It is a challenge for evolutionary theory to explain the prevalence of sexually reproducing species.  That’s because of the twofold cost of sex:  a sexually reproducing species produces half as many offspring per generation as an asexually reproducing population of the same size.  So not only must there be some other advantage to sexual reproduction, it has to be large enough to outweigh that substantial cost.

One theory is that the genetic mixing that comes from sex allows a species to shed disadvantageous mutations.  An asexual species can only accumulate them.  This advantage can be large enough to overcome the twofold cost of sex.  But the problem with this theoretical explanation is that in these models the advantage of sex is too large, so large that the kind of sex we see universally among all sexually reproducing species, sex between two parents, is dominated by tri-parental sex.  This was shown by Perry, Reny, and Robson who consider a particular kind of menage a trois in which each mating requires two males and one female, and each offspring receives half of its genetic material from the mother and one quarter from each of the fathers.

This avoids a tri-fold cost of sex:

Because the cost of males is determined not by the ratio of males to females in each mating instance but, rather, by the population ratio of males to females, de-termining the population ratio is central. We therefore turn to Fisher’s celebrated equilibrium argument (Fisher, 1930). Applying the same logic to 1/2 – 1/4 – 1/4 sex, we note first that the total reproductive value of all of the males in any generation is precisely equal to that of all of the females in that generation. This is because, un-der 1/2-1/4-1/4 sex, all of the females supply half of the genes of all future generations. But then the remaining half must be supplied by all of the males. Consequently, as Fisher argued, equilibrium requires the offspring sex ratio to equate parental expenditure on male and female offspring. Maintaining the usual assumption that offspring of either sex are equally costly to raise to maturity, we conclude that the equilibrium sex ratio must be one–each male therefore mates with two females and vice versa. But this means that the cost of males is twofold–there is no additional cost of males over biparental sex.

I bring this up because (in an older working paper version) they also considered the leading competing theory for the advantage of sexual reproduction, The Red Queen hypothesis.  Here the argument is that species are constantly trying to out-evolve parasites.  Genetic mixing makes them a moving target.  Perry, Reny, and Robson showed that, unlike the deleterious mutations theory, the Red Queen story rationalizes biparental sex over other forms of sex.  Thus, from the point of view of sex as an evolved mechanism for solving some problem, only the Red Queen can explain the kind of sex we see.

And I bring that up because just last week I heard this story about a new experiment that validates the Red Queen hypothesis.