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Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models. Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978-2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values.