The regression of age with size,a neglected aspect of growth. ∗

Abstract

Growth, always an attractive study, has of recent years received the attention of several distinct types of workers who have amassed much data for man, for some domesticated animals of economic importance, for the ever-useful white rat and guinea pig, and for a very few invertebrates. Almost invariably the results have been presented as average weights or lengths at stated ages. Thus presented, the growth data of most animals agree in certain general features. There is an early period of rapid growth which gradually slackens with age. In some forms growth continues, though at a very reduced rate, throughout life; in others, notably in man and birds, growth completely ceases for a long period of adult life. This is followed by a period of declining size.

A graph constructed from these values shows the average length (or weight) for any age. Recently while working on the growth of the razor clam, a bivalve of considerable commercial value, which is in need of protective legislation, a growth curve of this kind was used in studying the possible effects of different proposed legal sizes, and, as often happens in work of this sort, it became desirable to determine the average age of clams of different lengths. At first it would appear that the same graph contained these values if the process of reading were merely reversed. Is such a process correct?

The correlation between age and weight or length is nonlinear; the correlation ratio, as usually calculated, is very high, often exceeding 0.9. As is well known in ordinary linear correlations, the line of regression of x on y is not the same as that of y on x, though with correlations above 0.9 the difference is not great.