Historically, the growth of animals has been described by a variety of functions which relate size increase to a unit of time. These functions vary from a straight-line relationship to the more complex asymptotic-type curve. Fish growth is often represented by a function which is asymptotic to some average maximum size the fish will attain. A useful regression formula for representing these curves has three parameters, with a representing the asymptotic value of y. Stevens (1951) showed the utility of this basic curve by writing Gompertz's law, the logistic curve, and Mitscherlich's law in this form. It is also possible to write the growth curves of von Bertalanffy (1938) in this way.

The objective of this paper is to present a useful method for fitting Beverton's (1954) modification of the von Bertalanffy growth-in-length curve, but the method is adaptable to any curve which can be written in the basic form of equation. The tables in the Appendix, and the worked example should provide sufficient information for fitting a von Bertalanffy curve.

In the past, the methods used to fit a von Bertalanffy curve to observed fish length have required inefficient techniques such as guessing-by-eye (von Bertalanffy, 1938) or approximation-through-transformation (Beverton and Holt, 1957; Ricker, 1958). The method presented in this paper is not only easy to use, but is based on the efficient, well-accepted technique of least squares. Under the assumption of normality, the least squares method produces estimates which are equivalent to maximum likelihood estimates.

With computers, other iterative methods or an adaption of the described method may be used to obtain very accurate estimates of the parameters of the von Bertalanffy curve. Stevens (1951) developed an iterative procedure for fitting (1) and Nelder (1961) gives an iterative method for fitting a generalized logistic curve which includes (1) as a special case. Nelder's method does not require the x's to be equally spaced and assumes a constant variance for log y rather than for y. However, the following description and the tables in the Appendix should be useful to workers who do not have access to a computer.

The surf fishing investigation was begun when a need for more knowledge of the most important surf species became apparent.

Discussions held with surf fishermen and biologists familiar with surf fishing conditions, indicated an apparent decline in fishing success. As a first step, a study was made to determine the most important game species in the fishery. A preliminary survey indicated that these were barred surfperch, Amphistichus argenteus, California corbina, Menticirrhus undulatus, spotfin croaker, Roncador stearnsi, yellowfin croaker, Umbrina roncador, and opaleye, Girella nigricans. The latter was not studied by the project because it is more truly a rocky shore dweller than a surf inhabitant.

The essential life histories of the four remaining species (hereafter designated project species) were studied. A voluntary catch record system and a creel census were used to provide information on the relative importance of each and fishing success along the entire southern California coast.

This information was needed before steps could be taken to insure sound management of the resource.

The results of the surf fishing investigation will appear in two separate publications: this bulletin on barred surfperch and a later one on California corbina, and spotfin and yellowfin croakers.

The present paper deals almost exclusively with the barred surfperch, family Embiotocidae, the most important species to the surf fisherman. Barred surfperch range from Bodega Bay, central California, to Santa Rosalia Bay, central Baja California. Although found primarily in or near the breaking surf along sandy beaches they were captured by project personnel in 15 fathoms of water in Santa Monica Bay during June 1957. A trawl boat operator reported that he took large barred surfperch regularly in 40 fathoms off Morro Bay during the winter. Ulrey and Greeley (1928) had previously reported one trawled from 28 fathoms in Santa Monica Bay.

Objective

Design

Results

Conclusions