Vertebral size‐at‐age heterogeneity in gummy shark harvested off southern Australia

Abstract

Stochastic parametrization of growth heterogeneity was applied to investigate the distribution of vertebral band radius‐at‐age in three populations of gummy shark Mustelus antarcticus Günther harvested with very different fishing effort and different mesh‐sizes of gillnet. Three examples of four parameter growth models were developed where the random von Bertalanffy growth rate K is represented alternatively by three positive distributions to avoid negative tails in size‐at‐age distribution. Models with gamma and log‐normal distributions of K fitted the data equally well and both fitted better than a model with the Weibull distribution. Various results are presented from the model developed with the gamma distribution of K. Heterogeneity in vertebral growth is presented as a series of quantiles of distribution of band radius‐at‐age. Probability density functions of band radius are presented for sharks at four selected ages, and cross‐sections of these probability densities against age are presented for three selected values of band radius. Heterogeneity of growth rate K in a population is presented as tables of 10% quantiles and as graphs of probability densities. The differences in the patterns of vertebral growth for male and female sharks separately, between Bass Strait during 1973–1976, Bass Strait during 1986–1987 and South Australia during 1986–1987 are generally consistent with those determined from shark length‐at‐age in other published studies. However, the stochastic modelling approach adopted in the present study avoids having to make any assumptions about vertebral growth patterns of individual sharks and embraces heterogeneity in vertebral radius‐at‐age in the models which allows for better evaluation of alternative hypotheses for explaining the observed differences in growth patterns.