Evolutionary Reduction of Mutation Rates in a Multivariate, Multilocus Model

Lee Altenberg

Submitted.


The modifier gene model.
Abstract
The evolution of genetic systems has been studied through the use of modifier gene models, in which a selectively neutral gene controls genetic transmission of other genes under selection. Analytical studies to obtain a general understanding of the dynamics have faced tradeoffs between different features for tractability. No study has been able to obtain results for arbitrary selection on multiple loci undergoing multiple genetic transformation events. Here techniques from Karlin (1982) are applied to a multilocus model of mutation with multivariate control over mutation rates, and the reduction principle is found to operate. Constraining assumptions are that mutation distributions follow the transition probabilities of reversible Markov chains, and that all loci are tightly linked. The extension of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele, below which will cause a new modifier allele to increase when rare, and above which cause it to go extinct. This manifold is the same structure as found in a multivariate multilocus model of recombination modification by Zhivotovsky, Feldman, and Christiansen (1994). A discussion of the near-equilibrium models that depart from the reduction principle concludes with a conjecture about the structural causes.
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