rogers@ARSUN.ANTHRO.UTAH.EDU (Alan R. Rogers) (10/23/90)
Ann Eileen Miller Baker writes >Can equilibrium occur that quickly? No. Yet we run simulations for 200 >generations or so until the equilibrium is reached. I don't know a way around >this problem: the equilibrium is easily defined, the other stuff is not, >though the other stuff may be a more realistic reflection of house mouse >populations near human habitation. Henry Harpending and I have argued (Evolution, 40(6):1312) that equilibrium is usually reached much faster than this. The slow convergence seen is theoretical models occurs because the theory is predicting something other than what we usually measure. Most theory deals either with probabilities of identity by descent or with moments (variances & covariances) about some "theoretical" mean value (either the allele frequency of some ancestral generation, or of an external continent or is the value toward which selection is pushing the system). In empirical work, on the other hand, we can only work with moments about the mean allele frequency of the current generation, or with genetic distances. Harpending and I showed that the things that we measure converge *much* faster. The half-life of convergence is log(2)/(2 log[(1-s)lambda2]), where s is the rate of emigration from outside the study area, and lambda2 is the second largest eigenvalue of the migration matrix. The median half-live of the 12 human populations in our sample was 5 generations. Jim Wood published a similar result at nearly the same time, which is cited in our paper. Alan Rogers INTERNET: rogers@anthro.utah.edu USMAIL : Dept. of Anthropology, Univ. of Utah, S.L.C., UT 84112 PHONE : (801) 581-5529