J. theor. Biol. (1999) 200, 343}344 Article No. jtbi.1999.0999, available online at http://www.idealibrary.com on

LETTER TO THE EDITOR

Testing the Phylogenetic Stability of Early Tetrapods

Clack (1998) described Eucritta melanolimnetes, average stability of all triplets is a measure of an Early Carboniferous tetrapod, and used parsi- overall phylogenetic stability. Leaf and phylo- mony to investigate its evolutionary relationships genetic stability measures can utilize any nume- to other early tetrapods. Through comparison of rical technique for assessing the support for a most parsimonious tree and nine trees of one phylogenetic relationships. Here, we use a mea- additional step in length, Clack concluded that sure based on the widely used technique of boot- &&The phylogeny from the current data set is not strapping (Felsenstein, 1985). The bootstrap particularly robust'' and claimed that &&This in- proportion (BP) of any phylogenetic hypothesis stability undoubtedly results from the extreme is the proportion of bootstrap trees that include degree of character con#ict that Eucritta pres- the hypothesis (or a weighted proportion in the ents.'' We have developed measures of leaf and case of multiple trees from a single bootstrap overall phylogenetic stability that allow such replicate). There are three possible 3-taxon state- claims about the impact of individual leaves to be ments for each triplet. The measure of triplet tested. stability used here is the absolute di!erence be- Phylogenetic trees represent hypotheses of tween the BPs of the two best-supported 3-taxon evolutionary relationships for a set of terminal statements for the triplet. taxa or leaves. Most studies of the robustness of We reanalysed the data from Clack (1998) with phylogenetic trees focus on the support for, or uninformative characters removed. Bootstrap- stability of, clades. However, trees can also be ping was performed using PAUP 3.1.1 (Swo!ord, thought of as collections of less inclusive hy- 1993) with 500 replicates, 10 random addition potheses of phylogenetic relationships, such as sequences and TBR branch swapping. Leaf and 3-taxon statements, with implications for the phylogenetic stabilities were determined using assessment of support (Wilkinson, 1994). For RadCon (Thorley and Page, 1999). Two leaves, example, a single unstable leaf can result in clades Crassigyrinus and =hatcheeria, are less stable with minimum robustness despite strong support than Eucritta (Fig. 1). Interestingly, earlier au- for the phylogenetic relationships of the remain- thors, albeit in reference to earlier reconstruc- ing leaves (Wilkinson, 1996). Measures of leaf tions, described these leaves as &&uniquely stability allow the contribution of each leaf to primitive and aberrant'' (Panchen, 1985) and of overall phylogenetic stability to be determined. &&uncertain phylogenetic a$nities'' (Lombard and The rationale for the measures is very simple. Bolt, 1995). The phylogenetic relationships of a set of leaves Although Crassigyrinus and =hatcheeria are are a function of the relationships among each less stable than Eucritta, it is possible that their subset of three leaves (triplet). The support for instability is due to character con#ict introduced the relationships within each triplet provides a by Eucritta. In order to test the impact of the measure of the stability of that triplet. Stable and character data for individual leaves on overall unstable leaves will tend to occur in stable and phylogenetic stability we compared the stabilities unstable triplets, respectively. The average stabil- of all triplets when the leaf is not included in the ity of the triplets including a leaf provides a analysis with their stabilities when the leaf is measure of the stability of that leaf. Similarly, the included. Triplet stability measures when the leaf

0022}5193/99/019343#02 $30.00/0 ( 1999 Academic Press 344 LETTER TO THE EDITOR

phylogenetic hypotheses. For example, they can be used to identify unstable and potentially prob- lematic leaves and they enhance our capacity to test claims regarding the in#uence of speci"c leaves. In this case, our results demonstrate that Crassigyrinus and =hatcheeria are the most un- stable leaves in Clack's (1998) phylogeny and that its overall instability is neither solely nor prim- arily due to Eucritta.

JOSEPH L. THORLEY School of Biological Sciences, ;niversity of Bristol, Bristol, BS81;G, ;.K. and Department of Zoology, ¹he Natural History Museum, ¸ondon, S=75BD, ;.K.

MARK WILKINSON Department of Zoology, ¹ FIG. 1. Bootstrap consensus tree of early tetrapods with he Natural History Museum, clade bootstrap proportions and leaf stabilities. ¸ondon, S=75BD, ;.K.

(Received on 12 May 1999, Accepted in revised is included were determined by pruning the leaf form on 13 July 1999) from the set of bootstrap trees and condensing identical trees from the same bootstrap replicate. The weight of each remaining tree was then set to REFERENCES be the inverse of the number of non-identical CLACK, J. A. (1998). A new Early Carboniferous tetrapod trees in the replicate. Statistical signi"cance was with a meH lange of crown-group characters. Nature 394, 66}69. tested using the Wilcoxon signed ranks tests FELSENSTEIN, J. (1985). Con"dence limits on phylogenies: an (two-tailed) of the di!erences in stability of the approach using the bootstrap. Evolution 39, 783}791. triplets when the leaf is included or not included. LOMBARD,R.E.&BOLT, J. R. (1995). A new primitive = Removing Eucritta or =hatcheeria increased tetrapod, hatcheeria deltae from the Lower Carbonifer- ous of Iowa. Palaeontology 38, 471}494. overall phylogenetic stability but the di!erences PANCHEN, A. L. (1985). On the amphibian Crassigyrinus were not statistically signi"cant (increase" scoticus Watson from the Carboniferous of Scotland. 0.20%, p"0.47 and 0.58%, p"0.77, respective- Philos. ¹rans. R. Soc. B 309, 505}568. SWOFFORD, D. L. (1993). PA;P: Phylogenetic Analysis ly). In contrast, removal of Crassigyrinus signi"- ;sing Parsimony, version 3.1.1. Illinois Natural History cantly increased stability (1.88%, p"0.003). Survey. Assessing the strengths and weaknesses of in- THORLEY,J.L.&PAGE, R. D. M. (1999). RadCon 0.7. http:// taxonomy.zoology.gla.ac.uk/&jthorley/. ferred relationships is an important element of WILKINSON, M. (1994). Common cladistic information and phylogenetics. Leaf and phylogenetic stability its consensus representation: reduced Adams and reduced measures address aspects of hypothesis quality cladistic consensus trees and pro"les. Syst. Biol. 43, (with respect to given data) that are not revealed 343}368. WILKINSON, M. (1996). Majority-rule reduced consensus by measures of clade support and, thus contrib- methods and their use in bootstrapping. Mol. Biol. Evol. ute to a more comprehensive understanding of 13, 437}444.