Degrees of freedom in interspecific allometry: An adjustment for the effects of phylogenetic constraint
Version of Record online: 27 APR 2005
Copyright © 1994 Wiley-Liss, Inc., A Wiley Company
American Journal of Physical Anthropology
Volume 93, Issue 1, pages 95–107, January 1994
How to Cite
Smith, R. J. (1994), Degrees of freedom in interspecific allometry: An adjustment for the effects of phylogenetic constraint. Am. J. Phys. Anthropol., 93: 95–107. doi: 10.1002/ajpa.1330930107
- Issue online: 27 APR 2005
- Version of Record online: 27 APR 2005
- Manuscript Accepted: 8 SEP 1993
- Manuscript Received: 4 MAR 1993
- Interspecific allometry;
- Comparative methods;
- Phylogenetic constraint;
- Degrees of freedom;
- Nested analysis of variance
The data used in studies of bivariate interspecific allometry usually violate the assumption of statistical independence. Although the traits of each species are commonly treated as independent, the expression of a trait among species within a genus may covary because of shared common ancestry. The same effect exists for genera within a family and so on up the phylogenetic hierarchy. Determining sample size by counting data points overestimates the effective sample size, which then leads to overestimating the degrees of freedom that should be used in calculating probabilities and confidence intervals. This results in an inflated Type 1 error rate.
Although some workers (e.g., Felsenstein  Am. Nat. 125:1–15) have suggested that this issue may invalidate interspecific allometry as a comparative method, a correction for the problem can be approximated with variance components from a nested analysis of variance. Variance components partition the total variation in the data set among the levels of the nested hierarchy. If the variance component for each nested level is weighted by the number of groups at that level, the sum of these values is an estimate of an effective sample size for the data set which reflects the effects of phylogenetic constraint. Analysis of two data sets, using taxonomy to define levels of the nested hierarchy, suggests that it has been common for published studies of interspecific allometry to severely overestimate the number of degrees of freedom.
Interspecific allometry remains an important comparative method for evaluating questions concerning individual species that are not similarly addressed by the format of most of the newer comparative methods. With the correction proposed here for estimating degrees of freedom, the major statistical weakness of the procedure is substantially reduced. © 1994 Wiley-Liss, Inc.