The gametic algebraG is constructed for a random mating population of 2r-ploid individuals which differ in a single locus with the allelesA anda. It is assumed that every kind of segregation between chromosome- and chromatid segregation occurs with a given probability. This algebraG is a convex combination of 2r+1 genetic algebras which have a common canonical basis. The train roots of these algebras are calculated and shown to be monotonically descending. The algebraG possesses a one-dimensional manifold of idempotents. With a generalization of Gonshor's theorem on the convergence of the sequence of plenary powers of an element of unit weight it is shown that for every initial gametic distribution the distribution in the following generations converges towards an equilibrium state whose coordinates are polynomials in the frequency of the alleleA in the initial generation.
Convex Combination Canonical Basis Multiplication Table Binomial Coefficient Edinburgh Math
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