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- saaq2

where sxx represents the genotype-specific selection coefficient. Genotypes have higher fitness when they are rare since relative fitness decreases as the product of the selection coefficient and the genotype's frequency increases. Note that the selection coefficient itself is a constant and can be thought of as a per-capita decrease in relative fitness.

As with other models of selection, the equilibrium points in this model of natural selection can be found by determining when the change in allele frequency (Ap) is equal to zero. The expression for change in allele frequency over one generation of fecundity selection is

for the special case of the selection coefficient being equal for all genotypes, as derived in Math box 7.1. Two equilibrium points occur at fixation and loss

(p = 1.0 and p = 0.0) since the pq term in the numerator is zero. There is also an equilibrium point at p = 1/2 since the q - p term is zero.

Figure 7.5 shows the relative fitness values in equation 7.19 when all selection coefficients are equal to one. It is interesting to note that at p = 1/2 the fitness of the heterozygote is less than that of the two homozygotes, so this model of natural selection does not require overdominance for fitness to maintain genetic variation at equilibrium. However, with independent selection coefficients for each genotype there is not a stable polymorphism in general. With arbitrary fitness values for the three genotypes, there are many possible outcomes, many without stable polymorphism.

Natural selection with density-dependent fitness

An assumption in most models of natural selection is that populations are able to grow without any

Math box 7.1

The change in allele frequency with frequency-dependent selection

Start with the expression for change in allele frequency under viability selection given in equation 6.23:

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