Thursday, January 2, 2014

Discriminant Function Analysis and Phylogenetic Signal

Rob Scott and I just published a new paper in AJPA on the issues surrounding the use of Discriminant Function Analysis (DFA) in ecomorphology.

2014 - Barr, WA and Scott, RS. Phylogenetic comparative methods complement discriminant function analysis in ecomorphology.  American Journal of Physical Anthropology. 153:663 - 674. doi:10.1002/ajpa.22462

Ecomorphology uses anatomical characteristics to predict the ecological context in which an organism lived. This is possible because organisms adapt anatomically to the functional requirements of their lifestyles. However, ecomorphology may be complicated by the fact that both morphological and ecological traits tend to have phylogenetic signal. In other words, closely related species tend to be more similar than more distantly related species. This can make it difficult to tease apart the effects of functional adaptation from those of phylogenetic signal. 

One of the most common statistical methods in ecomorphology is DFA.  The purpose of our study was to evaluate the performance of DFA in situations with varying levels of phylogenetic signal.

We used phylogenetic simulations to create datasets that were related to a phylogenetic tree, but were functionally unrelated to a set of ecological characteristics, which had varying levels of phylogenetic signal.  We simulated data in which (1) both the morphological characters and ecological categories had phylogenetic signal, (2) only the morphological characters had phylogenetic signal, (3) only the ecological category had phylogenetic signal, and (4) when neither the morphology nor the category had phylogenetic signal. 

Remember: in all cases there was no biomechanical connection between habitat and morphology. We then ran DFA on the resulting datasets. The results are summarized in the figure below. 

This figure shows the mean success rates of DFA on the vertical axis, and % of DFAs that were significant on the horizontal axis.  When we randomized habitats, DFAs were rarely significant. However, when the actual habitats (with phylogenetic signal) were used, the DFAs are very often statistically significant in cases where the morphological variables have phylogenetic signal.  We used Phylogenetic Generalized Least Squares (PGLS) on these same datasets, and found that PGLS reliably rejects the hypothesis of a biomechanical link between category and morphology.

Thus, we concluded that PGLS should be used to validate characters before including them in DFA.