A simple genealogical structure of strongly balanced allelic lines and trans-species evolution of polymorphism.

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Abstract
Different alleles undergoing strong symmetric balancing selection show a simple genealogical structure (allelic genealogy), similar to the gene genealogy described by the coalescence process for a sample of neutral genes randomly drawn from a panmictic population at equilibrium. The only difference between the two genealogies lies in the different time scales. An approximate scaling factor for allelic genealogy relative to that of neutral gene genealogy is [square root of S/(2M)].[In[S/(16 pi M2)]]-3/2, where M = Nu and S = 2Ns (N, effective population size; u, mutation rate to selected alleles per locus per generation; s, selection coefficient). The larger the value of square root of S/M (greater than or equal to 100), the larger the scaling factor. These findings, supported by simulation results, allow one to apply the theoretical results of the coalescence process directly to the allelic genealogy. Combined with the trans-species evolution of the major histocompatibility complex polymorphism for which balancing selection is believed to be responsible, allelic genealogy predicts that the number of breeding individuals in the human population could not be as small as 50-100 at any time of its evolutionary history. The analysis appears to contradict the founder principle as being important in recent mammalian evolution.