General selection model

The general selection model (GSM) is a model of population genetics that describes how a population's allele frequencies will change when acted upon by natural selection.

Equation
The General Selection Model applied to a single gene with two alleles (let's call them A1 and A2) is encapsulated by the equation:


 * $$\Delta q=\frac{pq \big[q(W_2-W_1) + p(W_1 - W_0)\big ]}{\overline{W}}$$
 * where:


 * $$p$$ is the frequency of allele A1
 * $$q$$ is the frequency of allele A2
 * $$\Delta q$$ is the rate of evolutionary change of the frequency of allele A2
 * $$W_0,W_1, W_2$$ are the relative fitnesses of homozygous A1, heterozygous (A1A2), and homozygous A2 genotypes respectively.
 * $$\overline{W}$$ is the mean population relative fitness.

In words:

The product of the relative frequencies, $$pq$$, is a measure of the genetic variance. The quantity pq is maximized when there is an equal frequency of each gene, when $$p=q$$. In the GSM, the rate of change $$\Delta Q$$ is proportional to the genetic variation.

The mean population fitness $$\overline{W}$$ is a measure of the overall fitness of the population. In the GSM, the rate of change $$\Delta Q$$ is inversely proportional to the mean fitness $$\overline{W}$$—i.e. when the population is maximally fit, no further change can occur.

The remainder of the equation, $$ \big[q(W_2-W_1) + p(W_1 - W_0)\big ]$$, refers to the mean effect of an allele substitution. In essence, this term quantifies what effect genetic changes will have on fitness.