Explanation and prediction and the maintenance of sexual reproduction

Evolutionary biology has often sat rather uneasily with fundamental principles of scienti®c explanation. Hempel (1965) has pointed out that, in science, there is an equivalence of explanation and prediction. In other words, a theory and/or a set of observations A can be said to explain a set of observations B if, and only if, B is predictable from knowledge of A. This criterion, widely accepted in epistemological philosophy, is often not satis®ed in adaptive explanations of the phenotype. Frequently, an evolutionary explanation for a phenotypic trait is postulated, but one in which the trait is logically predicted by the explanatory idea only if quantitative values of unobserved parameters fall in a certain range. Measurement of the parameters can be dauntingly dif®cult. What, regrettably often, happens instead, is that the explanatory idea is accepted as correct on the basis of its intuitive reasonableness or appeal. Once this has happened, then the conjunction of the trait to be explained and the explanatory hypothesis are seen as jointly constituting evidence that the unobserved parameters fall in the required range. The explanations of the continued persistence of sexual reproduction in the face of a theoretical two-fold advantage for apomictic parthenogens form a good example of an incomplete logical coupling between explanation and prediction. The fundamental problem has been expressed by Maynard Smith (1978) as being that, if the number of surviving offspring produced by a female is independent of the sex of these offspring, and whether or not they are produced sexually or asexually, then a dominant mutation generating apomictic parthenogenesis would be expected to have a two-fold ®tness advantage relative to its allele in a wild population. Given that such apomictic mutations are possible, why are sexual species not replaced by their apomict descendants? Very large numbers of hypotheses have been suggested to try to account for the persistence of sex, in the face of this expected two-fold advantage. These hypotheses postulate mechanisms whereby sexually produced offspring have a higher Darwinian ®tness than their asexual competitors. Such models create a short-term advantage to sex, such that the sexual subset of the population will be able to resist invasion from apomictic mutations. Clearly, there is another suite of explanations for sex which invoke a duration of asexual species which is short in palaeontological time, although long enough for an asexual mutation to have time to selectively replace its sexual progenitor. West et al. (1999) argue that traditional ways of looking at the advantage of sex may be falsely unitary, in that they tend to contrast different models and look for data sets which will convincingly resolve amongst them. In particular, considering the two most strongly supported theories of forces giving advantages to sexual organisms, that of environmental ̄uctuation and the Red Queen, and the Mutational Deterministic hypothesis of synergistic deleterious mutations, they believe that the ubiquity of parasites and of deleterious mutations predicts that realistic models of sex must combine these two processes. I believe that the set of models for sexual reproduction, taken either singly or together, do not, at present, meet the criterion for being a true explanation. They are still insuf®cient in their details for us to be able to predict the widespread occurrence of sexual reproduction if we did not know of this independently of our modelling efforts. Indeed, what has been motivating the search for a single unitary explanation for the persistence of sex has been the conviction that precisely one of the models will,