which is the logistic growth version of equation 6.19.

Both the numbers of individuals of each genotype and the allele frequency under density-dependent natural selection can be seen in Fig. 7.6 when the AA genotype has the highest carrying capacity. Starting out with a very small N, the numbers of individuals of all genotypes increase over time. However, once N approaches the lowest carrying capacity, Kaa in this illustration, the number of aa individuals peaks and then declines. This happens because the absolute fitness of aa approaches one in the fewest generations while the other two genotypes continue to add individuals to their populations because their carrying capacities are higher. The same phenomenon also occurs to the Aa genotype because it has the next lowest carrying capacity. The AA genotype has the highest carrying capacity and the number of individuals of that genotype eventually grows to the point where it makes up the entire population.

The general result for density-dependent selection is that the carrying capacities of the three genotypes will determine the eventual genotype and allele frequencies when populations approach their carrying capacities. When KAA is the highest then the A allele goes to fixation and when Kaa is the largest then the a allele goes to fixation. Alternatively, when KAa is the largest then there is an equilibrium with both alleles segregating and when KAa is the smallest then either A or a will reach fixation depending on initial allele frequencies. These results are qualitatively identical to those for unbounded growth.

In contrast, the results of density-dependent and density-independent natural selection do not agree when population size is restricted to low numbers. The total population size N may be much less than the carrying capacity in highly disturbed or inhospitable environments where individuals have low reproductive output or high turnover. To see this, consider equations 7.27-7.29 for genotype absolute

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