A new graphic method of describing the growth of animals.

TLDR: Growth curves, when conventionally plotted as length on age, are difficult to compare and classify; the usual mathematical methods of fitting them, such as the logistic and the Gompertz are rather laborious and incon venient for application to large numbers of individuals.

Abstract: Growth curves, when conventionally plotted as length on age, are difficult to compare and classify. Moreover, the usual mathematical methods of fitting them, such as, the logistic and the Gompertz are rather laborious and incon venient for application to large numbers of individuals. Fortunately, for many purposes, it is unnecessary to describe the whole growth curve; for the part below the inflection point is completed early and the part above the inflection point—the “? self-inhibiting― phase, covers the period of life when differences in growth are likely to be most striking. That phase of the growth curve can be appropriately represented by a straight line, the charac teristics of which can be treated statistically, by the following graphic method: Using arithmetic graph paper, with body length represented along both the x axis and along the y axis, plot length at ages 1, 2, 3, 4, 5@ n on the x axis against length at ages 2, 3, 4, 5, 6. n + 1, respectively, on the y axis. For several species on which I have found published length data, these points fall along a straight line. This line can be regarded as a sort of transformation of the usual growth curve, and in the following discussion I will call it that. The nine examples given in Figures 1—3are based on average lengths of large samples. When lengths of individual specimens are plotted by this method, a straight-line relationship is still obvious, though the points deviate more widely from the linethan when averages are used. These deviationsdoubtless result from several causes, among which random variations in environmental experience and errors of observation readily suggest themselves. For a few species the published growth data failed to produce a straight line. In these cases, the course of growth may differ from that in other animals; or the observed anomalies may reflect some artifactual effect in the data. Among those species for which this “? transformation― results in a straight line, the growth increments corresponding to equal time intervals, for example, be tween years of age (12 —? 11,13 —? 12,14 —? i@, @l,—? i@), have the following inter relations; where 1,, refers to the length at any given age, i.e., at the end of any given time interval :2