Friday 19 September 2014

Genetic Drift

Effective population size (Ne) measures the magitude of genetic drift: the smaller the effective population size, the greater the drift.

There are two ways of defining effective population sizes: one is based on the sampling variance of allele frequencies (i.e., how an allele's frequency might vary from one generation to the next), and the other utilizes the concept of inbreeding (i.e., the probability that the two alleles within an individual are identical by descent from a common ancestor).

Under most simple population size give identical values for Ne, in more complex situations this is not the case.

It is not easy to relate the effective population size (Ne) to the census size of a population (N), as there are many parameters that can affect his relationship, only some of which are relevant to humans.

With no favouring of either outcome, the fixation probability of an allele in the absence of selection is equal to its frequency of 1/2N.

The average time to fixation (t) in generations has been shown to be:
t=4Ne

The long-term effective population size has been shown to be approximately equal to the harmonic mean, rather than the arithmetic mean of the population sizes over time. The harmonic mean is the reciprocal of the mean of the reciprocals: (1/t) sum_{i=1}^{t}(1/Ni) for t generations.

Founder effects relate to the process of colonization and the genetic separation of a subset of the diversity present within the source population. In contrast, bottlenecks refer to the reduction in size of a single, previously large, population and a loss of prior diversity.

In general, the higher the reproductive variance, the lower the effective population size, because parental contributions become more and more unequal. It is worth nothing that when reproductive variance is less than expected under a Poisson distribution then Ne can be greater than N. 

Reproductive variance: The variance in number of offspring produced by a group of individuals.

Subpopulation: A randomly mating population that exchanges migrants with other populations to form a meta-population.

Meta-population: A group of populations connected by migration.

Fst: the fixation indices is a measure of the deviation of observed heterozygote frequencies from those expected under Hardy-Weinberg theorem. Fst compares the mean amount of genetic diversity found within subpopulations (Hs: the expected heterozygosity) to the genetic diversity of the meta-population (Ht).
Fst=(Ht-Hs) /Ht





 

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