David M. Hillis

Bio: David M. Hillis is an academic researcher from University of Texas at Austin. The author has contributed to research in topics: Phylogenetic tree & Monophyly. The author has an hindex of 71, co-authored 191 publications receiving 28377 citations. Previous affiliations of David M. Hillis include American Museum of Natural History & University of Miami.

An Empirical Test of Bootstrapping as a Method for Assessing Confidence in Phylogenetic Analysis

Abstract: Bootstrapping is a common method for assessing confidence in phylogenetic anal? yses. Although bootstrapping was first applied in phylogenetics to assess the repeatability of a given result, bootstrap results are commonly interpreted as a measure of the probability that a phylogenetic estimate represents the true phylogeny. Here we use computer simulations and a laboratory-generated phylogeny to test bootstrapping results of parsimony analyses, both as measures of repeatability (i.e., the probability of repeating a result given a new sample of characters) and accuracy (i.e., the probability that a result represents the true phylogeny). Our results indicate that any given bootstrap proportion provides an unbiased but highly imprecise measure of repeatability, unless the actual probability of replicating the relevant result is nearly one. The imprecision of the estimate is great enough to render the estimate virtually useless as a measure of repeatability. Under conditions thought to be typical of most phylogenetic analyses, however, bootstrap proportions in majority-rule consensus trees provide biased but highly con? servative estimates of the probability of correctly inferring the corresponding clades. Specifically, under conditions of equal rates of change, symmetric phylogenies, and internodal change of 70% usually correspond to a probability of >95% that the corresponding dade is real. However, under conditions of very high rates of internodal change (approaching randomization of the characters among taxa) or highly unequal rates of change among taxa, bootstrap proportions >50% are overestimates of accuracy. (Boot? strapping; accuracy; repeatability; phylogeny; parsimony; precision; statistical analyses; simu? lations.)

Ribosomal DNA: molecular evolution and phylogenetic inference.

Abstract: Ribosomal DNA (rDNA) sequences have been aligned and compared in a number of living organisms, and this approach has provided a wealth of information about phylogenetic relationships. Studies of rDNA sequences have been used to infer phylogenetic history across a very broad spectrum, from studies among the basal lineages of life to relationships among closely related species and populations. The reasons for the systematic versatility of rDNA include the numerous rates of evolution among different regions of rDNA (both among and within genes), the presence of many copies of most rDNA sequences per genome, and the pattern of concerted evolution that occurs among repeated copies. These features facilitate the analysis of rDNA by direct RNA sequencing, DNA sequencing (either by cloning or amplification), and restriction enzyme methodologies. Constraints imposed by secondary structure of rRNA and concerted evolution need to be considered in phylogenetic analyses, but these constraints do not appear to impede seriously the usefulness of rDNA. An analysis of aligned sequences of the four nuclear and two mitochondrial rRNA genes identified regions of these genes that are likely to be useful to address phylogenetic problems over a wide range of levels of divergence. In general, the small subunit nuclear sequences appear to be best for elucidating Precambrian divergences, the large subunit nuclear sequences for Paleozoic and Mesozoic divergences, and the organellar sequences of both subunits for Cenozoic divergences. Primer sequences were designed for use in amplifying the entire nuclear rDNA array in 15 sections by use of the polymerase chain reaction; these "universal" primers complement previously described primers for the mitochondrial rRNA genes. Pairs of primers can be selected in conjunction with the analysis of divergence of the rRNA genes to address systematic problems throughout the hierarchy of life.

Signal, Noise, and Reliability in Molecular Phylogenetic Analyses

Abstract: DNA sequences and other molecular data compared among organisms may contain phylogenetic signal, or they may be randomized with respect to phylogenetic history. Some method is needed to distinguish phylogenetic signal from random noise to avoid analysis of data that have been randomized with respect to the historical relationships of the taxa being compared. We analyzed 8,000 random data matrices consisting of 10-500 binary or four-state characters and 5-25 taxa to study several options for detecting signal in systematic data bases. Analysis of random data often yields a single most-parsimonious tree, especially if the number of characters examined is large and the number of taxa examined is small (both often true in molecular studies). The most-parsimonious tree inferred from random data may also be considerably shorter than the second-best alternative. The distribution of tree lengths of all tree topologies (or a random sample thereof) provides a sensitive measure of phylogenetic signal: data matrices with phylogenetic signal produce tree-length distributions that are strongly skewed to the left, whereas those composed of random noise are closer to symmetrical. In simulations of phylogeny with varying rates of mutation (up to levels that produce random variation among taxa), the skewness of tree-length distributions is closely related to the success of parsimony in finding the true phylogeny. Tables of critical values of a skewness test statistic, g1, are provided for binary and four-state characters for 10-500 characters and 5-25 taxa. These tables can be used in a rapid and efficient test for significant structure in data matrices for phylogenetic analysis.

Increased taxon sampling greatly reduces phylogenetic error.

