Deterministic Hypothesis Research Articles

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;

ENVIRONMENTAL STRESS AND THE MAINTENANCE OF SEX IN A FRESHWATER SNAIL.

Synergism among mutations can lead to an advantage to sexual reproduction, provided mutation rates are high enough (the mutational deterministic hypothesis). Here we tested the idea that competition for food can increase the advantage to sexual reproduction, perhaps by increasing the synergism among mutations in asexual individuals. We compared the survivorship of sexual and asexual snails (Potamopyrgus antipodarum) under two treatments: starved and fed. We predicted higher mortality for asexual snails when starved, but found that sexual and asexual individuals survived at the same rate, independent of treatment. These results suggest that the distribution of sex in this snail may not be explained by variation in competition among populations.

Test of synergistic interactions among deleterious mutations in bacteria

Identifying the forces responsible for the origin and maintenance of sexuality remains one of the greatest unsolved problems in biology. The mutational deterministic hypothesis postulates that sex is an adaptation that allows deleterious mutations to be purged from the genome; it requires synergistic interactions, which means that two mutations would be more harmful together than expected from their separate effects. We generated 225 genotypes of Escherichia coli carrying one, two or three successive mutations and measured their fitness relative to an unmutated competitor. The relationship between mutation number and average fitness is nearly log-linear. We also constructed 27 recombinant genotypes having pairs of mutations whose separate and combined effects on fitness were determined. Several pairs exhibit significant interactions for fitness, but they are antagonistic as often as they are synergistic. These results do not support the mutational deterministic hypothesis for the evolution of sex.

Selection Against Deleterious Mutations and the Maintenance of Biparental Sex

The mutational deterministic hypothesis postulates an advantage to sexual over asexual reproduction when mutation rates are on the order of 1.0 per genome per generation, provided that selection takes the form of a synergistic epistasis. While the efficacy of this mechanism has been investigated for infinite populations, its ability to protect sex in finite populations exhibiting stochastic dynamics remains untested. Stochastic processes have the potential to undermine protection for sex in two ways: (1) asexual lineages derived from sexual ancestors may, by chance, be founded by individuals bearing fewer than the equilibrium mean number of mutations, and (2) once established, such lineages will undergo random perturbations in the rates at which they grow and accumulate mutations. In the present study, I show using computer simulation that sexual populations of as many as 10,000 individuals are susceptible to invasion by asexual lineages for mutation rates higher than predicted under the mutational deterministic hypothesis. My simulations differ from previous investigations in that they model the progress of asexual lineages into sexual populations as both stochastic and deterministic processes for various mutation rates, selection regimes, and population sizes. It is suggested that ecological factors, such as parasitism or release from competition, could interact with selection against deleterious mutations to protect sex. To provide the sole explanation for sex, however, may require that selection against deleterious mutations be accompanied by mutation rates on the order of 2.0 per genome per generation.

A formulation of the determinism hypothesis

The author tries to formulate what a determinist believes to be true. The formulation is based on some concepts defined in a systems-theoretical manner, mainly on the concept of an experiment over the sets A m (a set of m-tuples of ‘input values’) and B n (a set of n-tuples of ‘output values’) in the time interval (t 1, ..., t k ) (symbolically E[t 1,..., t k , A m , B n ]), on the concept of a behavior of the system S m,n (=(A m , B n )) on the basis of the experiment E[t 1, ..., t k , A m , B n ] and, indeed, on the concept of deterministic behavior .... The resulting formulation of the deterministic hypothesis shows that this hypothesis expresses a belief that we always “could find” some “hidden parameters”.