Why is a Two-Environment System Not Rich Enough to Explain the Evolution of Sex?

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Abstract
In a single-locus symmetrical model, sexual reproduction has been shown to have an immediate absolute advantage over parthenogenesis in a fluctuating environment. This environment has been described as a certain lottery over n + 1 possible seasons (where n .gtoreq. 3); n hostile seasons, for each of which the individual has a corresponding resistant allele (in the same locus) without which the individual would almost surely die in that same season; and one additional season, usually the most frequent one (and, hence, actually the normal case), in which either no selection or a very moderate one operates on the locus. This single-locus model is modified to apply to primarily haploid populations. Two extreme cases of the model are analyzed: in one, the order of appearance of the hostile seasons is fixed (to create a cycle); in the other, they appear very rarely and randomly with intermediate seasons of moderate heterozygote selection. Thus, the following properties are demonstrated. 1. The benefit of the sexual population is maintained (as long as n .gtoreq. 3), whatever the cost of sex may be. Hence, the model can serve as an explanation for the stability of sex when its cost is greater than two (e.g., if the cost of searching for a mate or courting is considered). It may also give some hint about the origin of sex, since the cost of evolving such an adaptation must be in orders of magnitude greater than only the cost of its maintenance. 2. For a stable polymorphism in only one locus, it is shown that sex offers a substantial advantage from the reshuffling of gametes alone. The advantage is measured in terms of the change in the frequencies of sexual and asexual reproduction resulting from natural selection on the individual level. This, the evolution of recombination, traditionally identified with the evolution of sex, may now be treated separately (which somewhat reduces the complexity of this last problem though it does not elimiate it). 3. It is demonstrated that a relatively low cost of evolution is required to sustain the advantage of sex. In its most acute form, the model implies a cost of about 70% at each catastrophe (i.e., the extinction of 70% of the population), which occurs occasionally. In its least extreme from, the model implies a cost of only 30%-45% catastrophe time, whereas the assumptions of the model seem only more natural. If only partial extinction is allowed in each catastrophe, the advantage of sex is still maintained if the catastrophe is sufficiently intense. In this case, the cost is still lower than the figures mentioned above. This relatively low cost of evolution overcomes a major difficulty with most of the previous works on the subject by allowing the application of the model to low-fertility populations. 4. A natural application of the model may be to the interaction of host and parasite, following Jaenike (1978), Hamilton (1980), and others. Though a specific ecological model has not been investigated, a plausible example of the conditions of the model may be a sequence of random sudden outbursts of different parasites.

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