Alternative methods for calculating percentage prediction error and their implications for predicting body mass in fossil taxa

Since body mass covaries with many ecological aspects of an animal, body mass prediction of fossil taxa is a frequent goal of paleontologists. Body mass prediction often relies on a body mass prediction equation (BMPE): a bivariate relationship between a predictor variable (e.g., molar occlusal area, femoral head breadth) and body mass as observed in extant taxa. A variety of metrics have been used to assess the reliability of BMPEs, including percentage prediction error (%PE), which involves predicting body masses of a test sample comprising individuals with associated masses. A mean %PE can be calculated in two ways: 1) as the mean %PE of multiple individual predictions (%MPE), or 2) as the %PE of mean body mass generated from the mean predictor value of multiple individuals (here termed %PEM). Differences between these two approaches have never been formally examined and no formal protocols have been recommended. Using a large sample of cercopithecoid primates (406 individuals from 50 species/subspecies) with associated body masses, body mass is predicted with six previously published interspecific BMPEs. Both %MPE and %PEM are calculated and compared. For all BMPEs, the distributions of differences between %MPE and %PEM exhibit positive skew and have medians significantly greater than zero, indicating that the examined prediction equations are more accurate at predicting mean body mass when they are applied to mean predictor values. The decreased predictive accuracy of %MPE relative to %PEM likely stems from changing the unit of analysis from mean values (in the reference sample) to individual values (in the test sample) when calculating %MPE. Empirical results are supported with a simulated dataset. Implications for body mass prediction in fossil species are discussed.