IBD and IBS based definitions for FST, FIS and FIT

Consider the process FFg in the main text. As we assume that the genes under consideration are neutral, the expected allele frequency for any individual equals to that in the ancestral generation, EE�xxiiiiiiii � = ppiiii . As xxiiiiiiii is an indicator function with values 0 or 1, it further holds that EE�xxiiiiiiii xxiiiiiiii � = ppiiii , and EE�xxiiiiiiii ′xxiiiiiiii � = 0 for ii ≠ ii′. The probability that the alleles ii and ii′ in a gene j are of the same type u for the individuals i and i' is given by EE�xxiiiiiiii xxii′iiii ′ii �. The probability that two randomly chosen alleles in a gene j are of the same type u for the individuals i and i' is given by ∑ EE�xxiiiiiiii xxii′iiii ′ii� ii ,ii′ /4. This probability can be decomposed into two components. First, the alleles may be identical by descent, the ancestral allele being of type u. The probability of this event is θθiiii′ppiiii . The second option is that the alleles are not identical by descent, but the alleles in the ancestral generation were both of type ppiiii . As the probability of the latter event is (1 − θθiiii′)ppiiii 2 , we obtain