Euclidean geometry explains why lengths allow precise body mass estimates in terrestrial invertebrates: The case of oribatid mites
Euclidean geometry explains why lengths allow precise body mass estimates in terrestrial invertebrates: The case of oribatid mites
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DOI：
10.1016/j.jtbi.2008.09.033
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发表时间：
2009-02-07
影响因子：
2
通讯作者：
Migliorini, M.
中科院分区：
文献类型：
--
作者：
Caruso, T.;Migliorini, M.
由于需要艰苦的实验室工作以及获得数千个可能非常小的动物的可靠体重估计值所涉及的技术困难，基于将后者与体长（l）相关的方程的土壤无脊椎动物体重M的间接测量越来越多地被使用。这些方程的隐含假设是 dM/dV = delta，其中 V 是身体体积，delta 是恒定密度值。经典欧几里得标度意味着 V 与 l(3) 成正比，与 M 成正比。因此，当 l 可以提供 V 的良好估计并且遵守恒定增量的假设时，可以从 l 导出 M。在无脊椎动物中，重量与长度相关的方程表明功率模型始终提供最佳拟合。然而，作者仅关注将体重与长度测量变量联系起来的斜率的经验估计，有时拟合没有理论依据的指数和线性模型。本文阐述了幂律如何从基本欧几里德标度导出，并描述了上述假设下的预期异速生长指数。基于经典的欧几里得标度理论，等效球体被定义为体积等于必须估计其体重的生物体的理论球体。对土壤甲螨数据集的图示应用有助于澄清所有这些问题。最后，建议了根据 V 和 delta 更精确地估计 M 的一般程序。 (c) 2008 Elsevier Ltd. 保留所有权利。
Indirect measures of soil invertebrate body mass M based on equations relating the latter to body length (l) are becoming increasingly used due to the required painstaking laboratory work and the technical difficulties involved in obtaining some thousands of reliable weight estimates for animals that can be very small. The implicit assumption of such equations is that dM/dV = delta, where V is body volume and delta is a constant density value. Classical Euclidean scaling implies that V proportional to l(3) proportional to M. One may thus derive M from l when the latter can provide a good estimate of V and the assumption of a constant delta is respected. In invertebrates, equations relating weight to length indicate that the power model always provides the best fit. However, authors only focused on the empirical estimation of slopes linking the body mass to the length measure variables, sometimes fitting exponential and linear models that are not theoretically grounded. This paper explicates how power laws derive from fundamental Euclidean scaling and describes the expected allometric exponents under the above assumptions. Based on the classical Euclidean scaling theory, an equivalent sphere is defined as a theoretical sphere with a volume equal to that of the organism whose body mass must be estimated. The illustrated application to a data set on soil oribatid mites helps clarify all these issues. Lastly, a general procedure for more precise estimation of M from V and delta is suggested. (c) 2008 Elsevier Ltd. All rights reserved.