Markup /zellig/58824

Comment
Kinship coefficient \(F\) describes how more probable it is that a related person has the same gene as you when compared to an unrelated person. By definition \(p_y = F_{xy} + (1 - F_{xy})p\), where \(p_y\) - probabilty that the person y has a given gene, \(p\) - frequency of that gene in general population. Fixation index \(F_{ST}\) describes the same thing, but between subpopulations, so if you take a person from the same subpopulation as you, \(p_{same} = F_{ST} + (1 - F_{ST})p\) and if you take a person from a different subpopulation, \(p_{other} = - F_{ST} + (1 + F_{ST})p\) (at least in case of subpopulations of identical size, we are doing the simplest case here), which means that your kinship with a person from the same subpopulation is \(F_{ST}\) and with a person from from different subpopulation is \(-F_{ST}\).
<Maya space
In an uniform population (not divided into subpopulations), the kinship between a person and his child is 1/4. Choose a locus and a gene at that locus in yourself, there is 1/2 chance the child inherited this gene from you (as opposed to inheriting the allele from the other chromosome), and there is 1/2 chance you have picked that gene in your child (as opposed to picking a gene that it inherited from its mother.)
<BWC space
If we take subpopulations into account and if the mother is from the same subpopulation as the father, the kinship with the child jumps to \(1/4 + 3 F_{ST}/4\). The reasoning is as follows: with probability 1/2 you pick the allele it inherited from you, then with probability 1/2 is the same allele you've picked initially and with probability 1/2 it's the other allele that comes from you, which in turn is identical to the first allele with probability \(p_{same} = F_{ST} + (1 - F_{ST})p\). And with probability 1/2 you pick an allele coming from the mother, who is from the same subpopulation as you, so the probability of it being identical is also \(p_{same} = F_{ST} + (1 - F_{ST})p\). Finally, you have \(p_{child} = 1/4 + 3/4 (F_{ST} + (1 - F_{ST})p)\). Kinship coefficient is equal to \(F_{xy} = (p_y - p)/ (1 - p)\) after transforming the first equation. Transforming \(p_{child}\) gives:
• \(p_{child} = 1/4 + 3/4F_{ST} + 3/4p - 3/4F_{ST}p\)
• \(p_{child} - p  = 1/4 + 3/4F_{ST} - 1/4p - 3/4F_{ST}p\)
• \(p_{child} - p = (1 - p)(1/4 + 3/4F_{ST})\)
• \(1/4 + 3/4F_{ST} = (p_{child} - p)/(1-p)\)
The above means that \(F_{child} = 1/4 + 3/4F_{ST}\). In case of a mixed child \(F_{mixed} = 1/4 - F_{ST}/4\) (I'm NOT rewriting the derivation.)
<mutt space
Now the question is: at what \(F_{ST}\) the mixed child will be as related to its father as an unrelated person from his own subpopulation, i.e., when \(F_{ST} = 1/4 - 1/4F_{ST}\). That's a simple equation, the result of which is \(0.20\), which means that if a person chooses a partner from a population that is more distant than \(0.20\), his child will be less related to him than for example an adopted child of his race.