Some Contributions to the Class of Branching Processes with Several Mating and Reproduction Strategies

Abstract

This work deals with mathematical modeling of dynamical systems. We consider a class of two-sex branching processes with several mating and reproduction strategies. We provide some probabilistic and statistical contributions. We deduce general expressions for the probability generating functions underlying the probability model, we derive some properties concerning the behavior of the states of the process and we determine estimates for the offspring mean vectors governing the reproduction phase. Furthermore, we extend the two-sex model considering immigration of female and male individuals from external populations. The results are illustrated through simulated examples. The investigated two-sex models are of particular interest to mathematically describe the population dynamics of biological species with a single reproductive episode before dying (semalparous species).

Keywords

• mathematical modeling
• branching models
• two-sex models
• models with immigration
• population dynamics