Male gamete output of asexuals and the dynamics of populations polymorphic for reproductive mode

Most asexual plants retain male sexual function, albeit at levels much lower than their sexual counterparts. This phenomenon has not typically received full representation in mathematical models of the cost of sex. We formulate and analyze a genetic model of reproductive mode in order to study the evolutionary dynamics of populations consisting of both sexual and asexual individuals. Our model incorporates levels of production and fertility of male gametes produced by individuals that are asexual in their female function, that vary from zero to a level equal to that in a sexual individual. This encompasses a range of naturally occurring situations that has been beyond the scope of most previous theoretical studies. We show that the cost of sex is frequency-dependent in many biologically relevant situations. Consequently, the fitness advantage needed for sexuals to resist invasion by asexuals may frequently be much less than twofold. However, the fitness advantage required for sexuals successfully to invade an asexual population may be much higher. Moreover, the viability/fertility advantage required by sexuals to equal the fitness of asexuals is not necessarily equal to the intrinsic cost of sex, but may be greater when asexual individuals produce fertile male gametes. We also show that panmictic populations cannot be stably polymorphic for reproductive mode when fitnesses are constant, and that the conditions for the fixation of sexual or asexual genotypes are not affected by the degree of dominance at the locus determining reproductive mode. With frequency-dependence, and no possibility of stable polymorphism, the reproductive mode that finally evolves will, in many cases, depend upon the initial frequencies of asexual and sexual individuals.