Comparison of growth functions within and between lines of mice selected for large and small body weight

Abstract

Several criteria have been suggested for comparing different nonlinear growth functions to determine which function gives the best quantitative description of a given set of observed sigmoid growth curves. These criteria were then used to compare the logistic, Gompertz and Bertalanffy functions within and among lines of mice: a control line (C 1) and lines selected for large (H 6) and small (L 6) body weight at six weeks of age.A general comparison of the three growth functions was based on the differences in residual variances of the respective functions fitted to the growth data of individual mice. Since the three functions differ primarily in the fixed proportion of the asymptotic weight at which the inflexion point occurs, the growth function which will provide the minimum residual variance among the three considered is the one which most closely approximates the observed proportion. The results of this comparison indicated that the logistic function gave the best fit for both sexes of the H 6 and C 1 lines. While no significant differences in residual variances were evident in L 6 males, the Bertalanffy function had the smallest residual variance in L 6 females.The four derived traits of each growth function analyzed individually were the asymptote (A), age at inflexion (t (*)), rate at which a logarithmic function of body weight changes with time (k) and mean absolute growth rate with respect to body weight increase (v). The coefficient of variation among individuals within full-sib families was used to compare the relative variability of the analogous traits estimated from the three growth functions. The coefficients of variation of A, t (*) and k calculated from the logistic function were significantly (P < .01) smaller than those from both the Gompertz and Bertalanffy functions in all three lines, while there were no significant differences in the relative variability of v among the three lines. The genetic and phenotypic correlations between the analogous traits estimated from two different growth functions were sufficiently high in most cases to conclude that the same trait was being measured by the three growth functions. Each derived trait was analyzed for variation in lines, sexes, seasons and respective interactions. The sources of variation generally exhibited similar levels of significance for the analogous traits estimated by the three functions, although a few exceptions were found. These results suggest that although the logistic function provided the best description of the growth data, the same general conclusions about differences within and among the three lines would have been reached with any of the three functions. The four derived traits of the logistic curve were used to describe quantitatively the differences in growth among the H 6, L 6 and C 1 lines.