Several human diseases are now known to be caused by expansion of tandem repeat of trinucleotide sequences. At all such regions of the genome extensive polymorphisms of repeat sizes are found among normal individuals. The literature characterizing these polymorphisms is growing at a rapid pace; however, the mechanism through which such repeat expansion occurs and how disease frequencies are maintained in populations is not yet known precisely. Current experimental data imply the possibility of several alternative molecular mechanisms of repeat size expansion, but their consequences with respect to the population dynamics of genotype frequencies and to disease frequency variation within and between populations are not well known. The broad aim of this project is to address these questions by providing mathematical population genetic models of repeat expansions, in light of which data on genotype frequencies and allele size distributions will be studied in normal as well as affected individuals. Preliminary work done by this group of researchers indicates that finite dimensional Markovian mutation models, the theory of branching processes and coalescence theory can provide good mathematical descriptions of various "mutational" mechanisms of repeat size expansions and can thus explain the observed genotype distributions at such loci and the transition of allele size differences between offspring and parents in disease-prone families. These models will be pursued in greater detail using analytical as well as computer simulation methods, and will be applied to population data available through our collaborators. The anticipated results of this study will be significant in providing insight into the ancestry of the disease genes as well as into the conditions under which disease prevalence can be maintained. Outcomes of this project will also be relevant for understanding how molecular heterogeneity at tandemly repeating trinucleotide sequences affects disease progression through repeat size expansions.