Reproductive ecology and scientific inference of steepness: a fundamental metric of population dynamics and strategic fisheries management

The relationship between the biomass of reproductively mature individuals (spawning stock) and the resulting offspring added to the population (recruitment), the stock-recruitment relationship, is a fundamental and challenging problem in all of population biology. The steepness of this relationship is commonly defined as the fraction of recruitment from an unfished population obtained when the spawning stock biomass is 20% of its unfished level. Since its introduction about 20 years ago, 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 both unstructured and age-structured models. We show that if one has sufficient information to construct a density-independent population model (maximum per capita productivity and natural mortality for the unstructured case or maximum per capita productivity, natural mortality and schedules of size and maturity at age for the structured model) then one can construct a point estimate for steepness. Thus, steepness cannot be chosen arbitrarily. If one assumes that the survival of recruited individuals fluctuates within populations, it is possible, by considering the early life history, to construct a prior distribution for steepness from this same demographic information. We develop the ideas for both compensatory (Beverton-Holt) and over-compensatory (Ricker) stock-recruitment relationships. We illustrate our ideas with an example concerning bluefin tuna (Thunnus thynnus/orientalis, Scombridae). We show that assuming that steepness is unity when recruitment is considered to be environmentally driven is not biologically consistent, is inconsistent with a precautionary approach, and leads to the wrong scientific inference (which also applies for assigning steepness any other single value).