Using reproductive value to evaluate surplus production models for sharks

The data limitations common to shark populations have led to the use of surplus production models for the stock assessment of these species. This is despite their generally long life spans and late ages of maturity, traits that suggest their dynamics could be better described by age-structured models. Identification of factors that influence the fit of surplus production models will improve understanding of the limitations and the appropriate uses of these models, and can guide the allocation of resources for data collection. The correspondence between the functions for weight and for reproductive value is proposed as such a factor. This proposition is tested by a simulation procedure that fit a Schaefer model to biomass indices generated from a density-dependent, age-structured matrix model. Greater correspondence between weight and reproductive value is found to reduce the bias and variability of the Schaefer model estimates of virgin biomass under the condition that the biomass index is a measure of all ages in the population. A generalized linear model applied to the simulation results is used to compare the influence of several factors on the fit of the Schaefer model. The use of surplus production models to describe the dynamics of shark populations is discussed in general.