Population genetics of fragile X: A multiple allele model with variable risk of CGG repeat expansion

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Abstract
A model of the population genetics of fragile X that incorporates an arbitrarily large number of alleles based on CGG repeat number is presented. The probability of transition from a premutation to a full mutation upon maternal transmission depends on maternal allele size, as suggested by molecular data. Transitions among various sizes of premutation alleles upon both maternal and paternal transmission are also included using empirically determined transition probabilities. Multiple paths to the final full mutation allele are allowed. Algebraic results for equilibrium allele frequencies are presented for an arbitrary number of alleles, and numerical results are presented for the case of 9 alleles. The model predicts large frequencies for alleles near the normal premutation borderline and high mutation probabilities for the first few mutational steps. The model also predicts that the approach to equilibrium allele frequencies is quite slow, and that a premutation allele typically persists for many generations in a given family before the final transition to a full mutation allele. These nonequilibrium effects are sensitive to the transition probability from large normal alleles to small premutation alleles.