An alternative methodology for fitting selectivity curves to pre-defined distributions

A non-linear least-squares methodology for simultaneously estimating parameters of selectivity curves with a pre-defined functional form, across size classes and mesh sizes, using catch size frequency distributions, was developed based on the model of Kirkwood and Walker [Kirkwood, G.P., Walker, T.L, 1986. Gill net selectivities for gummy shark, Mustelus antarcticus Gunther, taken in south-eastern Australian waters. Aust. J. Mar. Freshw. Res. 37, 689-697] and [Wulff, A., 1986. Mathematical model for selectivity of gill nets. Arch. Fish Wiss. 37, 101-106]. Observed catches of fish of size class I in mesh m are modeled as a function of the estimated numbers of fish of that size class in the population and the corresponding selectivities. A comparison was made with the maximum likelihood methodology of [Kirkwood, G.P., Walker, T.I., 1986. Gill net selectivities for gummy shark, Mustelus antarcticus Gunther, taken in south-eastern Australian waters. Aust. J. Mar. Freshw. Res. 37, 689-697] and [Wulff, A., 1986. Mathematical model for selectivity of gill nets. Arch. Fish Wiss; 37, 101-106], using simulated catch data with known selectivity curve parameters, and two published data sets. The estimated parameters and selectivity curves were generally consistent for both methods, with smaller standard errors for parameters estimated by non-linear least-squares. The proposed methodology is a useful and accessible alternative which can be used to model selectivity in situations where the parameters of a pre-defined model can be assumed to be functions of gear size; facilitating statistical evaluation of different models and of goodness of fit. (C) 1998 Elsevier Science B.V.