Why Sex? and Why Only in Pairs?1

Understanding the purpose of sex remains one of the most important unresolved problems in evolutionary biology. The di¢ culty is not that there are too few theories of sex, the di¢ culty is that there are too many and none stand out. To distinguish between theories we suggest the following question: Why are there no triparental species in which an o¤spring is composed of the genetic material of three individuals? A successful theory should confer an advantage to biparental sex over asexual reproduction without conferring an even greater advantage to triparental sex. We pose our question in the context of two leading theories of sex, the (deterministic) mutational hypothesis that sex reduces the rate at which harmful mutations accumulate, and the red queen hypothesis that sex reduces the impact of parasitic attack by increasing genotypic variability. We show that the mutational hypothesis fails to provide an answer to the question because it implies that triparental sex dominates biparental sex, so the latter should never be observed. In contrast, we show that the red queen hypothesis is able to explain biparental sex without conferring an even greater advantage to triparental sex. 1Current version: November 2, 2015. We thank Elizabeth Elle, Alan Grafen, Sally Otto, the late Rob Seymour, Jasna Strus, and Dan Weil for very helpful comments and discussions, Dagan Eshar for expert Matlab advice, Hua Jiang for programming assistance, and the editor and an anonymous referee for very helpful suggestions. We gratefuly acknowledge …nancial support as follows: Perry, from the Israel Science Foundation (0321548) and from the ESRC (ES/K006347/1); Reny, from the National Science Foundation (SES-1227506); and Robson, from the Canada Research Chairs Program, the Human Evolutionary Studies Program, and the Social Sciences and Humanities Research Council of Canada. 2Department of Economics, University of Warwick, Coventry CV4 7AL. 3Department of Economics, The University of Chicago, Chicago, IL 60637 USA. 4Department of Economics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6. 1. Introduction The breadth and variety of methods by which di¤erent species reproduce through sex is nothing short of remarkable. Nonetheless, sexual reproduction displays a stunning regularity. Each sexually produced o¤spring 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 o¤spring is composed of the genetic material of three individuals? Answering this question –and similar questions regarding quadriparental sex, etc. –is bound to shed light on the purpose of sex itself, one of the most important unresolved problems in evolutionary biology (see, e.g., Otto and Lenormand (2002) or Rice (2002) on the importance of this question). Indeed, 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 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). On the other hand –and this point is central here –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. Little or no attention has been paid to the possibility that a theory of biparental sex might inadvertently confer an advantage to 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 or mating coordination costs — are