One-to-many mutualism – mutualism between single host individual and multiple symbiont individuals or strains – is often found in nature. However, most theoretical studies on the evolution of mutualism have focused on one-to-one and many-to-many systems so far, while one-to-many systems can be much less stable because of their asymmetric structure, i.e. only host has option to chose and/or discriminate their partners. Here I develop a simple mathematical model to describe the evolutionary dynamics of symbiont population, assuming the traits of the host are fixed.
I assume that in each generation of the symbiont each host chooses a number of symbionts from the environment. A fraction of the symbionts are chosen dependently on their benefit to the host x (preferential choice) and the rest are at random (random choice). In the symbiotic interaction the host offers a constant amount of resource to each symbiont. The symbiont contributes a fraction of the resource x for fitness of the host, while it spends the rest for its own reproduction. Thus symbionts more beneficial to the host (having high x) are more likely to be chosen by the host, while they gain less reproductive success from the symbiosis.
Results/Conclusions
I calculate evolutionary stable state (ESS) with respect to the trait x of the symbiont population. I find that it depends on only two parameters, the fraction of preferential choice of the symbiont by the host c and the strength of preference in the preferential choice k. At the ESS the symbiont population is monomorphic (all mutualists) when c is large or k is small, while it is dimorphic and consists of mutualists (x>0) and parasites (x=0) when c is small and k is large. In the latter case, the trait of the mutualists remains constant and the fraction of the parasites decreases as c increases. Consequently the fitness of the host increases with c at ESS. In contrast, the trait of the mutualists increases but the fraction of the parasites also increases as k increases, so that the fitness of the host remains constant.
“Choosy” hosts (having high k) should be favored in natural selection, because they are likely to choose more beneficial symbionts from the environment. However, they exploit mutualistic symbionts to drive the symbiont population more parasitic, which can offset the gain in their own fitness.