Using demographic methods to construct Bayesian priors for the intrinsic rate of increase in the Schaefer model and implications for stock rebuilding

Even though Bayesian methods can provide statistically rigorous assessments of the biological status of fish - eries resources, uninformative data (e.g., declining catch rate series with little variation in fishing effort) can produce highly imprecise parameter estimates. This can be counteracted with the use of informative Bayesian prior distributions (priors) for model parameters. We develop priors for the intrinsic rate of increase ( r) in the Schaefer surplus production model using demographic methods and illustrate the utility of this with an application to large coastal sharks in the Atlantic. In 1996, a U.S. stock assessment obtained a point estimate for r of 0.26. For such long-lived and low-fecund organisms, this could potentially be too high. Yet it was used to predict that within about 10 years, a 50% reduction in the 1995 catch level should result in >50% chance of increasing the population to the abundance required to produce maximum sustainable yield. In contrast, a Bayesian assessment that used demographic analysis to construct a prior for r with a median of 0.07 and coefficient of variation (CV) of 0.7 indicated that within 30 years, this policy would have only a very small chance of increasing the population to maximum sustainable yield. Resume : Bien que les techniques bayesiennes puissent fournir des estimations statistiquement rigoureuses du statut biologique des ressources halieuthiques, des donnees pauvres en information (e.g., un serie de taux de capture associee a un effort de peche peu variable) peuvent produire des estimations de parametres tres imprecises. Ce probleme peut etre contrecarre par l'utilisation de distributions bayesiennes a priori (priors) pour les parametres du modele. Nous avons developpe des distributions a priori pour le taux intrinseque de croissance ( r) dans le modele de production excedentaire de Schaefer a l'aide de methodes demographiques et nous illustrons l'utilite de cette approche en l'appliquant aux grands requins cotiers de l'Atlantique. En 1996, une evaluation de stock faite aux Etats-Unis a donne une estimation ponctuelle de r de 0,26. Pour des organismes a grande longevite et a faible fecondite, cette valeur est potentiellement trop elevee. Neanmoins, elle a servi a predire que, dans a peu pres 10 ans, une reduction de 50% dans le taux de capture de 1995 aurait pour consequence une probabilite de >50% de faire croitre la population suffisam- ment pour atteindre le niveau de rendement maximal soutenu. En revanche, une estimation de type bayesien qui a utilise une analyse demographique pour etablir une distribution a priori de r avec une mediane de 0,07 et un coefficient de variation de 0,7 indique qu'une telle politique de capture n'aurait, au bout de 30 ans, qu'une tres faible probabilite de permettre a la population d'atteindre le rendement maximal soutenu. (Traduit par la Redaction) Perspectives 1890

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