Sex may need more than one

The positive replies to our original paper (West et al., 1999) leave us in the pleasurable position of being able to keep our ®nal comments short. Kondrashov (1999) demonstrates what Seger (1999) called `physics envy'. The idea that the Mutational Deterministic hypothesis can be easily validated or rejected, once the minimum rate of deleterious mutations per genome per generation (U) is known, sounds great, especially if the magical number is U > 1. However, quantitative predictions (and assumptions) are almost always model-speci®c, so that there is unlikely to be a single, uncontroversial value, even if we ignore the large con®dence limits that are placed on estimates of U (see West et al., 1999). For instance, with reasonable levels of epistasis, a value of U > 1.5 is required (Charlesworth, 1990). If stochastic effects (which are unavoidable during the early phases of any clonal invasion) or variation in the extent of epistasis are included, then U > 2.0 is required (Howard, 1994; Otto & Feldman, 1997). In addition, irrespective of the value of U, the Mutational Deterministic hypothesis absolutely requires synergistic epistasis between deleterious mutations (Kondrashov, 1982). The idea that a single value of U will resolve the issue seems to us somewhat optimistic. We agree with Kondrashov (1999) that our particular form of pluralist explanation is required for only a small fraction (»0.2 < U < »2.0) of the entire parameter space (0 < U < ¥). However, that `small fraction' is the relevant parameter space: it is where the majority of estimates of the mutation rate in sexual species fall (West et al., 1999). A pressing goal now is to determine the virulence of parasites in the wild, and whether they in fact evolve to infect locally common host genotypes. If the latter is not true, or if parasites are not suf®ciently virulent to drive host gene frequency dynamics, then both the parasite-driven Red Queen and our particular form of pluralism are falsi®ed. We agree with Lenski (1999) that different factors may be responsible for the evolutionary origin and maintenance of sex. As we said, our discussion concerned the maintenance of sex. We also agree that experiments with Escherichia coli offer an exceptional opportunity to test for `a general tendency for genetic structures to exhibit synergistic epistasis among deleterious mutations' (Elena & Lenski, 1997). We note, however, that such experiments cannot test whether synergistic epistasis occurs in a type of organism where sexual reproduction predominates. Do larger, more complex genomes with higher mutation rates lead to synergistic epistasis (Szathmary, 1993; Falush, 1998; Hurst & Smith, 1998)? Do the higher numbers of parasites in larger species help cause truncation selection against individuals with large numbers of mutations? Estimating relevant parameters can be much harder in more complex and sexual species (West et al., 1998), but such results are crucial. We hope eventually to have a range of estimates of the mutation rate and the extent of epistasis from a number of sexual and asexual species, so that a whole slew of more subtle questions can be addressed. Red®eld's (1999) comments give us the opportunity to make the following points, orthogonal to our discussion of plurality. (1) Theoretical models suggest that the rate of crossing over is far more important than chromosome number in determining the effective amount of recombination (Burt, unpublished observations). (2) Variation in recombination rates across species are consistent with Red Queen and mutational models (Burt & Bell, 1987;