I recently read this 2017 article by Motty Perry (University of Warwick), Philip Reny (University of Chicago), and Arthur Robson (Simon Fraser University), which seemed like a fairly random addition to an issue of The Economic Journal (open access). I say random because the title is "Why sex? And why only in pairs?", and the paper details a mostly theory-driven explanation (along with some simulation results) of why reproductive sex occurs between couples, and not between three or more parents. Given that there is a Journal of Mathematical Biology, The Economic Journal seemed like an odd fit to me.
Nevertheless, this was an interesting paper to read. Perry et al. outline attempt to unravel the following puzzle:
The breadth and variety of methods by which different species reproduce through sex is nothing short of remarkable. Nonetheless, sexual reproduction displays a stunning regularity. We can state that:
Each sexually produced offspring of any known species is produced from the genetic material of precisely two individuals. That is, sex is always biparental.
The obvious, but overlooked, question is, why? In particular, why are there no triparental species in which an offspring is composed of the genetic material of three individuals?
They first note that:
...a complete theory of sex must strike a delicate balance. On the one hand – as is well known – it must explain why genetic mixing is sufficiently beneficial so that biparental sex overcomes the twofold cost of males it suffers because an equally sized asexual population would grow twice as fast (Maynard Smith, 1978). On the other hand – and this point is central here – genetic mixing must not be so beneficial that a further increase in fitness would be obtained from even more of it through triparental sex.
They then outline the two main competing theories: (1) the mutational hypothesis; and (2) the 'red queen' hypothesis. The mutational hypothesis contends that sex is advantageous (compared with asexual reproduction) because "it halts the otherwise steady accumulation of harmful mutations". In contrast, the 'red queen' hypothesis contends that each species is in a constant battle with parasites (or other dangerous organisms), and asexual reproduction, where each offspring is genetically identical to the parent, is highly vulnerable to extinction at the hands (or tentacles, or whatever) of a new parasite evolved to attack the specific genetic makeup of the species.
The problem with sexual reproduction (when compared with asexual reproduction) is the so-called 'two-fold cost of sex':
...that a sexual population with a one to one ratio of (unproductive) males to females produces half as many offspring as an equally sized asexual population... The simple reason for this is that every individual in the asexual population can reproduce whereas only half of the individuals in the sexual population – the females – can do so.
Now, a successful theory of sexual reproduction must explain why biparental sex is advantageous over asexual reproduction. However, it must also explain why triparental sex is not even more advantageous.
Using a fairly simple narrative approach, supported by a minimum of necessary mathematical detail. Perry et al. go on to show that:
Under the mutational hypothesis, triparental sex always dominates biparental sex and high genomic mutation rates only serve to increase this advantage. With all three options available, either asexuality would be best or triparental sex would be best. Accordingly, biparental sex should not be observed.
In contrast, there is a ray of hope with the red queen hypothesis. Using a deliberately simplified red queen model, we have shown that biparental sex can have even an overwhelming advantage over asexuality, yet there is no further gain from more than two parents.
So, there you have it. The (coolly-named) red queen hypothesis seems to be the winner.
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