Genetic Algebras Associated with Polyploidy

Abstract

The relationship between certain non-associative algebras and the deterministic theory of population genetics was first investigated by Etherington(3)-(8), who defined the concepts of baric, train and special train algebras. Gonshor(10)dealt with, among other topics, algebras corresponding to autopolyploidy, on the assumption that chromosome segregation operated. In this paper [ discuss algebras corresponding to more general systems of inheritance among polyploids, which have been discussed without using algebras by Haldane(11), Geiringer(9), Moran(13)and Seyffert (16). These algebras are special cases of what I have defined as segregation algebras, and mixtures of them. All the algebras corresponding to a fixed ploidy have a relationship which I have called special isotopy. An example shows that algebras arise in other genetic systems which are not isotopic to segregation algebras.