GARLAND, T., Jr.; IVES, A.R.; MIDFORD, P.E.; Univ. of Calif., Riverside; Univ. of Wisc.-Madison: Within-species Variation and Measurement Error in Phylogenetic Comparative Methods

Most phylogenetically based statistical methods assume that within-species variation is absent or negligible. Within-species variation has several components, including differences among populations, which can be eliminated by sampling from single populations. Alternatively, multiple populations can be kept separate during analyses. Within-population “measurement error” includes sampling variation, instrument-related error, low repeatability caused by fluctuations in behavioral or physiological state, variation related to age, sex, season or time of day, and individual variation within such categories. In the allometric context of estimating the true functional relationship between body size and a dependent variable (e.g., leg length, metabolic rate, home range area), it is well known that measurement error (often vaguely defined in practice) causes estimates of slopes to be biased downwards. Less well appreciated is the fact that measurement error inflates confidence intervals about slopes (and intercepts). Standard statistical methods are available to incorporate information on within-population variation (similar to weighted regression), but they can be non-trivial to apply and have rarely been used in empirical studies that apply phylogenetic comparative methods. We show how estimates of within-population variation that are often available from published comparative data sets (e.g., standard errors) can be used to improve estimation of regression equations, correlations, and several univariate parameter estimates, including ancestral values and their standard errors as well as the K statistic, which describes the amount of phylogenetic signal in continuous-valued traits. The methods are illustrated with examples, and MatLab programs to perform the methods are made available. Supported by NSF DEB-0196384.