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With the purpose of modeling the demographic dynamics of biological species in which different mating and reproduction alternatives are feasible, in Molina et al. (2014) we introduced a new mathematical model based on discrete-time branching processes. Assuming that the reproduction phase is governed by probability distributions belonging to the power series family, some reproductive parameters for such species were estimated. In this work, in a more general statistical context, we generalize this research. By considering observations, u