Some explorations of the life history ratios to describe length composition, spawning-per-recruit, and the spawning potential ratio

Evaluating the status of data-poor fish stocks is often limited by incomplete knowledge of the basic life history parameters: the natural mortality rate (M), the von Bertalanffy growth parameters (L₁ and k), and the length at maturity (L_m). A common approach to estimate these individual parameters has been to use the Beverton–Holt life history invariants, the ratios M/k and L_m/L₁, especially for estimating M. In this study, we assumed no knowledge of the individual parameters, and explored how the information on life history strategy contained in these ratios can be applied to assessing data-poor stocks. We developed analytical models to develop a relationship between M/k and the von Bertalanffy growth curve, and demonstrate the link between the life history ratios and yield- and spawning-per-recruit. We further developed the previously recognized relationship between M/k and yield- and spawning-per-recruit by using information on L_m/L₁, knife-edge selectivity (L_c/L₁), and the ratio of fishing to natural mortality (F/M), to demonstrate the link between an exploited stock’s expected length composition, and its spawning potential ratio (SPR), an internationally recognized measurement of stock status. Variation in length-at-age and logistic selectivity patterns were incorporated in the model to demonstrate how SPR can be calculated from the observed size composition of the catch; an advance which has potential as a cost-effective method for assessing data-poor stocks. A companion paper investigates the effects of deviations in the main assumptions of the model on the application of the analytical models developed in this study as a cost-effective method for stock assessment.