Fishery simulation model for sharks applied to the Gummy Shark, Mustelus antarcticus Gunther, from Southern Australian waters

Abstract

A dynamic pool simulation model is derived and applied to the gummy shark stock of the southern shark fishery. Inputs to the model are fishing effort reported by fishers for hooks and for gill-nets with mesh sizes of 6 inches (152 mm), 7 inches (178 mm) and 8 inches (203 mm) along with estimates for growth, natural mortality, catchability, hook and gill-net mesh selectivity, size at maturity and fecundity of females, sex ratio at birth, and length-weight relationships. Growth is described by the von Bertalanffy equation; hook selectivity is constant with length for sharks recruited to the fishery; gill-net selectivity is based on the probability density distribution of the gamma function where selectivity varies with the mesh size of the gill-nets and the length of the sharks; number of births is related to the proportion of females mature at each length, and the relationship between number of births and maternal weight is linear; parturition is annual and time is standardized so that parturition occurs at the beginning of each year; sex ratio at birth is based on observations of a 1: 1 sex ratio of embryos; and allometric weight-length is based on the power curve. Natural mortality of recruits, catchability, reproduction and growth parameters are held constant, but density-dependent natural mortality of prerecruits is varied in proportion to stock abundance. The model is used to simulate effects of historical longline fishing effort and gill-net fishing effort for each mesh size on stock biomass, numbers of sharks in the stock, and numbers of births. The performance of the model is evaluated by comparing simulated annual catches and the simulated mean weight of sharks captured with annual catches reported by the fishers and the mean weight of sharks sampled in commercial landings. Uncertainties surrounding estimates of some of the parameters are discussed. Notwithstanding its shortcomings, the model indicates that the stock of gummy shark has been severely reduced and is in danger of further depletion unless immediate action is taken to reduce the commercial catch.