  We consider a four-parametric $(a, b, \alpha, \beta)$ family of Volterra
quadratic stochastic operators for a bisexual population (i.e., each organism
of the population must belong either to the female sex or the male sex). We
show that independently on parameters each such operator has at least two fixed
points. Moreover, under some conditions on parameters the operator has
infinitely many (continuum) fixed points. Choosing parameters, numerically we
show that a fixed point may be any type: attracting, repelling, saddle and
non-hyperbolic. We separate five subfamilies of quadratic operators and show
that each operator of these subfamilies is regular, i.e. any trajectory
constructed by the operator converges to a fixed point.
