Equilibrium between the “genuine mutualists” and “symbiotic cheaters” in the bacterial population co-evolving with plants in a facultative symbiosis

The mathematical model for evolution of the plant-microbe facultative mutualistic interactions based on the partners' symbiotic feedbacks is constructed. Using the example of rhizobia-legume symbiosis, we addressed these feedbacks in terms of the metabolic (C↔N) exchange resulting in the parallel improvements of the partners' fitness (positive feedbacks). These improvements are correlated to the symbiotic efficiency dependent on the ratio of N2-fixing bacterial strains (“genuine mutualists”) to the non- N2-fixing strains (“symbiotic cheaters”) in the root nodules. The computer experiments demonstrated that an interplay between the frequency-dependent selection (FDS) and the Darwinian (frequency-independent) selection pressures implemented in the partners' populations ensures an anchoring or even domination for the newly generated host-specific mutualists (which form N2-fixing nodules only with one of two available plant genotypes) more successfully than for the non-host-specific mutualists (which form N2-fixing nodules with both plant genotypes). The created model allows us to consider the mutualistic symbiosis as a finely balanced polymorphic system wherein the equilibrium in bacterial population may be shifted in favor of “genuine mutualists” due to the partner-stipulated selection for an improved symbiotic efficiency implemented in the plant population.