Department of Biology, Colorado State University, Fort Collins, CO 80523-1878, USA.
J Exp Biol. 2012 Feb 15;215(Pt 4):569-73. doi: 10.1242/jeb.061739.
The allometric method, which often is attributed to Julian Huxley, entails fitting a straight line to logarithmic transformations of the original bivariate data and then back-transforming the resulting equation to form a power function in the arithmetic scale. Development of the technique was strongly influenced by Huxley's own research on growth by the enlarged 'crusher' claw in male fiddler crabs (Uca pugnax). Huxley reported a discontinuity in the log-log plot of chela mass vs body mass, which he interpreted as an abrupt change in relative growth of the chela at about the time crabs attain sexual maturity. My analysis of Huxley's arithmetic data indicates, however, that the discontinuity was an artifact caused by logarithmic transformation and that dynamics of growth by the crusher claw do not change at any point during development. Arithmetic data are well described by a power function fitted by nonlinear regression but not by one estimated by back-transforming a line fitted to logarithms. This finding and others like it call into question the continued reliance on the allometric method in contemporary research.
传统的比较生长率方法，通常归因于朱利安·赫胥黎，它涉及到对原始双变量数据的对数转换拟合一条直线，然后将得到的方程反变换形成算术尺度上的幂函数。该技术的发展受到赫胥黎自己对雄性招潮蟹（Uca pugnax）增大的“破碎机”爪生长的研究的强烈影响。赫胥黎报告说，在螯的质量与身体质量的对数-对数图上存在不连续性，他将其解释为螯的相对生长在螃蟹达到性成熟时突然发生变化。然而，我对赫胥黎的算术数据的分析表明，不连续性是对数变换引起的假象，并且在发育过程中，破碎机爪的生长动态在任何时候都没有变化。算术数据很好地由通过非线性回归拟合的幂函数描述，但不能由拟合到对数的线反变换估计的幂函数描述。这一发现和其他类似的发现质疑了在当代研究中继续依赖比较生长率方法的做法。
