Hypothesis testing in comparative and experimental studies of function-valued traits.
Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.
Griswold
Cortland K
CK
School of Biological Sciences, Washington State University, Pullman, WA 99164, USA. ckg@email.arizona.edu
Gomulkiewicz
Richard
R
Heckman
Nancy
N
D000704:Analysis of Variance; D000818:Animals; D005075:Biological Evolution; D008954:Models, Biological; D015233:Models, Statistical; D019655:Quantitative Trait, Heritable; D018709:Statistics, Nonparametric