Natural selection can be modeled quantitatively by weighting genotypes according to their relative fitness.

Suppose a population begins with genotype frequencies

$$f_{AA},\quad f_{Aa},\quad f_{aa}$$

and corresponding relative fitnesses

$$w_{AA},\quad w_{Aa},\quad w_{aa}.$$

After selection, the genotype contributions are proportional to

$$f_{AA}w_{AA},\qquad f_{Aa}w_{Aa},\qquad f_{aa}w_{aa}.$$

Their sum

$$\bar w=f_{AA}w_{AA}+f_{Aa}w_{Aa}+f_{aa}w_{aa}$$

is the mean fitness used to normalize the surviving or reproducing population.

Worked example

Start with genotype frequencies

$$f_{AA}=0.25,\quad f_{Aa}=0.50,\quad f_{aa}=0.25,$$

and fitnesses

$$w_{AA}=1,\quad w_{Aa}=1,\quad w_{aa}=0.5.$$

The weighted contributions are

$$0.25,\quad 0.50,\quad 0.125,$$

so

$$\bar w=0.875.$$

After normalization,

$$f'{AA}=0.286,\quad f'{Aa}=0.571,\quad f'_{aa}=0.143.$$

The frequency of allele $A$ among these individuals is

$$p'=f'{AA}+\frac12f'{Aa}\approx0.286+0.286=0.572.$$

It began at $p=0.50$, so selection increased $A$ in one generation.

Selection changes allele frequencies because genotypes contribute unequally to the next generation. Dominance affects how selection 'sees' alleles through phenotype: a harmful recessive allele can remain hidden from selection in heterozygotes, so it may decline slowly when rare.