The Quadratic Relation in Differential Growth

Abstract

IT was shown¹ that the growth in width of the abdomen of the female pea crab, Pinnotheres pisum, did not show simple allometry², but a continuously variable allometric relation, relative to carapace width. For purely empirical purposes a general polynomial relation was fitted to the two measurements³, but the quadratic proved a very good ‘fit’ and it was later pointed out (Reeve, E. C. R., personal communication) that no appreciable improvement was effected by fitting higher powers of the polynomial. It is possible, therefore, that the relation between abdomen-width (y) and carapace-width (x) may be defined, not only adequately but also significantly, by the simple equation y=a + bx + cx², where a, b, c are constants for any particular abdominal segment, and are parameters for the abdomen as a whole³.