Combining a Length-Based Mortality Model with a Surplus Production Model

In a data-limited situation, integrating disparate data types can be valuable for a stock assessment. We present a model for integrating three data types: mean length observations, catch, and effort to estimate mortality rates, biomass, and biological reference points.  The addition of effort data to the mean length observations in the Gedamke-Hoenig mortality estimator can be used to estimate the catchability coefficient and natural mortality rate; the catchability coefficient scales the fishing effort to provide an annual estimate of fishing mortality.  With catch and effort data, the surplus production model provides estimates of fishing mortality and reference points for maximum sustainable yield.  The common parameter, the catchability coefficient, allows the two models to be combined and the three data types are used in one likelihood framework.  Model output from the combined model includes those from the production model and an estimate of natural mortality.  The inclusion of mean length data obtained from biological sampling may be helpful when catch and effort data alone do not provide enough contrast for convergence in the production model.  The properties of the combined model are explored through simulation and an application to western Atlantic skipjack tuna (Katsuwonus pelamis) is presented as a case study.