Symbiosis emergence and abandonment in nature: a coordination game approach

Abstract: We employ an n-player coordination game to model mutualism emergence and abandonment. We illustrate our findings in the context of the host--host interactions among plants in plant-mycorrhizal fungi (MF) mutualisms. The coordination game payoff structure captures the insight that mutualistic strategies lead to robust advantages only after such "biological markets" reach a certain scale. The game gives rise to three types of Nash equilibria, which correspond to the states derived in studies of the ancestral reconstruction of the mycorrhizal symbiosis in seed plants. We show that all types of Nash equilibria correspond to steady states of a dynamical system describing the underlying evolutionary process. We then employ methods from large deviation theory on discrete-time Markov processes to study stochastic evolutionary dynamics. We provide a sharp analytical characterization of the stochastic steady states and of the transition dynamics across Nash equilibria and employ simulations to illustrate these results in special cases. We find that the mutualism is abandoned and re-established several times through evolutionary time, but the mutualism may persist the majority of time. Changes that reduce the benefit-to-cost ratio associated with the symbiosis increase the likelihood of its abandonment. While the mutualism establishment and abandonment could result from direct transitions across the mutualistic and non-mutualistic states, it is far more likely for such transitions to occur indirectly through intermediate partially mutualistic states. The MF-plant mutualism might be (partially or fully) abandoned by plants even if it provides overall superior fitness.