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PubMed1998

Effects of branch length errors on the performance of phylogenetically independent contrasts.

We examined Type I error rates of Felsenstein's (1985; Am. Nat. 125:1-15) comparative method of phylogenetically independent contrasts when branch lengths are in error and the model of evolution is not Brownian motion. We used seven evolutionary models, six of which depart strongly from Brownian motion, to simulate the evolution of two continuously valued characters along two different phylogenies (15 and 49 species). First, we examined the performance of independent contrasts when branch lengths are distorted systematically, for example, by taking the square root of each branch segment. These distortions often caused inflated Type I error rates, but performance was almost always restored when branch length transformations were used. Next, we investigated effects of random errors in branch lengths. After the data were simulated, we added errors to the branch lengths and then used the altered phylogenies to estimate character correlations. Errors in the branches could be of two types: fixed, where branch lengths are either shortened or lengthened by a fixed fraction; or variable, where the error is a normal variate with mean zero and the variance is scaled to the length of the branch (so that expected error relative to branch length is constant for the whole tree). Thus, the error added is unrelated to the microevolutionary model. Without branch length checks and transformations, independent contrasts tended to yield extremely inflated and highly variable Type I error rates. Type I error rates were reduced, however, when branch lengths were checked and transformed as proposed by Garland et al. (1992; Syst. Biol. 41:18-32), and almost never exceeded twice the nominal P-value at alpha = 0.05. Our results also indicate that, if branch length transformations are applied, then the appropriate degrees of freedom for testing the significance of a correlation coefficient should, in general, be reduced to account for estimation of the best branch length transformation. These results extend those reported in Díaz-Uriarte and Garland (1996; Syst. Biol. 45:27-47), and show that, even with errors in branch lengths and evolutionary models different from Brownian motion, independent contrasts are a robust method for testing hypotheses of correlated evolution.

Computer Simulation↗

PubMed2002

Improvement of distance-based phylogenetic methods by a local maximum likelihood approach using triplets.

We introduce a new approach to estimate the evolutionary distance between two sequences. This approach uses a tree with three leaves: two of them correspond to the studied sequences, whereas the third is chosen to handle long-distance estimation. The branch lengths of this tree are obtained by likelihood maximization and are then used to deduce the desired distance. This approach, called TripleML, improves the precision of evolutionary distance estimates, and thus the topological accuracy of distance-based methods. TripleML can be used with neighbor-joining-like (NJ-like) methods not only to compute the initial distance matrix but also to estimate new distances encountered during the agglomeration process. Computer simulations indicate that using TripleML significantly improves the topological accuracy of NJ, BioNJ, and Weighbor, while conserving a reasonable computation time. With randomly generated 24-taxon trees and realistic parameter values, combining NJ with TripleML reduces the number of wrongly inferred branches by about 11% (against 2.6% and 5.5% for BioNJ and Weighbor, respectively). Moreover, this combination requires only about 1.5 min to infer a phylogeny of 96 sequences composed of 1,200 nucleotides, as compared with 6.5 h for FastDNAml on the same machine (PC 466 MHz).

Computer Simulation↗

PubMed2002

Episodic chromosomal evolution in Planipapillus (Onychophora: Peripatopsidae): a phylogenetic approach to evolutionary dynamics and speciation.

Planipapillus, a clade of onychophorans from southeastern Australia, exhibits substantial chromosomal variation. In the context of a robust phylogeny based on nuclear and mitochondrial sequence data, we evaluate models of chromosomal evolution and speciation that differ in the roles assigned to selection, mutation, and drift. Permutation tests suggest that all chromosome rearrangements in the clade have been centric fusions and, on the basis of parsimony and maximum-likelihood methods with independent estimates of branch lengths, we conclude that at least 31 centric fusions have been fixed in Planipapillus. A likelihood-ratio test approach, which is independent of our point estimates of ancestral states, rejects an evolutionary model in which the mutation rate is constant and centric fusions are effectively neutral. In contrast to the nucleotide sequence data, which are consistent with neutrality and rate constancy, centric fusions in Planipapillus are underdominant, spontaneous fusion rates vary among lineages, or both. We predict an inverse relationship between rates of chromosomal evolution and historical population size. Chromosomal evolution may play a role in speciation in Planipapillus, both by interactions between centric fusions with monobrachial homology and by the accumulation of multiple weakly underdominant fusions.

