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

Abstract

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 variability in recruitment, measurement error, and sampling selectivity up to the size where about one third of the distribution is affected. 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.Résumé : Nous présentons une méthode du maximum de vraisemblance servant à estimer les paramètres de croissance et de mortalité d'une population par l'analyse simultanée de données sur les fréquences de taille et les incréments de croissance. Le modèle fait appel à la fonction de croissance de von Bertalanffy avec variabilité entre les individus dans les deux paramètres qui déterminent le taux de croissance, et à la mortalité dépendante de la taille. Le fait d'analyser les incréments de croissance en combinaison avec les fréquences de taille réduit la possibilité de confondre statistiquement le taux de mortalité naturelle ave le paramètre K de von Bertalanffy. Nous supposons des conditions stables (recrutement constant) pour la distribution des tailles, de sorte que la méthode ne dépend pas des modes d'âge dans la distribution. Nous évaluons le biais et la précision des estimations obtenues pour des distributions ayant la croissance comme facteur dominant, typiques de l'oursin rouge (Strongylocentrotus franciscanus) dans le nord de la Californie, mais la méthode et son évaluation pourraient être appliquées avec autant de facilité aux distributions dont le facteur dominant est la mortalité ou aux distributions bimodales. La méthode fournit de bonnes estimations avec des échantillons de 200 individus seulement pour la distribution des tailles et avec 30 incréments de croissance. Les résultats sont robustes par rapport à la variabilité aléatoire du recrutement, aux erreurs de mesure et à la sélectivité de l'échantillonnage jusqu'à une taille où environ un tiers de la distribution est touché. Pour avoir un...

Alongshore advection and marine reserves: consequences for modeling and management

“…In the absence of fishing, the mean age of individuals in the model was 9.6 yr. Growth of individuals in each subpopulation was governed by a von Bertalanffy equation with Gaussian-distributed variability in maximum size (Smith et al 1998). Beverton-Holt postsettlement density-dependence was included in the model (Beverton & Holt 1957).…”

“…Wing et al 1998), suggesting that even a model of larval dispersal including advection and diffusion might not be sufficient. Larvae are thought to be transported by physical forces that vary on time scales of hours to weeks, producing variability in recruitment rates on similar time scales .…”

“…At short time scales, recruitment appears extremely variable in time and space and has been related to changes in currents occurring shortly before settlement (e.g. Shanks 1986, Wing et al 1998, Shanks et al 2000. At longer time scales, spatial variability in dispersal is more regional than local, and temporal variability might be correlated with long time-scale physical processes, such as El Niño Southern Oscillation or the Pacific Decadal Oscillation (e.g.…”

Reproductive sources and sinks within a sea urchin, Evechinus chloroticus, population of a New Zealand fjord

“…Von Bertalanffy with variable L ∞ : Parameters of the von Bertalanffy growth equation with a maximum likelihood estimate of variance in L ∞ were calculated for each study site using a combination of growth increment and size frequency data by the methods of Smith et al (1998). Because it was determined that size frequency distributions were relatively stable over the growth increment period, we used size frequency distributions representing the sum of 2 sample periods in this analysis.…”

“…The maximum likelihood model used by Smith et al (1998) incorporates Sainsbury's (1980) assumptions on individual variability in growth and includes parameters that allow L ∞ and K to be random variables. The method assumes that populations have steady state recruitment rates and are at stable size distribution, although its results are robust to some departures from these assumptions (Smith et al 1998).…”