Sex Differences in the Swordtail Xiphophorus hellerii Revealed by a New Method to Investigate Volumetric Data

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.