How robust are Bayesian posterior inferences based on a Ricker model with regards to measurement errors and prior assumptions about parameters?

Abstract

We present a Bayesian approach of a Ricker stock-recruitment (S/R) analysis accounting for measurement errors on S/R data. We assess the sensitivity of posterior inferences to (i) the choice of Ricker model parameterizations, with special regards to management-related ones, and (ii) prior parameter distributions. Closed forms for Ricker parameter posterior distributions exist given S/R data known without error. We use this property to develop a procedure based on the Rao-Blackwell formula. This procedure achieves integration of measurement errors by averaging these closed forms over possible S/R data sets sampled from distributions derived from a stochastic model relating field data to the S and R variables. High-quality Bayesian estimates are obtained. The analysis of the influence of different parameterizations and of the priors is made easier. We illustrate our methodological approach by a case study of Atlantic salmon (Salmo salar). Posterior distributions for S and R are computed from a mark-recapture stochastic model. Ignoring measurement errors underestimates parameter uncertainty and overestimates both stock productivity and density dependence. We warn against using management-related parameterizations because it makes the strong prior assumption of long-term sustainability of stocks. Posterior inferences are sensitive to the choice of prior. The use of informative priors as a remedy is discussed.Résumé : Nous présentons une analyse Bayesienne d'un modèle stock-recrutement (S/R) de Ricker qui intègre les erreurs de mesure sur les données S/R. Nous étudions la sensibilité des inférences a posteriori (i) à différentes paramétrisations du modèle de Ricker, notamment à celles reliées à la gestion, et (ii) aux distributions a priori sur les paramètres. Conditionnellement à une série S/R connue sans erreur, les distributions a posteriori des paramètres peuvent s'exprimer analytiquement. Nous développons une procédure de Rao-Blackwell qui s'appuie sur cette propriété. Les erreurs de mesure sont intégrées en moyennant ces formes analytiques sur un échantillon de séries S/R tirées dans leur distribution a posteriori issue d'un modèle stochastique reliant les données de terrain aux variables S et R. Les estimateurs bayesiens obtenus sont de grande qualité et l'étude de sensibilité aux choix des différentes paramétrisations et des priors est facilitée. Nous illustrons notre approche méthodologique par un cas d'étude sur le Saumon atlantique (Salmo salar). Les distributions a posteriori de S et R sont issues d'un modèle probabiliste de capture-recapture. Ignorer les erreurs de mesure sous-estime l'incertitude et surestime la productivité du stock et la densité dépendance. Nous ne recommandons pas l'utilisation systématique des paramètres reliés à la gestion car cela nécessite l'hypothèse a priori que le stock peut se renouveler seul. Les inférences a posteriori sont sensibles au choix des priors. L'utilisation de priors informatifs pourrait permettre d'y remédier.

Interannual changes in recruitment of the Atlantic salmon (Salmo salar) population in the River Oir (Lower Normandy, France): relationships with spawners and in-stream habitat

“…A long series of data (20 years) has been collected on ecological characteristics, as well as on the distribution and abundance of salmon within the river. Previous papers utilizing these data focused on analysing the stock-recruitment relationship, and showed that average recruitment and smolt production in the River Oir was relatively low compared with northern European and Canadian rivers Rivot et al, 2001Rivot et al, , 2004. Moreover, the research facilitated the development of tools for decision analysis related to the sustainable management of salmon fisheries at a regional level (Prévost and Porcher, 1996;Rivot et al, 2001).…”

“…Previous papers utilizing these data focused on analysing the stock-recruitment relationship, and showed that average recruitment and smolt production in the River Oir was relatively low compared with northern European and Canadian rivers Rivot et al, 2001Rivot et al, , 2004. Moreover, the research facilitated the development of tools for decision analysis related to the sustainable management of salmon fisheries at a regional level (Prévost and Porcher, 1996;Rivot et al, 2001). Here, we analyse the data series with two main objectives: (i) to evaluate the river's salmon production and the status of the population; (ii) to analyse the evolution of the parameters of Atlantic salmon population dynamics in a stream in relation to variance in the environment, including especially the impact of anthropogenic activities in the drainage basin.…”

The reverse effects of random perturbation on discrete systems for single and multiple population models

“…However, in this study we only consider the simplest case, in which perturbation is a random positive constant. Although such type of perturbation exists in real world [33,34] , there are many different types of perturbations which could exist, such as the density dependent [35,36] and independent normal distributions [37][38][39] . Moreover, different types of perturbations could have different biological meanings and also may result in different dynamic behavior for population models.…”

Forecasting spatially structured populations: the role of dispersal and scale

“…And certainly it is the case that the spectrum of dynamical behaviours emanating from this model can be found in nature (Turchin and Taylor, 1992;Dennis and Taper, 1994;Cushing et al, 1996;Cushing et al, 2003). There are abundant applications of this model in fisheries and wildlife (Paulik and Bayliff, 1967;McCarthy, 1996;Elliott et al, 1997;Saitoh et al, 1997;Myers and Mertz, 1998;Halls et al, 2000;Chen and Irvine, 2001;Rivot et al, 2001;Taper and Gogan, 2002;McCarthy et al, 2003;Travis, 2003;Zheng and Kruse, 2003).…”