Packard Gary C
Department of Biology, Colorado State University, Fort Collins, CO 80523, USA.
Biol Open. 2024 Sep 15;13(9). doi: 10.1242/bio.060587. Epub 2024 Sep 16.
Students of biological allometry have used the logarithmic transformation for over a century to linearize bivariate distributions that are curvilinear on the arithmetic scale. When the distribution is linear, the equation for a straight line fitted to the distribution can be back-transformed to form a two-parameter power function for describing the original observations. However, many of the data in contemporary studies of allometry fail to meet the requirement for log-linearity, thereby precluding the use of the aforementioned protocol. Even when data are linear in logarithmic form, the two-parameter power equation estimated by back-transformation may yield a misleading or erroneous perception of pattern in the original distribution. A better approach to bivariate allometry would be to forego transformation altogether and to fit multiple models to untransformed observations by nonlinear regression, thereby creating a pool of candidate models with different functional form and different assumptions regarding random error. The best model in the pool of candidate models could then be identified by a selection procedure based on maximum likelihood. Two examples are presented to illustrate the power and versatility of newer methods for studying allometric variation. It always is better to examine the original data when it is possible to do so.
生物异速生长学的学生们使用对数变换已有一个多世纪了，目的是将在算术尺度上呈曲线的双变量分布线性化。当分布呈线性时，拟合该分布的直线方程可以进行逆变换，以形成一个双参数幂函数来描述原始观测值。然而，当代异速生长研究中的许多数据未能满足对数线性的要求，因此无法使用上述方法。即使数据在对数形式下是线性的，通过逆变换估计的双参数幂方程也可能会对原始分布中的模式产生误导性或错误的认知。更好的双变量异速生长研究方法是完全放弃变换，通过非线性回归将多个模型拟合到未变换的观测值上，从而创建一组具有不同函数形式和关于随机误差的不同假设的候选模型。然后，可以通过基于最大似然的选择程序在候选模型组中识别出最佳模型。给出了两个例子来说明研究异速生长变化的新方法的强大功能和通用性。只要有可能，最好检查原始数据。
