Understanding the purpose of sex remains one of the most important unresolved problems in evolutionary biology (Otto and Lenormand, 2002; Rice, 2002). Two leading theories of sex are the mutational deterministic hypothesis that sex reduces mutational load, and the Red Queen hypothesis that sex permits a host organism to maintain parity in a never-ending conict with parasites. These theories have similar predictions and have been di¢ cult to distinguish. We propose to distinguish between them by asking if either is consistent with the fact that sexually produced o¤spring have only two parents, not three or more. It is shown that the mutational deterministic hypothesis implies that a suitable triparental system dominates biparental sex, so the latter should never be observed, contrary to fact. In contrast, it is shown that the Red Queen hypothesis can explain biparental sex without conferring an additional advantage to triparental sex. Keywords: Biparental sex; Triparental sex; Purpose of sex; Twofold cost of sex; Deleterious mutations; Red queen. 1. Introduction The breadth and variety of methods by which di¤erent species reproduce through sex is stunning. Yet, sexual reproduction displays a remarkable regularity. Each sexually produced o¤spring of any known species is produced 1The Hebrew University of Jerusalem, Jerusalem, 91904 Israel, University of Essex. The University of Chicago, Chicago, IL 60637 USA. Simon Fraser University, Burnaby, BC, Canada V5A 1S6. All authors contributed equally to this work. from the genetic material of precisely two individuals. That is, sex is always biparental. Curiously, this fact has not been exploited to distinguish between competing theories of sex. Indeed, the main objective of the maintenance of sex literature is to explain why genetic mixing is su¢ ciently bene
cial so that biparental sex overcomes the twofold cost of males it su¤ers because an equally-sized asexual population would grow twice as fast (Maynard Smith, 1978). But the fact that sex is always biparental implies that genetic mixing must not be so bene
cial that a further increase in
tness would be obtained from even more of it through triparental sex or quadriparental sex, etc. A theory of sex, therefore, must strike a delicate balance genetic mixing must be advantageous, but not too advantageous. Whether any current theory of sex strikes this balance has never been considered despite the potential power such consideration holds for distinguishing between theories. Indeed, little or no attention has previously been paid to whether a theory of biparental sex inadvertently confers an advantage to, say, triparental sex. Perhaps this is because one is tempted to dismiss triparental sex on the grounds that the associated costs be they the cost of unproductive males, mating coordination costs, or the cost of developing the requisite genetic machinery are prohibitive. But, insofar as such arguments have been provided at all, they are unpersuasive. For example, they fail to take into account the key point that any argument against the transition from biparental sex to triparental sex may be even more persuasive for ruling out the transition from asexual reproduction
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