Modeling change of haplotype distributions in random mating populations using random sets

Several mathematical models have been developed to describe the genetic structure of populations. Most of these models focus on only one, or few genetic loci. In this paper, we develop a model to describe a large number of loci simultaneously. Such a model is appropriate for recent large-scale studies of single nucleotide polymorphisms (SNP). Building on the earlier work of Geiringer (1944) and the more recent mathematical formalization proposed by Dawson (2000), we suggest modeling the system using random sets. We can then use this model to find the recursion law for the change of haplotype frequencies between successive generations.