Estimating stock-recruitment steepness from life history information: A case study of north Pacific bluefin tuna, Thunnus orientalis

The relationship between spawning stock and the resulting offspring added to the population (recruitment) is a fundamental research problem in fisheries science. The steepness of the stock-recruitment relationship is commonly defined as the fraction of unfished recruitment obtained when spawning biomass is 20% of its unfished level. Steepness has become widely used in fishery management, where it is usually treated as a statistical quantity. Here, we investigate the reproductive ecology of steepness, using biomass dynamics and age-structured models with compensatory recruitment dynamics. We show that if one has sufficient life history information to construct a density-independent population model then one can derive an associated estimate of steepness. Thus, steepness cannot be chosen arbitrarily. Given that survival of recruited individuals fluctuates randomly within a stock, a prior distribution for steepness can be estimated using Monte Carlo simulation and information about early life history survival and demographic parameters. We apply our approach to estimate a Bayesian prior distribution for steepness of North Pacific bluefin tuna (Thunnus orientalis) and develop an extension for depensatory recruitment dynamics. We show that assuming that steepness is unity when recruitment is considered to be environmentally driven is not biologically consistent and leads to the wrong scientific inference.