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.

See also

• Darwinian Fitness
• Hardy-Weinberg principle
• Population genetics