Graphical Representation of Growth Gradients

Abstract

GROWTH gradients in animals have been represented by a method described by Huxley¹, based on growth constants, that is, the values of α in the allometry formula², y = bx^a. Huxley¹ has discussed the inadequacy of his graphical method and the formal difficulties of devising a better, but no attempt seems to have been made to overcome these difficulties. It is thought that the simple mathematical considerations below constitute a solution to the formal obstacles in the way of the quantitatively accurate representation of certain types of growth gradient. The gradients referred to here are gradients in heterauxesis³ in which the growth intensities are in the direction of the axis along which the gradient lies. Multiplicative growth in length only is discussed, but similar concepts apply to multiplicative growth in area, volume and weight.