover, we found conditions for the ecological and evolutionary stability of the resident host-symbiont pair, which does not allow invasion by rare mutants (each mutant dies out by ecological selection). We concluded that, within the context of our simplified model conditions, a host-symbiont system with mixed-mode transmission is evolutionarily stable unconditionally only if the host can maximize the Malthusian parameters of the infected and non-infected lineages using the same strategy. Finally, we performed a game-theoretical analysis of our selection situation and compared two stability definitions.
Keywords: Dynamical systems; Game theory; Leslie matrix; Mutant invasion; Obligate symbiosis.
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