Abstract
The gametic algebra for a 2 m-ploid population with n + 1 alleles has the following property: The automorphism group of the algebra is isomorphic to A( n), the affine group of R n .(1) This fact leads to an interesting algebraic problem: the classification of all baric algebras having the property (1). A type of baric algebras, namely α-algebras, is defined by prescribing their automorphisms. These algebras have dimension m+n m and verify (1). We construct a class of α-algebras that are closely related to gametic algebras and give a classification of all α-algebras in the case 1 ⩽ m ⩽ 5, n arbitrary.
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