Animals↗

PubMed2003

Estimation of divergence times for major lineages of primate species.

Although the phylogenetic relationships of major lineages of primate species are relatively well established, the times of divergence of these lineages as estimated by molecular data are still controversial. This controversy has been generated in part because different authors have used different types of molecular data, different statistical methods, and different calibration points. We have therefore examined the effects of these factors on the estimates of divergence times and reached the following conclusions: (1) It is advisable to concatenate many gene sequences and use a multigene gamma distance for estimating divergence times rather than using the individual gene approach. (2) When sequence data from many nuclear genes are available, protein sequences appear to give more robust estimates than DNA sequences. (3) Nuclear proteins are generally more suitable than mitochondrial proteins for time estimation. (4) It is important first to construct a phylogenetic tree for a group of species using some outgroups and then estimate the branch lengths. (5) It appears to be better to use a few reliable calibration points rather than many unreliable ones. Considering all these factors and using two calibration points, we estimated that the human lineage diverged from the chimpanzee, gorilla, orangutan, Old World monkey, and New World monkey lineages approximately 6 MYA (with a range of 5-7), 7 MYA (range, 6-8), 13 MYA (range, 12-15), 23 MYA (range, 21-25), and 33 MYA (range 32-36).

Animals↗

PubMed2006

How can third codon positions outperform first and second codon positions in phylogenetic inference? An empirical example from the seed plants.

Greater phylogenetic signal is often found in parsimony-based analyses of third codon positions of protein-coding genes relative to their corresponding first and second codon positions, even for early-derived ("basal") clades. We used the Soltis et al. (2000; Bot. J. Linn. Soc. 133:381-461) data matrix of atpB and rbcL from 567 seed plants to quantify how each of six factors (observed character-state space, frequencies of observed character states, substitution probabilities among nucleotides, rate heterogeneity among sites, overall rate of evolution, and number of parsimony-informative characters) contributed to this phenomenon. Each of these six factors was estimated from the original data matrix for parsimony-informative third codon positions considered separately from first and second codon positions combined. One of the most parsimonious trees found was used as the constraint topology; branch lengths were estimated using likelihood-based distances, and characters were simulated on this tree. Differential frequencies of observed character states were found to be the most limiting of the factors simulated for all three codon positions. Differential frequencies of observed character states and differential substitution probabilities among states were relatively advantageous for first and second codon positions. In contrast, differential numbers of observed character states, differential rate heterogeneity among sites, the greater number of parsimony-informative characters, and the higher overall rate of evolution were relatively advantageous for third codon positions. The amount of possible synapomorphy was predictive of the overall success of resolution.

Base Sequence↗

PubMed2005

Rooting a phylogenetic tree with nonreversible substitution models.

BACKGROUND: We compared two methods of rooting a phylogenetic tree: the stationary and the nonstationary substitution processes. These methods do not require an outgroup. METHODS: Given a multiple alignment and an unrooted tree, the maximum likelihood estimates of branch lengths and substitution parameters for each associated rooted tree are found; rooted trees are compared using their likelihood values. Site variation in substitution rates is handled by assigning sites into several classes before the analysis. RESULTS: In three test datasets where the trees are small and the roots are assumed known, the nonstationary process gets the correct estimate significantly more often, and fits data much better, than the stationary process. Both processes give biologically plausible root placements in a set of nine primate mitochondrial DNA sequences. CONCLUSIONS: The nonstationary process is simple to use and is much better than the stationary process at inferring the root. It could be useful for situations where an outgroup is unavailable.

Animals↗

PubMed1998

Phylogenetic analysis of reptilian hemoglobins: trees, rates, and divergences.

