生长模型的误差函数及其数学特征

生长曲线是估计动物年龄的重要方法之一,在野生动物生态学中,动物的体重往往被用作估计动物年龄的主要指标。然而,在动物体重测定过程中经常会出现一些偏差。例如,动物的日常活动（ 进食、饮水、排泄等）通常会引起动物体重的变化,这样在不同时间测定动物的体重就会产生偏差;此外,在测定动物体重的过程中,我们往往称量到一定的精确度。这些偏差将直接导致对动物年龄的估计误差。本文分析了4种常见生长模型（Logistic、Gompertz、Bertalanffy、Richards)的误差函数的数学特征。结果表明,由动物日常活动导致的年龄估计误差在动物的幼龄阶段为量小,而由称量精确度导致的年龄估算误差在生长曲线的拐点处为最小。

Mathematical Properties of the Error Functions of Some Commonly Applied Growth Models

To estimate the age of an animal by its body weight according to an empirical growth curve is one of the practical methods in field ecology. But the presence of variations occurred in the process of growth data collecting, often generate errors in age estimation. For example, the body weight of an animal may vary continually due to its daily activities. Moreover, in some cases, the measuring precision can also generate errors. In this paper: we analyzed the mathematical feature of the error functions of some commonly applied growth equations (i.e. the Logistic, Gompetz, Spillman, Bertalanffy and Richards functions). The results reveal that the smallest error caused by daily activities occurs in the early life stage of an animal. However, the least error caused by the measuring precision occurs at the inflexion point of each growth model.