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The Bernstein algebra DnGα of simple Mendelian inheritance is the n-fold duplicate of the gametic algebra Gα with basis A1,..., Aα and structure constants [image omitted]. We simplify and generalize results of Bernad et al. and Peresi by showing that every identity for Gα follows from Costa's shape identity C, and that every identity for the zygotic algebra DGα follows from the recombination identity R. We use computer algebra to determine the identities of degree ≤7 for the copular algebra D2Gα. [ABSTRACT FROM AUTHOR]