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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Frequency of A allele for locus 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Frequency of A allele for locus 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Frequency of A allele for locus 1

Although there is no general set of equilibrium gamete frequencies for two-locus selection with an arbitrary set of fitness values, many special cases have been examined that have produced some general conclusions (see Hastings 1981, 1986; reviewed by Ewens 2004). By itself, low frequencies of recombination (small r) make it more likely that selection will result in gametic disequilibrium at equilibrium gamete frequencies even with random mating. The combination of non-additive gene action and infrequent recombination also make gametic disequilibrium at equilibrium gamete frequencies more likely. High rates of self-fertilization (strong departure from random mating) adds an additional force on gamete frequencies that can either compliment or act in opposition to selection and recombination (Hastings 1985; Holsinger & Feldman 1985). Since mean fitness may decrease with selection and recombination, Fisher's fundamental theorem does not hold for two-locus selection (see Turner 1981; Hastings 1987). A critical conclusion from examining two-locus natural selection is that generalizing from the results of one-locus selection models to multiple loci may be biologically misleading except in limiting cases such as when there is very little recombination and there is no epistasis.

7.2 Alternative models of natural selection

• Moving beyond the assumptions of fitness as constant viability in an infinitely growing population.

• Natural selection via different levels of fecundity.

• Natural selection with frequency-dependent fitness.

• Natural selection with density-dependent fitness.

The model of natural selection considered thus far equates fitness with the viability of genotypes. This is equivalent to assuming that while individuals of different genotypes vary in survival to adulthood, all genotypes are equal in terms of any other phenotypes that may impact numbers of progeny an individual contributes to the next generation. Looking again at Fig. 6.3, you can see that there are numerous points in the reproductive life cycle where genotypes may have differential success or performance. Genotypes may differ in phenotypes such as the production and survival of gametes, mating success, gamete genetic compatibility with other gametes, and parental care. It is even possible that some alleles at a locus have an advantage during segregation of homologous chromosomes and are more likely to be found in gametes, a phenomenon called meiotic drive (see the historical background on this process in Birchler et al. 2003). Each of these points in the life cycle is a situation where genotypes will potentially have different levels of performance, eventually leading to different frequencies of genotypes in the progeny. The basic viability model of natural selection also assumes that fitness values are constant through time and space. Instead, it may be that fitness actually changes in response to the conditions found in different populations or in response to the changes in genotype frequency brought on by natural selection. In order to accommodate these potential biological situations, modifications to the model of natural selection are required. This section is devoted to extending the basic viability model of natural selection in a variety of ways to predict how natural selection works for different components of fitness and for changing fitness values. It is not possible to cover all possible models of natural selection exhaustively since there are many. Instead, each of the three models detailed in this section gives some insight into the dynamics of natural selection when one of the major assumptions of the one-locus, two-allele viability model is changed.

Naturalselection via different levels of fecundity

Natural selection due to differences in genotype viability is sometimes called hard selection since genotype frequency changes come about from the death of individuals and their complete failure to reproduce. In contrast, natural selection due to differences in the fecundity (production of offspring) of individuals with different genotypes causes changes in the frequency of genotypes within the progeny of each generation. Fecundity selection is called soft selection because all individuals in the parental generation reproduce, although by differing amounts.

A fecundity model for natural selection on a diallelic locus requires a different approach than was taken for viability selection. A major difference is that fitness depends on the pair of genotypes that mate. This means that there are nine different fitness values in a fecundity selection model, as shown in Table 7.4. Another difference is that predicting the genotype frequencies of the progeny is going to be slightly more complicated than for simple random mating. Variation in fecundity may alter the number of progeny produced by each mating pair from the frequency expected by random mating alone. This requires accounting for the expected progeny genotype frequencies that arise from each mating pair weighted by the fecundity of that mating pair as

Table 7.4 Fitness values based on the fecundities of mating pairs of male and female genotypes for a diallelic locus along with the expected genotype frequencies in the progeny of each possible male and female mating pair weighted by the fecundity of each mating pair. The frequencies of the AA, Aa, and aa genotypes are represented by X, Y, and Z respectively.

Fitness value

Male Female -

genotype genotype. . . AA Aa aa f11 f12 f13

f21 f23 f23

f31 f32 f33

Expected progeny genotype frequency

Parental mating

Fecundity

Total frequency

0 0

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