General selection model
# 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:

    $\Delta q={\frac {pq{\bigq(W_{2}-W_{1})+p(W_{1}-W_{0}){\big ]}}{\overline {W}}}$
    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, ${\bigq(W_{2}-W_{1})+p(W_{1}-W_{0}){\big ]}$, refers to the mean effect of an allele substitution. In essence, this term quantifies what effect genetic changes will have on fitness.

