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The Quadratic Relation in Differential Growth

Naturevolume 180page1293 (1957) | Download Citation



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.

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  1. 1

    Williams, G., and Needham, A. E., Proc. Zool. Soc., A, 108, 539 (1938).

  2. 2

    Huxley, J. S., Needham, J., and Lerner, I. M., Nature, 148, 225 (1941).

  3. 3

    Needham, A. E., Proc. Roy. Soc., B, 137, 115 (1950).

  4. 4

    Fowden, L., New Biol., 23, 65 (1957).

  5. 5

    Medawar, P. B., Proc. Roy. Soc., B, 132, 133 (1944).

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  1. Dept. of Zoology and Comparative Anatomy, University Museum, Oxford

    • A. E. NEEDHAM


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