Estimation of growth and mortality parameters from size frequency distributions lacking age patterns : the red sea urchin (Strongylocentrotus franciscanus) as an example

We present a maximum likelihood procedure for estimating population growth and mortality parameters by simultaneously analysing size frequency and growth increment data. The model uses von Bertalanffy growth with variability among individuals in the two parameters that determine growth rate, and size-dependent mortality. Analyzing growth increments together with size frequencies reduces the statistical confounding of the natural mortality rate with von Bertalanffy's K parameter. We assume steady-state (constant recruitment) conditions for the size distributions; hence the method does not depend on age modes in the distribution. We evaluate the bias and precision of estimates obtained for growth-dominated distributions typical of the red sea urchin ( Strongylocentrotus franciscanus ) in northern California, although the method and its evaluation could be applied as easily to mortality-dominated or bimodal distributions. The method provides good estimates with sample sizes as low as 200 individuals in a size distribution and 30 growth increments. Results are robust to random variabilit y in recruitment, measurement error, and sampling selectivity up to the size where about one third of the distribution is affecte d. Estimation of the fishing mortality rate could require size distributions from both an unharvested and a harvested population. Estimates of growth and mortality rates depend critically on reliable growth data. Resume : Nous presentons une methode du maximum de vraisemblance servant a estimer les parametres de croissance et de mortalite d'une population par l'analyse simultanee de donnees sur les frequences de taille et les increments de croissance. Le modele fait appel a la fonction de croissance de von Bertalanffy avec variabilite entre les individus dans les deux parametres qui determinent le taux de croissance, et a la mortalite dependante de la taille. Le fait d'analyser les increments de croissan ce en combinaison avec les frequences de taille reduit la possibilite de confondre statistiquement le taux de mortalite naturelle ave le parametre K de von Bertalanffy. Nous supposons des conditions stables (recrutement constant) pour la distribution des tailles, de sorte que la methode ne depend pas des modes d'âge dans la distribution. Nous evaluons le biais et la precision des

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