In 1932, Julian Huxley introduced biologists around the world to a simple method for fitting two-parameter power equations, $$ Y\, = \,b \times \, X^{k} $$ Y = b × X k , to bivariate observations that follow a curvilinear path on the arithmetic (= linear) scale. The method entails fitting a straight line to logarithmic transformations of the data and then (at least implicitly) back-transforming the resulting equation to the arithmetic domain. This general approach continues to be in wide use by students of biological allometry despite its several limitations and shortcomings. For example, Huxley’s allometric method requires that the bivariate data of interest follow the path of a straight line in log domain (i.e., that the data be loglinear). However, many datasets that are otherwise suitable for allometric analysis do not meet the requirement for loglinearity and consequently are beyond the scope of Huxley’s method. Such data can usually be examined in the untransformed state by nonlinear regression, and the regression approach enables investigators to fit models with different functional form and random error. Moreover, by combining nonlinear regression with a categorical variable, investigators can compare sets of observations that follow curvilinear paths on the arithmetic scale. The regression protocol is illustrated by re-examining data for relative growth by the internal hinge ligament in a bivalve mollusk and by the elongated snout in garfish (Actinopterygii). The methodology promoted by Huxley has played a major role in development of the field of biological allometry, but the procedure has been superseded by nonlinear regression.

中文翻译：

---

Julian Huxley 和相对增长的量化

1932 年，Julian Huxley 向世界各地的生物学家介绍了一种拟合双参数幂方程的简单方法，$$ Y\, = \,b \times \, X^{k} $$ Y = b × X k ，在算术（= 线性）尺度上遵循曲线路径的双变量观测值。该方法需要将一条直线拟合到数据的对数变换，然后（至少隐式地）将所得方程反向变换到算术域。尽管存在一些局限性和缺点，但这种通用方法仍被生物异速生长的学生广泛使用。例如，赫胥黎的异速生长方法要求感兴趣的二元数据遵循对数域中的一条直线路径（即，数据是对数线性的）。然而，许多适合异速生长分析的数据集不满足对数线性的要求，因此超出了赫胥黎方法的范围。此类数据通常可以通过非线性回归在未转换状态下进行检查，回归方法使研究人员能够拟合具有不同函数形式和随机误差的模型。此外，通过将非线性回归与分类变量相结合，研究人员可以比较在算术尺度上遵循曲线路径的观察集。回归协议通过重新检查双壳类软体动物内部铰链韧带的相对生长数据和长尾鱼 (Actinopterygii) 的细长鼻子的数据来说明。Huxley 提倡的方法论在生物异速生长领域的发展中发挥了重要作用，