If we take a male and female, cross them, and collect one son and one daughter to produce the next generation (and continually do this for many generations) - (full-sib mating design) how much genetic variance is lost per generation/how do we calculate this?

Assume all sites initially have allelic variation, and we imagine a diploid sexual species.


A classical result from the Wright-Fisher model of genetic drift is that at each generation the heterozygosity ($2x(1-x)$) is expected to decrease by $\frac{1}{2N}$ due to genetic drift. ($x$ is the frequency of one of the two alleles). In your example the expected loss of heterozygosity is $¼$. This same result has been derived from coalescent theory and a similar result is derived from the birth-death Moran model. The issue is that this model assume bi-allelic loci only.

Let's think of 1 tetra-alellic (4 alleles) locus and let's assume that the 4 alleles in our two original parents are all different. We can draw the 16 possible pairs of offsprings and see the probability to lose 0, 1 or 2 alleles in the next generation

lose 0 allele: ¼
lose 1 allele: ½
lose 2 alleles: ¼
lose more than 2 alleles: 0
Therefore, the expected number of lost alleles is $1$!

We can then do the same (calculate the probability mass function) for two parents with 3 alleles and then 2 alleles (with various frequencies). It is not very complicated. But it would be much better to have a general model to describe the loss of heterozygosity through time for more than 2 alleles. This paper probably gives this solution but I haven't read it yet. I will probably read it once and I will improve my answer then!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.