Fitting of Fox Model with Autoregressive of Order One Using Expected Value Parameters

Abstract

Fishing plans can be expressed in terms of surplus production. Although Schaefer model is most widely used surplus production model, it provides a curve of symmetrical parabola, which need not necessarily be always true to the natural phenomena since maximum sustainable yield (MSY) may vary considerably depending on temporal and spatial changes in the ecosystem. However, in Fox model, catch increases asymmetrically towards the total biomass with increasing effort, which is more realistic than Schaefer model, and hence biologists prefer to Fox model. Further, when we are dealing with catch-effort fisheries data, which are observed over continuous time periods, the data points are generally correlated among themselves. Prajneshu and Ravichandran (2003) emphasized the importance of reparameterization of the parameters for fitting of nonlinear Fox model in fisheries to reduce large correlations among the parameter estimates. Thus, by examining the presence of autocorrelation in the observations, in the present study a method of fitting a Fox model with serially correlated error structure using expected value parameters is proposed which is illustrated with an example, considering the catch-effort data observed from Gobind sagar reservoir, India