Abstract: This paper addresses to the demographic dynamics of biological populations with sexual reproduction. We continue the research developed in previous papers where the probabilistic evolution of this type of populations was mathematically described through the metodology based on two-sex branching processes. In this paper, we carry out a specific study using the probability distributions most frequently considered to describe reproductive phenomena in biological species with sexual reproduction (bivariate Poisson, bivariate geometric, and trinomial distributions). We focus on the statistical estimation of the mean vectors associated with such offspring probability distributions. By considering the Bayesian statistical methodology, estimators are derived. A proposal to assess the reliability of the two-sex model is included. As illustration, a simulated study contextualized in Labord’s chameleons populations is presented and a comparative analysis among the offspring distributions considered is discussed. To this purpose, the necessary statistical software is developed.

Keywords: Mathematical modeling, Biological species with sexual reproduction, Branching processes, Two-sex processes, Bayesian statistical inference, Bivariate power series distribution family

Pages: 334-342