Bayesian inference and data cloning in the calibration of population projection matrices

ABSTRACT

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.

KEYWORDS:

• Age-structured population
• Bayesian MCMC algorithm
• Data cloning
• Leslie matrix
• Projection matrices

MATHEMATICS SUBJECT CLASSIFICATION:

• 92D25
• 62F15

Acknowledgments

The authors thank the referee for all his/her helpful comments that improved the article. This research has been partially supported by grant MTM2010-17366 (first author), by grant MTM2010-17323 (second author), and by grant MTM2011-23864 (third author).