The quantitative investigation of the vertebrate brain and the applicability of allometric formulae to its study

Abstract

A new method for the estimation of the parameters in the allometric equation is described whereby both the estimates and their standard errors are determined in a simple manner. The fitting of curves to biological data is discussed, and the lack of equivalence between a form containing exponential parameters and its logarithmic tranformation shown. The classical method is extended to apply to this situation. The Dubois-Lapicque-Brummelkamp theory is discussed in the light of this work and shown to be untenable. In particular, there is no basis for the view that, if the form y = bx α is fitted to the brain and body weights of vertebrates, the interspecific value of α is 5/9 and its intraspecific value is 0·26. A final maximum brain weight is demonstrated for some species which is independent of the adult body weight. The analysis of mental development in terms of 'cephalization constants’ is not in accord­ance with the facts, and a much deeper analysis of the comparative anatomy involved must be made if a quantitative study of the ontogenetic and phylogenetic development of the brain is to be achieved.