Multiphasic growth and allometry.

Abstract

Multiphasic growth assumes increase in body weight, or in other body measures, to be a result of more than one growth phase. Therefore, the concept of allometry can be extended from relation between body measures to relation between phases of growth. For two phases of growth, body weight (W) and tail length (L) can be partitioned into W1 + W2 and L1 + L2. Here, W1 and W2 correspond to phases 1 and 2 of weight and L1 and L2 to phases 1 and 2 of length, where each phase is described by a logistic function. Diphasic functions were applied to growth curves for body weight and for tail length of mice that were progeny of a transgenic male mated to random-bred NMRI females. A group of 20 female and male mice with high body weight at week 12, assumed to be transgenic, and a group of 20 with normal body weight, assumed to be non-transgenic, were selected for comparison. Body weight and tail length were measured about weekly from 3 to 26 weeks of age. Allometric relations between phases for weight (W1 and W2) and tail length (L1 and L2) are presented using predicted values based on estimated parameters of the diphasic growth functions. Differences between ages at maximum gain and ratios of duration of phases were analyzed. Growth in second phase of body weight appeared to be unrelated to growth in first phase of body weight and unrelated to growth in tail length. Growth in each phase of tail length appeared to be close to a simple allometric relation with growth in first phase of body weight. It is now feasible to study multiphasic allometric relations of growth between phases of one body measure and between phases of different body measures by comparing estimates of parameters of the multiphasic growth function.