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.