Title: Stochastic modeling in dynamical populations through two-sex branching processes: Inferential and computational results
Authors: Manuel Molina - University of Extremadura (Spain) [presenting]
Manuel Mota - University of Extremadura (Spain)
Alfonso Ramos - University of Extremadura (Spain)
Abstract: In the general context of stochastic modeling, branching processes are appropriate mathematical models to describe the probabilistic evolution of dynamical systems. They are an active research area of theoretical and practical interest with applicability to such fields as biology, demography, epidemiology, genetics, population dynamics, and others. Branching processes have especially played a major role in modeling the demographic dynamics of biological populations whose size evolves over time due to random births and deaths. In particular, in order to describe the dynamics of biological populations with sexual reproduction, several classes of two-sex branching processes have been introduced. We will focus the attention on the class of two-sex branching processes where several mating strategies and a variety of reproductive possibilities are considered. It is also assumed the most realistic situation which both phases, mating and reproduction, could be influenced by the numbers of females and males in the population. By considering the most general non-parametric statistical setting, several inferential and computational questions about the most informative reproductive parameters included in the mathematical model are investigated. As an illustration, the proposed methodology is applied to describe the demographic dynamics of some salmonid populations.