Bayesian Dynami Modeling of Sto k - Re ruitmentRelationships

Assessing the relationship between spawning sto k size and the resulting number of adult o spring (re ruitment) is one of the most fundamental issues in sheries sto k assessment and an important ornerstone for management de isions on harvest poli ies in many sheries. This paper proposes a Bayesian state-spa e model for tting sto kre ruitment urves. This approa h eliminates at least two of the four major problems en ountered in traditional sto k-re ruitment analyses, that of "errors-in-variables bias" and "time-series bias". The state-spa e model takes the temporal dependen ies of the observations into a ount through a onditional modeling of the observations, given unknown states, and spe i ation of Markovian transition of states. Both pro ess and observation errors are expli itly aptured in the state-spa e model and quanti ed through posterior distributions of the parameters via the Bayesian paradigm. Beyond bias elimination, this approa h is apable of quantifying fundamental un ertainties in parameter estimates and risks of management poli ies. Problems with posterior omputations are over ome using Metropolis-Hastings-within-Gibbs sampling. This novel Bayesian state-spa e approa h to sto k-re ruitment analysis is illustrated using a dataset on Fraser River pink salmon. The Ri ker urve is employed to des ribe the dependen e of re ruitment on the spawning sto k size. The state-spa e model is implemented using the readily available software pa kage BUGS.