Likelihood methods for the von Bertalanffy growth curve

Abstract

Likelihood methods for the von Bertalanffy growth curve are examined under the assumption of independent, normally distributed errors. The following are examined: determining the best method of estimation, relationships between methods of estimation , failure of assumptions , constructing confidence regions, and applying likelihood ratio tests. An example is presented illustrating many of the methods discussed in theory. The paper may be viewed as an application of classic nonlinear least squares methods to the von Bertalanffy curve. As such, the concepts discussed are generally applicable and the paper may serve as an introduction to nonlinear least squares. Since the application of the von Bertalanffy (1938) growth curve by Beverton and Holt (1957) to the yield per recruit problem, this curve has been widely used in fisheries biology. The original curve has been generalized (Richards 1959; Chapman 1961). However, this paper will not deal with the more general Chapman-Richards growth curve. Nor will it deal with the biological motivation for these curves which have been discussed by the cited authors. Instead , I confine my study to the classic von Bertalanffy curve and examine what appears to be reasonable methods for the statistical treatment of data.