Time series analysis of catch-at-length data

Abstract

Solutions of differential equations describing the variation, caused by growth, fishing, and natural mortality of the number of fish in a length interval are more complicated than the equations used in catch-at-age analysis. The numerical estimation presented in this paper was based on a simplified equation. Growth is described by a parametric model. Fishing mortality rates are defined as a multivariate stochastic process. The possibility of estimating growth and fishing mortality rates from catch-at-length data was investigated by simulated data, generated in accordance with exact differential equations, and by actual data where catch-at-age data were also available. Unknown parameters, stocks and fishing mortality rates were obtained from the Kalman filter. The accuracy of the estimates was lower than with catch-at-age data of similar variability. In catch-at-length analyses the improvement in estimates from earlier years obtained by backward calculation was smaller than in catch-at-age analyses. Estimation of irregular variations in growth was too inaccurate to have practical value.