Phylogeny, Regression, and the Allometry of Physiological Traits

Abstract

Physiological and ecological allometries often pose linear regression problems characterized by (1) noncausal, phylogenetically autocorrelated independent (x) and dependent (y) variables (characters); (2) random variation in both variables; and (3) a focus on regression slopes (allometric exponents). Remedies for the phylogenetic autocorrelation of species values (phylogenetically independent contrasts) and variance structure of the data (reduced major axis [RMA] regression) have been developed, but most functional allometries are reported as ordinary least squares (OLS) regression without use of phylogenetically independent contrasts. We simulated Brownian diffusive evolution of functionally related characters and examined the importance of regression methodologies and phylogenetic contrasts in estimating regression slopes for phylogenetically constrained data. Simulations showed that both OLS and RMA regressions exhibit serious bias in estimated regression slopes under different circumstances but that a modified orthogonal (least squares variance-oriented residual [LSVOR]) regression was less biased than either OLS or RMA regressions. For strongly phylogenetically structured data, failure to use phylogenetic contrasts as regression data resulted in overestimation of the strength of the regression relationship and a significant increase in the variance of the slope estimate. Censoring of data sets by simulated extinction of taxa did not affect the importance of appropriate regression models or the use of phylogenetic contrasts.

Gravity and the evolution of cardiopulmonary morphology in snakes

“…We do not take a model fitting approach here because the available methods do not seem biologically relevant, and because they require the assertion of even more as yet unsubstantiated assumptions. In simulations where the exact timings of evolutionary divergences (ancestral nodes) and character states were known, and different rates of evolution were applied, the Felsenstein (1985) PIC method was found to correlate most closely with true contrast values (O'Connor et al, 2007; Sieg et al, 2009). …”

A Macrophysiological Analysis of Energetic Constraints on Geographic Range Size in Mammals

“…Because shared evolutionary history among species can cause interspecific trait similarity, it may inflate statistical power in comparative analyses, possibly leading to erroneous conclusions [23,24,98,99]. Nevertheless, current methods for accounting for phylogenetic autocorrelation in comparative studies (e.g., PGLS) are not a panacea for resolving these issues because (1) most phylogenies are incomplete and include unresolved relationships (‘soft’ polytomies), and (2) specific models of trait evolution, such as Brownian motion, must be assumed to perform the analyses, yet are not empirically supported [100].…”

Metabolic Scaling in Animals: Methods, Empirical Results, and Theoretical Explanations

“…The problem also potentially applies to intraspecific studies of related individuals because closely related individuals are more likely to be similar that distantly related ones, though this is rarely acknowledged except in quantitative genetic studies that partition phenotypic variation into genetic and other components (106,243; see also 153 for a demonstration of the link between quantitative genetic and comparative analyses). Violation of the assumption of independence in interspecific analyses leads to inflated degrees of freedom, increased Type I error rates, overestimation of the strength of regression relationships, and a significant increase in the variance of the scaling exponent estimate (119,125,160,295,343). Blomberg et al (34) have shown that for studies with 20 or more species, most traits show significant phylogenetic signal, defined as the tendency for related species to resemble each other.…”