In mutualism between unicellular hosts and their endosymbionts, symbiont's cell division is often synchronized with its host's, ensuring the permanent relationship between endosymbionts and their hosts. The evolution of synchronized cell division thus has been considered to be an essential step in the evolutionary transition from symbionts to organelles. However, if symbionts would accelerate their cell division without regard for the synchronization with the host, they would proliferate more efficiently. Thus, it is paradoxical that symbionts evolve to limit their own division for synchronized cell division. Here, we theoretically explore the condition for the evolution of self-limited cell division of symbionts, by assuming that symbionts control their division rate and that hosts control symbionts' death rate by intracellular digestion and nutrient supply. Our analysis shows that symbionts can evolve to limit their own cell division. Such evolution occurs if not only symbiont's but also host's benefit through symbiosis is large. Moreover, the coevolution of hosts and symbionts leads to either permanent symbiosis where symbionts proliferate to keep pace with their host, or the arms race between symbionts that behave as lytic parasites and hosts that resist them by rapid digestion.
Keywords: mutualism; symbiogenesis; symbiosis; synchronized cell division; vertical transmission; virulence.