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Title: Estimation of the carrying capacity in branching processes via weighted least square estimation Authors:  Carmen Minuesa Abril - University of Extremadura (Spain) [presenting]
Peter Braunsteins - University of Amsterdam (Netherlands)
Sophie Hautphenne - The University of Melbourne (Australia)
Abstract: In the context of branching processes that describe populations with logistic growth, the purpose is the estimation of their parameters. We focus on the parameter representing the maximum population size of the species that an environment can maintain in view of the available resources, known as the carrying capacity. To this end, we make use of the family of discrete-time population-size-dependent branching processes. In these processes, individuals reproduce independently with an offspring distribution that depends on the current number of individuals in the population. Assuming a parametric framework for the probability laws describing the reproduction, we present some weighted least square estimators of the target parameters. The asymptotic properties, such as consistency and asymptotic normality, of the proposed estimators are illustrated via several examples. We also apply them to estimate the carrying capacity of an endangered population of birds: the black robin.