CAVEAT ON USE OF DELESSE PRINCIPLE OF AREAL ANALYSIS FOR ESTIMATING COMPONENT VOLUME DENSITIES
CAVEAT ON USE OF DELESSE PRINCIPLE OF AREAL ANALYSIS FOR ESTIMATING COMPONENT VOLUME DENSITIES
复制标题
DOI：
10.1111/j.1365-2818.1974.tb03979.x
复制
发表时间：
1974-01-01
期刊：
影响因子：
--
通讯作者：
CRUZORIVE, LM
中科院分区：
文献类型：
--
作者：
MAYHEW, TM;CRUZORIVE, LM
在体视学工作中，通常通过调用面分析的德莱西原理来估计组分体积密度。无论形态测量方法是基于横截面积、线性截距还是点密度的测量，这都是正确的。继我们前面考虑的特殊情况下，一个球形组件的球形包含体积，我们在这里提出一个警告，使用这个基本原则。本报告表明，体积密度的估计可以通过应用两个主要的配方，这是基于面积分析的“立方体”和“球形”的数学模型。需要强调的是，德莱塞关系的这些公式在所有实际情况下在数学上都是不等价的;因此，如果不能正确理解每个公式应适用的实际情况，可能会导致在获得的体积密度数据中引入统计偏差。强调和澄清了制剂应用的条件，并提供了一些生物学实例。虽然这些问题主要是针对生物学家提出的，但它们也与地球和材料科学家以及一般的形态计量学家有关。
In stereological work, component volume densities are estimated routinely by invoking the Delesse principle of areal analysis. This is true whether the morpho‐metric methods are based on the measurement of transectional areas, linear intercepts or point densities. Following our earlier consideration of the special case of a spherical component in a spherical containing volume, we here present a warning on the use of this fundamental principle. This report demonstrates that estimates of volume densities may be derived by application of two main formulations which are based on the areal analysis of ‘cubical’ and ‘spherical’ mathematical models. It is emphasized that these formulations of the Delesse relationship are not mathematically equivalent in all practical instances; failure to appreciate the correct practical circumstances in which each should be applied may lead therefore to the introduction of a statistical bias into the volume density data which are obtained. The conditions under which the formulations should be applied are stressed and clarified and some biological examples are provided. Whilst the problems are presented in a form which is aimed primarily at the biologist, they are also pertinent to the earth and materials scientists and to morphometrists in general.