Mutualistic symbiosis can be regarded as interspecific division of labour, which can improve the productivity of metabolites and services but deteriorate the ability to live without partners. Interestingly, even in environmentally acquired symbiosis, involved species often rely exclusively on the partners despite the lethal risk of missing partners. To examine this paradoxical evolution, we explored the coevolutionary dynamics in symbiotic species for the amount of investment in producing their essential metabolites, which symbiotic species can share. Our study has shown that, even if obtaining partners is difficult, ‘perfect division of labour’ (PDL) can be maintained evolutionarily, where each species perfectly specializes in producing one of the essential metabolites so that every member entirely depends on the others for survival, i.e. in exchange for losing the ability of living alone. Moreover, the coevolutionary dynamics shows multistability with other states including a state without any specialization. It can cause evolutionary hysteresis: once PDL has been achieved evolutionarily when obtaining partners was relatively easy, it is not reverted even if obtaining partners becomes difficult later. Our study suggests that obligate mutualism with a high degree of mutual specialization can evolve and be maintained easier than previously thought.

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.

Mutualism based on reciprocal exchange of costly services must avoid exploitation by 'free-rides'. Accordingly, hosts discriminate against free-riding symbionts in many mutualistic relationships. However, as the selective advantage of discriminators comes from the presence of variability in symbiont quality that they eliminate, discrimination and thus mutualism have been considered to be maintained with exogenous supply of free-riders. In this study, we tried to resolve the 'paradoxical' co-evolution of discrimination by hosts and cooperation by symbionts, by comparing two different types of discrimination: 'one-shot' discrimination, where a host does not reacquire new symbionts after evicting free-riders, and 'resampling' discrimination, where a host does from the environment. Our study shows that this apparently minor difference in discrimination types leads to qualitatively different evolutionary outcomes. First, although it has been usually considered that the benefit of discriminators is derived from the variability of symbiont quality, the benefit of a certain type of discriminators (e.g. one-shot discrimination) is proportional to the frequency of free-riders, which is in stark contrast to the case of resampling discrimination. As a result, one-shot discriminators can invade the free-rider/nondiscriminator population, even if standing variation for symbiont quality is absent. Second, our one-shot discriminators can also be maintained without exogenous supply of free-riders and hence is free from the paradox of discrimination. Therefore, our result indicates that the paradox is not a common feature of evolution of discrimination but is a problem of specific types of discrimination.

Mutualism is thought to face a threat of coextinction cascade because the loss of a member species could lead to the extinction of the other member. Despite this common emphasis on the perils of such knock‐on effect, hitherto, the evolutionary causes leading to extinction have been less emphasised. Here, we examine how extinction could be triggered in mutualism and whether an evolutionary response to partner loss could prevent collateral extinctions, by theoretically examining the coevolution of the host exploitation by symbionts and host dependence on symbiosis. Our model reveals that mutualism is more vulnerable to co‐extinction through adaptive evolution (evolutionary double suicide) than parasitism. Additionally, it shows that the risk of evolutionary double suicide rarely promotes the backward evolution to an autonomous (non‐symbiotic) state. Our results provide a new perspective on the evolutionary fragility of mutualism and the rarity of observed evolutionary transitions from mutualism to parasitism.