Phylogenetic relationships among reptiles were examined using previously published and newly determined hemoglobin sequences. Trees reconstructed from these sequences using maximum-parsimony, neighbor-joining, and maximum-likelihood algorithms were compared with a phylogenetic tree of Amniota, which was assembled on the basis of published morphological data. All analyses differentiated alpha chains into alphaA and alphaD types, which are present in all reptiles except crocodiles, where only alphaA chains are expressed. The occurrence of the alphaD chain in squamates (lizards and snakes only in this study) appears to be a general characteristic of these species. Lizards and snakes also express two types of beta chains (betaI and betaII), while only one type of beta chain is present in birds and crocodiles. Reconstructed hemoglobin trees for both alpha and beta sequences did not yield the monophyletic Archosauria (i.e., crocodilians + birds) and Lepidosauria (i.e., Sphenodon + squamates) groups defined by the morphology tree. This discrepancy, as well as some other poorly resolved nodes, might be due to substantial heterogeneity in evolutionary rates among single hemoglobin lineages. Estimation of branch lengths based on uncorrected amino acid substitutions and on distances corrected for multiple substitutions (PAM distances) revealed that relative rates for squamate alphaA and alphaD chains and crocodilian beta chains are at least twice as high as those of the rest of the chains considered. In contrast to these rate inequalities between reptilian orders, little variation was found within squamates, which allowed determination of absolute evolutionary rates for this subset of hemoglobins. Rate estimates for hemoglobins of lizards and snakes yielded 1.7 (alphaA) and 3.3 (beta) million years/PAM when calibrated with published divergence time vs. PAM distance correlates for several speciation events within snakes and for the squamate left and right arrow sphenodontid split. This suggests that hemoglobin chains of squamate reptiles evolved approximately 3.5 (alphaA) or approximately 1.7 times (beta) faster than their mammalian equivalents. These data also were used to obtain a first estimate of some intrasquamate divergence times.

Alligators and Crocodiles↗

PubMed1987

Nonuniformity of nucleotide substitution rates in molecular evolution: computer simulation and analysis of 5S ribosomal RNA sequences.

The effects of temporal (among different branches of a phylogeny) and spatial (among different nucleotide sites within a gene) nonuniformities of nucleotide substitution rates on the construction of phylogenetic trees from nucleotide sequences are addressed. Spatial nonuniformity may be estimated by using Shannon's (1948) entropy formula to measure the Relative Nucleotide Variability (RNV) at each nucleotide site in an aligned set of sequences; this is demonstrated by a comparative analysis of 5S rRNAs. New methods of constructing phylogenetic trees are proposed that augment the Unweighted Pair-Group Using Arithmetic Averages (UPGMA) algorithm by estimating and compensating for both spatial and temporal nonuniformity in substitution rates. These methods are evaluated by computer simulations of 5S rRNA evolution that include both kinds of nonuniformities. It was found that the proposed Reference Ratio Method improved both the ability to reconstruct the correct topology of a tree and also the estimation of branch lengths as compared to UPGMA. A previous method (Farris et al. 1970; Klotz et al. 1979; Li 1981) was found to be less successful in reconstructing topologies when there is high probability of multiple mutations at some sites. Phylogenetic analyses of 5S rRNA sequences support the endosymbiotic origins of both chloroplasts and mitochondria, even though the latter exhibit an accelerated rate of nucleotide substitution. Phylogenetic trees also reveal an adaptive radiation within the eubacteria and another within the eukaryotes for the origins of most major phyla within each group during the Precambrian era.

Animals↗

PubMed2006

The evolutionary radiation of Arvicolinae rodents (voles and lemmings): relative contribution of nuclear and mitochondrial DNA phylogenies.

BACKGROUND: Mitochondrial and nuclear genes have generally been employed for different purposes in molecular systematics, the former to resolve relationships within recently evolved groups and the latter to investigate phylogenies at a deeper level. In the case of rapid and recent evolutionary radiations, mitochondrial genes like cytochrome b (CYB) are often inefficient for resolving phylogenetic relationships. One of the best examples is illustrated by Arvicolinae rodents (Rodentia; Muridae), the most impressive mammalian radiation of the Northern Hemisphere which produced voles, lemmings and muskrats. Here, we compare the relative contribution of a nuclear marker--the exon 10 of the growth hormone receptor (GHR) gene--to the one of the mitochondrial CYB for inferring phylogenetic relationships among the major lineages of arvicoline rodents. RESULTS: The analysis of GHR sequences improves the overall resolution of the Arvicolinae phylogeny. Our results show that the Caucasian long-clawed vole (Prometheomys schaposnikowi) is one of the basalmost arvicolines, and confirm that true lemmings (Lemmus) and collared lemmings (Dicrostonyx) are not closely related as suggested by morphology. Red-backed voles (Myodini) are found as the sister-group of a clade encompassing water vole (Arvicola), snow vole (Chionomys), and meadow voles (Microtus and allies). Within the latter, no support is recovered for the generic recognition of Blanfordimys, Lasiopodomys, Neodon, and Phaiomys as suggested by morphology. Comparisons of parameter estimates for branch lengths, base composition, among sites rate heterogeneity, and GTR relative substitution rates indicate that CYB sequences consistently exhibit more heterogeneity among codon positions than GHR. By analyzing the contribution of each codon position to node resolution, we show that the apparent higher efficiency of GHR is due to their third positions. Although we focus on speciation events spanning the last 10 million years (Myr), CYB sequences display highly saturated codon positions contrary to the nuclear exon. Lastly, variable length bootstrap predicts a significant increase in resolution of arvicoline phylogeny through the sequencing of nuclear data in an order of magnitude three to five times greater than the size of GHR exon 10. CONCLUSION: Our survey provides a first resolved gene tree for Arvicolinae. The comparison of CYB and GHR phylogenetic efficiency supports recent assertions that nuclear genes are useful for resolving relationships of recently evolved animals. The superiority of nuclear exons may reside both in (i) less heterogeneity among sites, and (ii) the presence of highly informative sites in third codon positions, that evolve rapidly enough to accumulate synapomorphies, but slow enough to avoid substitutional saturation.

