Multiple regression, not ratios, for analyzing relative appendage size

Abstract In recent years, research has increasingly identified changes in animal body shape occurring concomitantly with climate change. Shape changes, or ‘shape-shifting’, are believed to reflect a temporal extension of Allen’s rule, wherein appendages increase in size in response to warmer temperatures. Shape-shifting responses are considered in terms of increases in appendage size relative to body size, however, the statistical methods of analyzing relative appendage size differ between studies. There have been two statistical methods by which changes in relative appendage size have predominantly been investigated: (1) a multiple regression approach, wherein appendage size is made relative to body size by inclusion of body size as a covariate in the model, and (2) a ratio approach, wherein a ratio of appendage size to body size is calculated prior to modelling changes in the ratio over time. In this paper, we use simulated and real-world data to test both statistical approaches and how they impact assessments of shape-shifting. We demonstrate that the two approaches can yield different results across a range of body and appendage size change scenarios. We discuss the implications of this, and suggest that the multiple regression approach is more suitable for detecting changes in relative appendage size because it properly accounts for allometric scaling. We further suggest that the ratio approach does not adequately disentangle changes in ratio that are caused exclusively by variation in body size. We conclude that the multiple regression approach is more appropriate for investigations of shape-shifting, especially when other factors may also be changing through time. While we demonstrate these principles using examples and data of changes through time, the same would apply for appendage size changes over spatial scales (i.e. Allen’s rule).