Qualitative behavior of a selectively neutral allelic model.
A model of Fleming and Viot for describing frequency distributions for selectively neutral allelic populations and for multidimensional numerical genetic traits is studied, with specific attention given to two qualitative aspects that are derived: the coherence of the random wandering distribution and the tendency to cluster at microscopic scales. A new quantity, called the clustering or occupation index, is introduced to measure relative patchiness of the distribution in terms of a limiting subcell occupation frequency. Results of one- and two-dimensional computer-generated simulations are presented which provide an estimate of the theoretical expected distribution of allelic types. Evidence of the robustness of the model, in the sense that it arises from a variety of assumptions about the reproductive mechanism, is presented in the Appendix.
D000483:Alleles; D000818:Animals; D003201:Computers; D008433:Mathematics; D008957:Models, Genetic