Summary: In this paper, we investigate non-associative properties in algebraic hyperstructures as it plays out in the biological inheritance which is expressed in the genotypic and phenotypic information that are passed to the progenies from the parental traits. This is with the intention to valuate with precision the non-associativity of weak associative properties in algebraic structures derived from some biological inheritance crossing. Examples of biological inheritance crossing which obey the WASS condition \(x\cdot(y\cdot z)\cap(x\cdot y)\cdot z\ne\emptyset\) for the \(1,2,3\)-variable forms were found (though the corresponding identities were not obeyed). The structures \((H,\otimes)\) were found to be hypergroupoids or hyperquasigroups which obey 1-variable identity (3-power associativity) or 2-variable identities (LAP, RAP or flexibility) or 3-variable identities (extra-1 or extra-2 or extra-3). Such hyperstructures can be termed to be 3-power associative, flexible, left (right) alternative or extra; in their precise measure of weakness in associativity.
For the entire collection see [Zbl 1448.65007].