# Population size and genetic drift - What are the evidences?

Wright-Fisher model

From the Wright-Fisher model of genetic drift, the random sampling of allele from one generation to the next is taken from a binomial distribution with parameters $2N$ and $p$, where $N$ is the population size and $p$ the frequency of an allele of interest.

Strength of Genetic drift

The strength of genetic drift can be measured in terms of two different statistics:

• variance in allele frequency from one generation to the next
• loss of heterozygosity per generation

Variance in allele frequency from one generation to the next

From the above, it is relatelively straight forward to show that the variance in allele frequency in the successive generation is

$$\text{var}\left(p'\right) = \frac{p(1-p)}{2N}$$

, where $N$ is the population size.

Loss of heterozygosity

Heterozygosity decays by $1-\frac{1}{2N}$ every generation

$$H_t = H_{t-1}\left(1-\frac{1}{2N}\right)$$

, where $H_t$, is the expected heterozygosity at time $t$.

Source

See Gillespie: Population Genetics - A concise guide chapter 2 for more info on these predictions.

Question

Do we have empirical evidence that the decay rate in heterozygosity and/or the variance in allele frequency due to genetic drift follows these predictions?

• I suppose it's quite complex, would need large amounts of replication and have to neutralise/standardise selection and mutation across replicates - maybe mutation accumulation experiments would be worth investigating – rg255 Apr 20 '16 at 6:22
• This paper looks interesting researchgate.net/publication/… but it's not quite what you are looking for I think – rg255 Apr 20 '16 at 6:30
• In natural populations? No. This is why people generally talk about "effective population size". (I'm not a fan of this term though -- if we mean "the diffusion parameter of allele frequencies" or "the rate of decay of heterozygosity", we should just say so!) – Daniel Weissman Apr 20 '16 at 14:49
• Not necessarily in natural population. I was rather thinking about experimental evolution. Someone may have produced an experimental evolution where the population is as close as possible to a wright-fisher population (random mating, constant population, no selection, non-overlapping generation; so that $N=Ne$) and test whether the model offers good predictions. – Remi.b Apr 20 '16 at 16:05