Using the Past to Predict the Present: Confidence Intervals for Regression Equations in Phylogenetic Comparative Methods

TLDR

Phylogenetic comparative methods, including independent contrasts and generalized least squares, assess statistical relationships among traits. Regression equations derived from independent contrasts can be mapped back to the original data space, allowing confidence and prediction intervals for new observations, with accuracy improving as species placement on the phylogeny becomes more precise. The two methods are equivalent and can infer ancestral values, estimate relationships, and predict unmeasured species; reanalysis of avian BMR data shows significant differences between conventional and phylogenetic allometric equations, with passerines exhibiting lower evolutionary rates and smaller body masses, supporting clade‑specific allometric models.

Abstract

Two phylogenetic comparative methods, independent contrasts and generalized least squares models, can be used to determine the statistical relationship between two or more traits. We show that the two approaches are functionally identical and that either can be used to make statistical inferences about values at internal nodes of a phylogenetic tree (hypothetical ancestors), to estimate relationships between characters, and to predict values for unmeasured species. Regression equations derived from independent contrasts can be placed back onto the original data space, including computation of both confidence intervals and prediction intervals for new observations. Predictions for unmeasured species (including extinct forms) can be made increasingly accurate and precise as the specificity of their placement on a phylogenetic tree increases, which can greatly increase statistical power to detect, for example, deviation of a single species from an allometric prediction. We reexamine published data for basal metabolic rates (BMR) of birds and show that conventional and phylogenetic allometric equations differ significantly. In new results, we show that, as compared with nonpasserines, passerines exhibit a lower rate of evolution in both body mass and mass-corrected BMR; passerines also have significantly smaller body masses than their sister clade. These differences may justify separate, clade-specific allometric equations for prediction of avian basal metabolic rates.