Modelling stochastic fish stock dynamics using Markov Chain Monte Carlo

Abstract

A new age-structured stock dynamics approach including stochastic survival and recruitment processes is developed and implemented. The model is able to analyse detailed sources of information used in standard age-based fish stock assessment such as catch-at-age and effort data from commercial fleets and research surveys. The stock numbers are treated as unobserved variables subject to process errors while the catches are observed variables subject to both sampling and process errors. Results obtained for North Sea plaice using Markov Chain Monte Carlo methods indicate that the process error by far accounts for most of the variation compared to sampling error. Comparison with results from a simpler separable model indicates that the new model provides more precise estimates with fewer parameters.

Estimation of the parameters of fish stock dynamics from catch-at-age data and indices of abundance: can natural and fishing mortality be separated?

“…Similarly, de Valpine and Hilborn (2005) and Dennis et al (2006) fit nonlinear state-space models by a maximum likelihood approach, but without taking into account age structure. The Bayesian approach represents an alternative to the frequentist approach and has been applied increasingly within fisheries in the last decades (e.g., Patterson 1999;Millar and Meyer 2000;Lewy and Nielsen 2003). The Bayesian approach relies on evaluation of the posterior probability distribution P(⌰*Y) of the set of parameters ⌰ given data Y, prior distribution P(⌰) of the parameters, and a likelihood function P(Y*⌰).…”

“…The observations are connected to the population processes through models including error terms, allowing them to be uncertain. It is important to notice that this error in principle can not be interpreted as sampling error alone as it incorporates any deviation caused by misspecification of the functional relationship related to the true dynamical processes (see, for example, Lewy and Nielsen (2003) for a discussion).…”

“…One model class capable of addressing numerous sources of variability is the state-space framework, i.e., the available data (the estimates of catch at age and indices) are noisy observations from a hidden dynamical system (the population). For instance, Gudmundsson (1994) models the fishing mortality as a stochastic process where natural mortality is assumed known and constant, whereas Lewy and Nielsen (2003) assume that stock survival (the sum of natural and fishing mortality) for a given mortality rate is a stochastic process. The variability in fishing mortality is thus confounded with the variability in natural mortality (Lewy and Nielsen 2003).…”

“…For instance, Gudmundsson (1994) models the fishing mortality as a stochastic process where natural mortality is assumed known and constant, whereas Lewy and Nielsen (2003) assume that stock survival (the sum of natural and fishing mortality) for a given mortality rate is a stochastic process. The variability in fishing mortality is thus confounded with the variability in natural mortality (Lewy and Nielsen 2003). In the models of Schnute and Richards (1995) and Millar and Meyer (2000), natural mortality is considered unknown, but the stochastic variations in natural mortality are not separated from the variations in fishing mortality.…”

Estimating catch-at-age by combining data from different sources

“…They have also been used in stock assessments (Hilborn and Lierman 1998;Lewy and Nielsen 2003), estimation of depensation (Lierman and Hilborn 1997), and estimation of biological reference points (Prevost et al 2003).…”