Fitting of nonlinear Schaefer model

Abstract

Nonlinear Schaefer model is extensively used to obtain maximum sustainable yield and corresponding optimum fishing effort. One reason for its widespread use is that mere knowledge of catch and effort time-series data, which is readily
available for most fisheries, is sufficient to apply this model. Nonlinear estimation procedures, like Levenberg-Marquardt method are employed for fitting purposes as the inherent relationship is nonlinear. However, if the parameters of this model are replaced by ‘expected-value’ parameters, the resulting form, as a pleasant surprise, reduces to an exact linear form. Thus the nonlinear Schaefer model can be fitted easily by using “Multiple linear regression†technique. The procedure is illustrated on some shrimps catch - effort data.