  We consider an evolution algebra which corresponds to a bisexual population
with a set of females partitioned into finitely many different types and the
males having only one type. We study basic properties of the algebra. This
algebra is commutative (and hence flexible), not associative and not
necessarily power associative, in general. Moreover it is not unital. A
condition is found on the structural constants of the algebra under which the
algebra is associative, alternative, power associative, nilpotent, satisfies
Jacobi and Jordan identities. In a general case, we describe the full set of
idempotent elements and the full set of absolute nilpotent elements. The set of
all operators of left (right) multiplications is described. Under some
conditions on the structural constants it is proved that the corresponding
algebra is centroidal. Moreover the classification of 2-dimensional and some
3-dimensional algebras are obtained.
