Exploring and Explaining Complex Allometric Relationships: A Case Study on Amniote Testes Mass Allometry

While many allometric relationships are relatively simple and linear (when both variables are log transformed), others are much more complex. This paper explores an example of a complex allometric relationship, that of testes mass allometry in amniotes, by breaking it down into linear components and using this exploration to help explain why this complexity exists. These linear components are two size-independent ones and a size-dependent one, and it is the variations in the interactions between them across different body mass ranges that create the complexity in the overall allometric relationship. While the size-independent limits do not vary between amniote groupings, the slope and the intercept of the size-dependent component does, and it is this that explains why some amniote groups conform to allometric relationships with apparently very different forms. Thus, breaking this complex allometric relationship down into linear components allows its complexity to be explored and explained, and similar processes may prove useful for investigating other complex allometric relationships. In addition, by identifying size-independent upper and lower limits to the proportional investment in specific structures, it allows the prediction of when allometric relationships will remain simple and linear; and when they are likely to develop higher levels of complexity.