Packard Gary C, Boardman Thomas J
Department of Biology, Colorado State University, Fort Collins, Colorado 80523-1878, USA.
Physiol Biochem Zool. 2008 Jul-Aug;81(4):496-507. doi: 10.1086/589110.
The standard approach to most allometric research is to gather data on a biological function and a measure of body size, convert the data to logarithms, display the new values in a bivariate plot, and then fit a straight line to the transformations by the method of least squares. The slope of the fitted line provides an estimate for the allometric (or scaling) exponent, which often is interpreted in the context of underlying principles of structural and functional design. However, interpretations of this sort are based on the implicit assumption that the original data conform with a power function having an intercept of 0 on a plot with arithmetic coordinates. Whenever this assumption is not satisfied, the resulting estimate for the allometric exponent may be seriously biased and misleading. The problem of identifying an appropriate function is compounded by the logarithmic transformations, which alter the relationship between the original variables and frequently conceal the presence of outliers having an undue influence on properties of the fitted equation, including the estimate for the allometric exponent. Much of the current controversy in allometric research probably can be traced to substantive biases introduced by investigators who followed standard practice. We illustrate such biases with examples taken from the literature and outline a general methodology by which the biases can be minimized in future research.
大多数异速生长研究的标准方法是收集关于一种生物学功能和身体大小度量的数据，将数据转换为对数，在双变量图中展示新值，然后用最小二乘法对变换后的数据拟合一条直线。拟合线的斜率提供了异速生长（或比例）指数的估计值，该指数通常在结构和功能设计的基本原理背景下进行解释。然而，这类解释基于一个隐含假设，即原始数据符合在算术坐标图上截距为0的幂函数。只要这个假设不成立，所得的异速生长指数估计值可能会有严重偏差并产生误导。识别合适函数的问题因对数变换而变得更加复杂，对数变换改变了原始变量之间的关系，并常常掩盖了对拟合方程性质（包括异速生长指数估计值）有不当影响的异常值的存在。当前异速生长研究中的许多争议可能都可追溯到遵循标准做法的研究者引入的实质性偏差。我们用文献中的例子来说明这类偏差，并概述一种通用方法，通过该方法可在未来研究中将偏差最小化。
