  This paper considers a two-dimensional logistic model to study populations
with two genders. The growth behavior of a population is guided by two coupled
ordinary differential equations given by a non-differentiable vector field
whose parameters are the secondary sex ratio (the ratio of males to females at
time of birth), inter-, intra- and outer-gender competitions, fertility and
mortality rates and a mating function. For the case where there is no
inter-gender competition and the mortality rates are negligible with respect to
the density-dependent mortality, using geometrical techniques, we analyze the
singularities and the basin of attraction of the system, determining the
relationships between the parameters for which the system presents an
equilibrium point. In particular, we describe conditions on the secondary sex
ratio and discuss the role of the average number of female sexual partners of
each male for the conservation of a two-sex species.
