The formula for calculating the frequency of alleles in a population is the Hard-Weinberg equation (p+2pq+q=1)

So where p= the frequency of genotype AA, 2pq=the frequency of genotype Aa and q= the frequency of genotype aa these must add up 1.

 A population in which this situation exists is said to be in genetic equilibrium. When Hardy made this equation many people at the time thought that a dominant gene should eventually eliminate a recessive one because of its greater “strength”. Hardy pointed out that the tendency for an allele to be expressed in an individual is determined by how useful its effects are and that this had nothing to do with its frequency in the population.

For genetic equilibrium to exist the following conditions must be met:

1.       The population must be large. As chance plays a role in what alleles get passed to the next generation a small population means chance may be important.

2.       There must be no selection and all genotypes must be likely to contribute genes to the next generation

3.       There must be no mutation or mutation backwards and forwards at the same rate.

4.       There must be no immigration from where the allele frequencies are different. Emigration does not affect this unless one type of genotype is more likely to emigrate than another.

5.       Mating must be random. That is each genotype must be equally likely to mate with every other genotype. That some individuals are more successful in finding a mate is sexual selection and does not affect allele frequency although it will affect the proportions of various genotypes. Non-random mating can be of two types:

·         Inbreeding or mating between relatives. As a result of this the proportion of homozygotes increase. This is because matings heterzygote-heterzygote can produce more homozygotes than would be the case with random mating. Homozygote-homozygote can only produce homozygotes.

·         Outbreeding/outcrossing. The proportion of heterozygotes is higher than if the matings were random.

The significance of this for breeders is that we know that one or more of the above are at work and the horse gene pool will not be in equilibrium.  There will be a change in the frequency of alleles and consequently the various genotypes.