用三次设计法最优拟合Taylor幂法则模型

Optimum Fitting of Taylor's Power Law Curve by Three Designs

在用Taylor方法研究种群空间格局时,拟合Taylor幂法则V=a·m^b通常采用将原函数线性化为1nV=1na+b1nm,然后用线性最小二乘法拟合,求得参数a、b。这种方法不是最优的,本文提出用三次设计法最优拟合Taylor幂法则。实例验证也表明三次设计法简单、精确,优于通常采用的“对数线性化——最小二乘法”。采用前者的拟合残差远小于采用后者时的拟合残差。

When assessing and interpreting population spatial patterns with Taylor's Power Law model, transforming the Power function to provide a mathematically equivalent linear equation is a usual method for fitting Taylor's Power Law curve. However, it is not optimum fitting to the untransformed function, i. e. , Taylor's Power Law model itself. In this paper a three design method is introduced for determing the values of the parameters ( a&b ) of Taylor's Power Law model, which will give the minimum least-square fit to a set of data. It is proved to be superior to the usual method in practce.