Comparing the relative volumes of body parts is a useful tool in morphology, but it is not trivial to do this in animals that differ in overall size. To account for scaling differences, a “reference size” has to be determined and the original absolute volumes have to be “corrected for” by this scaling reference. However, the outcome of a statistical analysis is greatly affected by this “reference size,” and it is practically impossible to determine the “overall size” of a structure independent of the changes in the relative size of the parts of it. Here, a new method is introduced to compare the relative volumes of parts that does not need a scaling reference. The method transforms the absolute part volumes into a ratio matrix (volume ratio transformation, VRT). The VRT is free of any scaling factors and can be used to compare groups of animals. This paper also reviews various other errors made frequently when comparing brain morphology between animals. Finally, the VRT is applied to investigate sex differences in the swordtail fish (Xiphophorus hellerii), which show profound differences in the size of the valvula cerebelli.
Brain Behav Evol

中文翻译：

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一种研究体积数据的新方法揭示了剑尾剑鱼的性别差异。

比较身体各部分的相对体积是形态学中的一个有用工具，但在整体大小不同的动物中这样做并非易事。为了解决比例差异，必须确定“参考尺寸”，并且必须通过该比例参考“校正”原始绝对体积。然而，统计分析的结果受这种“参考尺寸”的影响很大，实际上不可能独立于结构各部分相对尺寸的变化来确定结构的“整体尺寸”。在这里，引入了一种新方法来比较不需要缩放参考的零件的相对体积。该方法将绝对零件体积转换为比率矩阵（体积比率转换，VRT）。VRT 没有任何比例因子，可用于比较动物组。本文还回顾了在比较动物之间的大脑形态时经常犯的各种其他错误。最后，应用 VRT 研究剑尾鱼的性别差异(Xiphophorus hellerii)，它们显示出小脑瓣膜大小的巨大差异。
大脑行为进化