  A quadratic stochastic operator (in short QSO) is usually used to present the
time evolution of differing species in biology. Some quadratic stochastic
operators have been studied by Lotka and Volterra. In the present paper, we
first give a simple characterization of Volterra QSO in terms of absolutely
continuity of discrete measures. Moreover, we provide its generalization in
continuous setting. Further, we introduce a notion of orthogonal preserving
QSO, and describe such kind of operators defined on two dimensional simplex. It
turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The
associativity of genetic algebras generated by orthogonal preserving QSO is
studied too.
