Random events in population genetics - How do we calculate the march to homozygosity?
The march to homozygosity
Over the long term, pure random drift causes the population to 'march' to homozygosity at a locus. Through random drift, all loci at which there are several selectively neutral alleles will tend to become fixed for only one gene.
The march to homozygosity in a small population proceeds because two copies of the same gene may combine in a single individual.
Two ways to make a homozygote:
1. Self-fertilization. There are 2N gamete types but because each individual produces many more than two gametes, there is a 1/(2N ) chance that a gamete will combine with another gamete of the same gamete type as itself. Self-fertilization can exist in hermaphrodite organisms such as box plant trees (pictured opposite).
2. Combining two identical genes made from the same gene but from another parent. If the frequency of an A gene is p , the chance that two A genes meet is p². If there are two types of homozygote, AA and aa , the chance of forming a homozygote will be p² + q² = f . The total chance of forming a homozygote by this method is the chance that a gamete does not combine with another copy of the parental gene multiplied by the chance that two independent genes combine to form a homozygote (f ). This total chance can be written as: 1- (1/(2N ))f .