A Bayesian state-space modelling framework for fitting a salmon stage-structured population dynamic model to multiple time series of field data

Abstract

The Bayesian state-space modelling framework allows us to derive inferences on stochastic stage-structured population dynamics models from multiple series of sequential observations with measurement or sampling errors. A state-space model works from the coupling of two models. The first one mimics the dynamics by conditional Markovian transitions between successive hidden states. The second model describes the observation process with random errors. Statistical inferences on states variables and parameters are easily performed via Bayesian Monte Carlo Markov chains (MCMC) methods. The flexibility of MCMC methods allows us to analyse a wide range of state-space models with non-linear relationships in the dynamic and observation equations, and non-Gaussian error structure just as well. The Bayesian paradigm is efficient for deriving quantitative diagnostics on a probability based rationale. We illustrate the value of this framework by fitting a stage-structured life cycle model for Atlantic salmon ( Salmo salar) to a data set resulting from the survey of the population of the river Oir (Lower Normandy, France) between 1984 and 2001. The system dynamics includes non-linear regulation and has a probabilistic structure accommodating for both the environmental and the demographic stochasticity. The observation model consists in capture-mark-recapture experiments for the evaluation of the runs of downstream migrating juveniles (smolts) and upstream migrating spawners, and random sampling for demographic features. A full Bayesian treatment of the model is carried out by means of Gibbs sampling. Outputs of main interest consist in the joint posterior distribution of all the model parameters and state variables such as the smolt and spawner runs.