Abstract: Several authors have argued recently that extensive taxon sampling has a positive and important effect on the accuracy of phylogenetic estimates. However, other authors have argued that there is little benefit of extensive taxon sampling, and so phylogenetic problems can or should be reduced to a few exemplar taxa as a means of reducing the computational complexity of the phylogenetic analysis. In this paper we examined five aspects of study design that may have led to these different perspectives. First, we considered the measurement of phylogenetic error across a wide range of taxon sample sizes, and conclude that the expected error based on randomly selecting trees (which varies by taxon sample size) must be considered in evaluating error in studies of the effects of taxon sampling. Second, we addressed the scope of the phylogenetic problems defined by different samples of taxa, and argue that phylogenetic scope needs to be considered in evaluating the importance of taxon-sampling strategies. Third, we examined the claim that fast and simple tree searches are as effective as more thorough searches at finding near-optimal trees that minimize error. We show that a more complete search of tree space reduces phylogenetic error, especially as the taxon sample size increases. Fourth, we examined the effects of simple versus complex simulation models on taxonomic sampling studies. Although benefits of taxon sampling are apparent for all models, data generated under more complex models of evolution produce higher overall levels of error and show greater positive effects of increased taxon sampling. Fifth, we asked if different phylogenetic optimality criteria show different effects of taxon sampling. Although we found strong differences in effectiveness of different optimality criteria as a function of taxon sample size, increased taxon sampling improved the results from all the common optimality criteria. Nonetheless, the method that showed the lowest overall performance (minimum evolution) also showed the least improvement from increased taxon sampling. Taking each of these results into account re-enforces the conclusion that increased sampling of taxa is one of the most important ways to increase overall phylogenetic accuracy.

A simple, fast, and accurate algorithm to estimate large phylogenies by maximum likelihood.

Abstract: The increase in the number of large data sets and the complexity of current probabilistic sequence evolution models necessitates fast and reliable phylogeny reconstruction methods. We describe a new approach, based on the maximum- likelihood principle, which clearly satisfies these requirements. The core of this method is a simple hill-climbing algorithm that adjusts tree topology and branch lengths simultaneously. This algorithm starts from an initial tree built by a fast distance-based method and modifies this tree to improve its likelihood at each iteration. Due to this simultaneous adjustment of the topology and branch lengths, only a few iterations are sufficient to reach an optimum. We used extensive and realistic computer simulations to show that the topological accuracy of this new method is at least as high as that of the existing maximum-likelihood programs and much higher than the performance of distance-based and parsimony approaches. The reduction of computing time is dramatic in comparison with other maximum-likelihood packages, while the likelihood maximization ability tends to be higher. For example, only 12 min were required on a standard personal computer to analyze a data set consisting of 500 rbcL sequences with 1,428 base pairs from plant plastids, thus reaching a speed of the same order as some popular distance-based and parsimony algorithms. This new method is implemented in the PHYML program, which is freely available on our web page: http://www.lirmm.fr/w3ifa/MAAS/. (Algorithm; computer simulations; maximum likelihood; phylogeny; rbcL; RDPII project.) The size of homologous sequence data sets has in- creased dramatically in recent years, and many of these data sets now involve several hundreds of taxa. More- over, current probabilistic sequence evolution models (Swofford et al., 1996 ; Page and Holmes, 1998 ), notably those including rate variation among sites (Uzzell and Corbin, 1971 ; Jin and Nei, 1990 ; Yang, 1996 ), require an increasing number of calculations. Therefore, the speed of phylogeny reconstruction methods is becoming a sig- nificant requirement and good compromises between speed and accuracy must be found. The maximum likelihood (ML) approach is especially accurate for building molecular phylogenies. Felsenstein (1981) brought this framework to nucleotide-based phy- logenetic inference, and it was later also applied to amino acid sequences (Kishino et al., 1990). Several vari- ants were proposed, most notably the Bayesian meth- ods (Rannala and Yang 1996; and see below), and the discrete Fourier analysis of Hendy et al. (1994), for ex- ample. Numerous computer studies (Huelsenbeck and Hillis, 1993; Kuhner and Felsenstein, 1994; Huelsenbeck, 1995; Rosenberg and Kumar, 2001; Ranwez and Gascuel, 2002) have shown that ML programs can recover the cor- rect tree from simulated data sets more frequently than other methods can. Another important advantage of the ML approach is the ability to compare different trees and evolutionary models within a statistical framework (see Whelan et al., 2001, for a review). However, like all optimality criterion-based phylogenetic reconstruction approaches, ML is hampered by computational difficul- ties, making it impossible to obtain the optimal tree with certainty from even moderate data sets (Swofford et al., 1996). Therefore, all practical methods rely on heuristics that obtain near-optimal trees in reasonable computing time. Moreover, the computation problem is especially difficult with ML, because the tree likelihood not only depends on the tree topology but also on numerical pa- rameters, including branch lengths. Even computing the optimal values of these parameters on a single tree is not an easy task, particularly because of possible local optima (Chor et al., 2000). The usual heuristic method, implemented in the pop- ular PHYLIP (Felsenstein, 1993 ) and PAUP ∗ (Swofford, 1999 ) packages, is based on hill climbing. It combines stepwise insertion of taxa in a growing tree and topolog- ical rearrangement. For each possible insertion position and rearrangement, the branch lengths of the resulting tree are optimized and the tree likelihood is computed. When the rearrangement improves the current tree or when the position insertion is the best among all pos- sible positions, the corresponding tree becomes the new current tree. Simple rearrangements are used during tree growing, namely "nearest neighbor interchanges" (see below), while more intense rearrangements can be used once all taxa have been inserted. The procedure stops when no rearrangement improves the current best tree. Despite significant decreases in computing times, no- tably in fastDNAml (Olsen et al., 1994 ), this heuristic becomes impracticable with several hundreds of taxa. This is mainly due to the two-level strategy, which sepa- rates branch lengths and tree topology optimization. In- deed, most calculations are done to optimize the branch lengths and evaluate the likelihood of trees that are finally rejected. New methods have thus been proposed. Strimmer and von Haeseler (1996) and others have assembled four- taxon (quartet) trees inferred by ML, in order to recon- struct a complete tree. However, the results of this ap- proach have not been very satisfactory to date (Ranwez and Gascuel, 2001 ). Ota and Li (2000, 2001) described