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Evolution algebras were introduced into Genetics to deal with the mechanismof inheritance of asexual organisms. Their distribution into isotopism classesis uniquely related with the mutation of alleles in non-Mendelian Genetics.This paper deals with such a distribution by means of Computational AlgebraicGeometry. We focus in particular on the two-dimensional case, which is relatedto the asexual reproduction processes of diploid organisms. Specifically, wedetermine the existence of four isotopism classes, whatever the base field is,and we characterize the corresponding isomorphism classes.

Classification of asexual diploid organisms by means of strongly isotopic evolution algebras defined over any field