Fission models of population variability.

Most models in population genetics are models of allele frequency, making implicit or explicit assumptions of equilibrium or constant population size. In recent papers, we have attempted to develop more appropriate models for the analysis of rare variant data in South American Indian tribes; these are branching process models for the total number of replicates of a variant allele. The spatial distribution of a variant may convey information about its history and characteristics, and this paper extends previous models to take this factor into consideration. A model of fission into subdivisions is superimposed on the previous branching process, and variation between subdivisions is considered. The case where fission is nonrandom and the locations of like alleles are initially positively associated, as would happen were a tribal cluster or village to split on familial lines, is also analyzed. The statistics developed are applied to Yanomama Indian data on rare genetic variants. Due to insufficient time depth, no definitive new inferences can be drawn, but the analysis shows that this model provides results consistent with previous conclusions, and demonstrates the general type of question that may be answered by the approach taken here. In particular, striking confirmation of a higher-than-average growth rate, and hence smaller-than-previously-estimated age, is obtained for the Yan2 serum albumen variant.