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The Evolutionary Reduction Principle for Linear Variation in Genetic Transmission

Summary: The Evolutionary Reduction Principle for
Linear Variation in Genetic Transmission
Lee Altenberg
University of Hawai`i at Manoa
The evolution of genetic systems has been analyzed through the use of modifier
gene models, in which a neutral gene is posited to control the transmission of other
genes under selection. Analysis of modifier gene models has found the manifesta-
tions of an "evolutionary reduction principle": in a population near equilibrium, a
new modifier allele that scales equally all transition probabilities between different
genotypes under selection can invade if and only if it reduces the transition prob-
abilities. Analytical results on the reduction principle have always required some
set of constraints for tractability: limitations to one or two selected loci, two alleles
per locus, specific selection regimes or weak selection, specific genetic processes
being modified, extreme or infinitesimal effects of the modifier allele, or tight link-
age between modifier and selected loci. Here, I prove the reduction principle in
the absence of any of these constraints, confirming a twenty-year-old conjecture.
The proof is obtained by a wider application of Karlin's Theorem 5.2 (1982) and
its extension to ML-matrices, substochastic matrices, and reducible matrices.
Keywords: evolution; evolutionary theory; modifier gene; recombination rate; mu-


Source: Altenberg, Lee - Department of Information and Computer Science, University of Hawai'i at Manoa


Collections: Computer Technologies and Information Sciences