Allometric Slopes Not Underestimated by Ordinary Least Squares Regression: A Case Study with Enchenopa Treehoppers (Hemiptera: Membracidae)

Abstract

Abstract The scaling of traits on body size—allometry—is a subject of broad interest in ecology and evolutionary biology, and one in which studies on insects and spiders have featured prominently. Allometric relationships are described with the slope of regressions of trait size (y) on body size (x). A common method—ordinary least squares (OLS) regression—is often expected to underestimate allometric slopes. The reason for this expectation is that OLS regression assumes that x is determined without error, which is expected to bias slope estimates unless the error in y is much larger than the error in x. However, alternative methods such as reduced major axis (RMA) regression suffer from problems of interpretability. Here, we test the hypothesis that OLS regression will underestimate allometric slopes. We used a natural experiment that arose in the course of training to measure insect genitalia, wherein measurement error for genitalia was larger before training than after training, and also differed by a very large amount between traits. Comparing allometric slopes estimated before and after training, and allometric slopes of traits having very different measurement errors, suggests that OLS regression is robust to measurement error in x and that it does not underestimate allometric slopes.