2 research outputs found
Average sex ratio and population maintenance cost
The ratio of males to females in a population is a meaningful characteristic
of sexual species. The reason for this biological property to be available to
the observers of nature seems to be a question never asked. Introducing the
notion of historically adapted populations as global minimizers of maintenance
cost functions, we propose a theoretical explanation for the reported stability
of this feature. This mathematical formulation suggests that sex ratio could be
considered as an indirect result shaped by the antagonism between the size of
the population and the finiteness of resources.Comment: 18 pages. A revised new version, where all the text was improved to
become more clear for the reade
A nonsmooth two-sex population model
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.Comment: 18 pages, 6 figures. Section 2, in which the model is presented, was
rewritten to better explain the elements of the proposed model. The
description of parameter "r" was correcte