A bisexual Galton-Watson branching process is a two-type branching
model, in which matings in one generation give rise to random numbers of both males
and females in the next. The mating function describes how many mating units are
formed from given numbers of males and females. In this paper we consider the
case that the distributions of the random numbers of males and females produced
by the mating units depend on some fertility parameters evolving randomly in time.
By means of a main stochastic comparison result, we show that the total population
increases, in some stochastic sense, as the positive dependence between the fertility
indexes increases. Simple examples of applications of this result are provided, together
with other similar results for a different model of population growth.