I've been reading up to try to understand how the kinship coefficient (or coefficient of coancestry) is calculated. https://brainder.org/2015/06/13/genetic-resemblance-between-relatives/ this is the best explanation I've been able to find so far. However, I've not been able to find an explanation that makes a clear distinction between genes and alleles.
In my initial reading of the above I factored in this fact and assumed that often when the author wrote gene he/she meant allele (an assumption which I now think is incorrect), and thus that identity by descent of a single allele between individuals would be enough to satisfy kinship in the context of the definition of the kinship coefficient. This lead me to confusion upon reading the kinship coefficient as mathematically defined from the condensed coefficients of identity:
D1 + 1/2(D3+D5+D7) + 1/4(D8)
Surely, I thought, the kinship coefficient should merely be the sum of the probabilities of all the possible ways in which the two individuals may share the same allele. And thus there is no reason to multiply the sum of D3, D5, and D7 by 1/2 and D8 by 1/4.
Finally to my question; Kinship coefficient is defined as the probability that two individuals are identical by descent at a single randomly selected gene. Remembering this, is the reason it is calculated in this way because in order for the gene between individuals to be fully identical in the case of D3, D5, and D7, an additional identical allele is required from one parent (an event with a probability of 1/2), and in the case of D8 additional identical alleles are required from both parents (an event with a probability of 1/4)?
I'd be very grateful if someone could clarify for me why it's calculated in this way.