  We consider the set of ($n\times n\times n$) cubic stochastic matrices of
type (1,2) together with different multiplication rules that not only retain
their stochastic properties but also endow this set with an associative
semigroup structure. Then we introduce different actions of the semigroup of
nonnegative column stochastic $n\times n$ matrices on the set of cubic
stochastic matrices of type (1,2) and study how these actions translate to the
cubic matrix slices and marginal distributions. Actions introduced here provide
an algebraic framework where considering different changes affecting the
transition probabilities ruling certain biological populations.
