Analytical reference points for age-structured models: Application to data-poor fisheries

Abstract

Analytical solutions for biological reference points are derived in terms of maximum lifetime reproductive rate. This rate can be calculated directly from biological parameters of maturity, fecundity, and natural mortality or a distribution for this rate can be derived from appropriate metadata. Minimal data needs and assumptions for determining stock status are discussed. The derivations lead to a re-parameterization of the common stock-recruit relationships, Beverton-Holt and Ricker, in terms of spawning potential ratio. Often, parameters in stock-recruit relationships are restricted by tight prior distributions or are fixed based on a hypothesized level of stock resilience. Fixing those parameters is equivalent to specifying the biological reference points. An ability to directly calculate reference points from biological data, or a meta-analysis, without need of a full assessment model or fisheries data, makes the method an attractive option for data-poor fisheries. The derivations reveal an explicit link between the biological characteristics of a species and appropriate management. Predicted stock status for a suite of shark species was compared with recent stock assessment results, and the method successfully identified whether each stock was overfished. © 2009 International Council for the Exploration of the Sea.