This equation is used to predict or explain the relative freqencies of alleles and different phenotypes/genotypes in a stable population, i.e one in which which the
frequencies of different forms of genes - alleles - are constant;
effectively in equilibrium from generation to generation.

The steady-state explanation depends on various conditions (see below), and if the equilibrium is affected it implies that selection is affecting gene frequency, as occurs during evolution and formation of new species (speciation).

The steady-state explanation depends on various conditions (see below), and if the equilibrium is affected it implies that selection is affecting gene frequency, as occurs during evolution and formation of new species (speciation).

It is important to have a clear understanding of the concepts of allele frequency, genotype frequency and phenotype frequency, and the differences between them!

The simplest case: consider a gene which exists in only 2 forms (alleles) : A (dominant) and a (recessive).

Let the frequency of the A allele be p and

let the frequency of the a allele be q.

Since both of these add up to 100% (frequency ranges from 0 to 1), p + q = 1 .

There are 3 genotypes: AA, Aa and aa

When considering genetic crosses, it is normal to consider these as potential parents and to use genetic diagrams or the Punnett square method to express the possible outcome from a pair of individuals, in terms of the likelihood of each possible genotype in the next generation.

In a population

AA could mate with
another AA,
or Aa or aa.

Aa could mate with another Aa, or AA or aa.

aa could mate with another aa, or Aa or AA.

The possible outcomes from each of these 9 combinations can be individually predicted using normal genetic techniques, but the number of permutations is rather daunting.

For instance, using just one of these examples: The frequencies of genotypes resulting from Aa mating with another Aa is given by

Here the alternative
alleles from
each individual parent are shown as single letters, and the resulting
possible
genotypes in
the next generation from this single interaction are
shown as
paired letters.

Aa could mate with another Aa, or AA or aa.

aa could mate with another aa, or Aa or AA.

The possible outcomes from each of these 9 combinations can be individually predicted using normal genetic techniques, but the number of permutations is rather daunting.

For instance, using just one of these examples: The frequencies of genotypes resulting from Aa mating with another Aa is given by

parental gametes |
|||

A | a | ||

parental gametes |
A | AA | Aa |

a | Aa | aa |

However by a slightly
different use of
the square format, the possible frequencies of genotypes in a
population can be calculated, by multiplying the
individual
probabilities:

allele freqencies | |||

p | q | ||

allele freqencies | p | p^{2} |
pq |

q | pq | q^{2} |

Here the alternative allele frequencies in the
population are shown as single letters, and the resulting genotype frequencies
in the population as their mathematical products (pxp, pxq, qxp, qxq). Of course pxq is the same as qxp, and they become 2pq.

p^{2} + 2pq + q^{2} = 1

[This is in fact (p+q)^{2}
= 1^{2}]

p

[This is in fact (p+q)

p^{2}
represents the genotype frequency for AA in the population

2pq represents the genotype frequency for Aa in the population

q^{2} represents the
genotype frequency for aa
in the population

2pq represents the genotype frequency for Aa in the population

q

If AA and Aa are indistinguishable, they will both show the same phenotype due to dominance, so it will be difficult to count them directly in the population.

However, the double recessives aa will be countable, so their frequency in the population can be calculated. This recessive phenotype frequency (= aa genotype frequency) is equal to q

By substituting the values for p and q into p

Male allele frequencies for affected and unaffected are identical to phenotype frequencies, typically p and q, not squared. There are no heterozygotes.

In females phenotype frequencies are the 'normal' 3 categories: p

Random mating

Equal viability of all genotypes (not likely if some are at an advantage/disadvantage - leading to directional or disruptive selection and hence new species formation)

No immigration/emigration

Diploid chromosomes - sex linkage requires different treatment (