Genetic Drift
Alleles are sampled from a population to make up the next generation. Anytime a random sample is taken it is likely to deviate slightly from the original population. Genetic drift is evolutionary sampling error. These deviations are not biased in any single direction towards an increase or decrease in frequency of a particular allele. However, these small deviations will accumulate over several generations and ultimately alleles will be lost until only a single allele remains in the population (assuming it is not reintroduced by mutation or from another population).
Exact Binomial Probabilities
Average Loss of Heterozygosity
If a small population becomes isolated so that there is no introduction of new alleles (for example in a captive breeding program or as a small number of founders on a new island) and genetic drift is a major force, the average loss of heterozygosity in the genome over multiple generations can be estimated.
[math]H_t = H_0 (1-\frac{1}{2N})^t[/math]
[math]H_t[/math] is the remaining heterozygosity at generation [math]t[/math].
[math]H_0[/math] is the initial heterozygosity at generation zero.
[math]t[/math] is the time in generations.
[math]N[/math] is the (diploid) population size.
This can be simplified by using an exponential approximation.
[math](1-\frac{1}{2N})^t \approx e^{- t/ 2N}[/math]
[math]H_t \approx H_0 e^{- t/ 2N}[/math]
The time until only half of the original genetic variation remains can be directly estimated as a rule-of-thumb.
[math]\frac{1}{2} = \frac{H_t}{H_0} \approx e^{- t/ 2N}[/math]
[math]\log{\frac{1}{2}} \approx \log{e^{- t/ 2N}}[/math]
[math]-0.6931 \approx - t/ 2N[/math]
