  We introduce an (evolution) algebra identifying the coefficients of
inheritance of a bisexual population as the structure constants of the algebra.
The basic properties of the algebra are studied. We prove that this algebra is
commutative (and hence flexible), not associative and not necessarily power
associative. We show that the evolution algebra of the bisexual population is
not a baric algebra, but a dibaric algebra and hence its square is baric.
Moreover, we show that the algebra is a Banach algebra. The set of all
derivations of the evolution algebra is described. We find necessary conditions
for a state of the population to be a fixed point or a zero point of the
evolution operator which corresponds to the evolution algebra. We also
establish upper estimate of the limit points set for trajectories of the
evolution operator. Using the necessary conditions we give a detailed analysis
of a special case of the evolution algebra (bisexual population of which has a
preference on type "1" of females and males). For such a special case we
describe the full set of idempotent elements and the full set of absolute
nilpotent elements.
