# 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:

${\displaystyle \Delta q={\frac {pq{\big [}q(W_{2}-W_{1})+p(W_{1}-W_{0}){\big ]}}{\overline {W}}}}$

where:
${\displaystyle p}$ is the frequency of allele A1
${\displaystyle q}$ is the frequency of allele A2
${\displaystyle \Delta q}$ is the rate of evolutionary change of the frequency of allele A2
${\displaystyle W_{0},W_{1},W_{2}}$ are the relative fitnesses of homozygous A1, heterozygous (A1A2), and homozygous A2 genotypes respectively.
${\displaystyle {\overline {W}}}$ is the mean population relative fitness.

In words:

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

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

The remainder of the equation, ${\displaystyle {\big [}q(W_{2}-W_{1})+p(W_{1}-W_{0}){\big ]}}$, refers to the mean effect of an allele substitution. In essence, this term quantifies what effect genetic changes will have on fitness.