Vladimir P. Passekov
On the Genetic Interpretation of Eigenvectors for the Generalized Model of Nonepistatic Selection
Preprint series: ESI preprints

MSC:

92D10 Genetics, {For genetic algebras, See 17D92}

92D15 Problems related to evolution

Abstract: A generalized nonepistatic selection model for diploid population with
nonoverlapping generations suggested by Karlin and Liberman is considered.
In the model, viabilities of genotypes are determined by combinations of
neutral/multiplicative interactions between loci. The structure of known
expressions for eigenvectors of the linearization matrix at the
polymorphic linkage equilibrium fixed point is analyzed.

1. Calculations of marginal characteristics show that the eigenvectors
can be interpreted as such deviations from the equilibrium that can be
observed only starting from a certain number of loci. That is, marginal
one-, two-locus gamete frequencies and so on up to, say, $k$ loci (the
threshold) satisfy multilocus linkage equilibrium relations.

2. In the neutral case, the more loci determine this threshold, the more
rapid is the decay of the appropriate disequilibrium. Eigenvalues of
linearization matrix are simplified to known expressions under neutrality.
Each eigenvalue is associated with the probability that a recombination
takes place in the appropriate set of loci. In the continuous-time model of
nonepistatic selection, the condition ''more recombination'' (in the sense
of increasing these probabilities for sets of loci by some quantities)
enhances the stability of the polymorphic equilibrium (decreasing
appropriate eigenvalues by the same quantities).
Keywords: population genetics, multilocus models, viability selection, nonepistatic selection, central equilibria, linearization, eigenvectors, disequilibria, rates of decay