NOTE 22G: The approximation used here, which ignores multiple crossings of lineages between the populations, gets much worse for larger m.
NOTE 22H: These estimates are quite rough and do not use all the information in the data. Moreover, they assume an extremely simple model in which species form instantaneously. Patterson et al. (2006) argue that the data suggest hybridization between diverging lineages; however, the data are consistent with a range of scenarios in which there may be a gradual reduction of gene exchange and geographic structure within species.
NOTE 22I: More precisely, we expect the number of incompatibilities to be Poisson distributed with expectation λ = 0.4, so that the chance of 0, 1, 2, ... incompatibilities is e–λ, λ e–λ, (λ2/2)e–λ, (λ3/2 × 3)e–λ, ... = 0.67, 0.27, 0.05, 0.007, …, with fitness reduced by 1, 0.9, 0.81, 0.73, ... with these Poisson probabilities. The average fitness calculated this way is almost the same as just setting (1 – s)λ, though.
NOTE 22J: The number of pairwise incompatibilities increases as n2; a rate that gets faster and faster as divergence proceeds. This is termed the “snowball effect.”
NOTE 22K: This simple model of the accumulation of Dobzhansky–Muller incompatibilities was developed by Turelli and Orr (1995, 2000).
NOTE 22L: This argument was made by Walsh (1982).
NOTE 22M: Interestingly, this is independent of the strength of selection against APBP. For a single locus under migration and selection, ΔpA ~ spAqA – mpA, and so polymorphism is possible only if m < s (Box 28.3). So, Dobzhansky–Muller divergence can be maintained even with gene flow, but the threshold rate of gene flow is one-quarter that with divergence at a single gene. (See Problems 18.7 and 22.7.)
NOTE 22N: There will be an additional time (~ –(1/s)loge(1/2N) = 200 generations) for the new allele to increase from low frequency to fixation.
NOTE 22O: This analysis is based on those of Kondrashov (2002) and Navarro and Barton (2002).