Analyzing catch-effort data by means of the Kalman filter

A method of analyzing catch-effort data that uses linear statistical theory, but that at the same time maintains a degree of biological realism, is described and applied to catch-effort data for two fisheries. The method is based on a linear state-space model for the evolution of an unobservable state variable, the natural logarithm of the stock biomass. An observable proxy for the state is the logarithm of catch per unit effort. Randomness can be present both in the stock dynamics and in the process of catching fish. In addition, both uncertainty and the possibility of convexity or concavity (hyperdepletion or hyperstability) in the relationship betwen stock abundance and catch per unit effort are included. The stock dynamics are modelled by a power law (log-linear) relationship between escapement and returning stock, with multiplicative log-normal noise. Maximum likelihood is used to estimate model parameters, with the Kalman filter being employed to generate the likelihood function. The method can easily be extended to include other assessments (besides catch per unit effort) of stock abundance. When only catch-effort data are available it is recommended that the primary use of the methodology be for predictions of catch per unit effort.