Animals↗

PubMed2002

Estimation of evolutionary parameters with phylogenetic trees.

An important issue in the phylogenetic analysis of nucleotide sequence data using the maximum likelihood (ML) method is the underlying evolutionary model employed. We consider the problem of simultaneously estimating the tree topology and the parameters in the underlying substitution model and of obtaining estimates of the standard errors of these parameter estimates. Given a fixed tree topology and corresponding set of branch lengths, the ML estimates of standard evolutionary model parameters are asymptotically efficient, in the sense that their joint distribution is asymptotically normal with the variance-covariance matrix given by the inverse of the Fisher information matrix. We propose a new estimate of this conditional variance based on estimation of the expected information using a Monte Carlo sampling (MCS) method. Simulations are used to compare this conditional variance estimate to the standard technique of using the observed information under a variety of experimental conditions. In the case in which one wishes to estimate simultaneously the tree and parameters, we provide a bootstrapping approach that can be used in conjunction with the MCS method to estimate the unconditional standard error. The methods developed are applied to a real data set consisting of 30 papillomavirus sequences. This overall method is easily incorporated into standard bootstrapping procedures to allow for proper variance estimation.

Animals↗

PubMed2003

Phylogenetically nested comparisons for testing correlates of species richness: a simulation study of continuous variables.

Explaining the uneven distribution of species among lineages is one of the oldest questions in evolution. Proposed correlations between biological traits and species diversity are routinely tested by making comparisons between phylogenetic sister clades. Several recent studies have used nested sister-clade comparisons to test hypotheses linking continuously varying traits, such as body size, with diversity. Evaluating the findings of these studies is complicated because they differ in the index of species richness difference used, the way in which trait differences were treated, and the statistical tests employed. In this paper, we use simulations to compare the performance of four species richness indices, two choices about the branch lengths used to estimate trait values for internal nodes and two statistical tests under a range of models of clade growth and character evolution. All four indices returned appropriate Type I error rates when the assumptions of the method were met and when branch lengths were set proportional to time. Only two of the indices were robust to the different evolutionary models and to different choices of branch lengths and statistical tests. These robust indices had comparable power under one nonnull scenario. Regression through the origin was consistently more powerful than the t-test, and the choice of branch lengths exerts a strong effect on both the validity and power. In the light of our simulations, we re-evaluate the findings of those who have previously used nested comparisons in the context of species richness. We provide a set of simple guidelines to maximize the performance of phylogenetically nested comparisons in tests of putative correlates of species richness.

Phylogeny↗

PubMed1986

Statistical properties of molecular tree construction methods under the neutral mutation model.

The statistical properties of three molecular tree construction methods--the unweighted pair-group arithmetic average clustering (UPG), Farris, and modified Farris methods--are examined under the neutral mutation model of evolution. The methods are compared for accuracy in construction of the topology and estimation of the branch lengths, using statistics of these two aspects. The distribution of the statistic concerning topological construction is shown to be as important as its mean and variance for the comparison. Of the three methods, the UPG method constructs the tree topology with the least variation. The modified Farris method, however, gives the best performance when the two aspects are considered simultaneously. It is also shown that a topology based on two genes is much more accurate than that based on one gene. There is a tendency to accept published molecular trees, but uncritical acceptance may lead one to spurious conclusions. It should always be kept in mind that a tree is a statistical result that is affected strongly by the stochastic error of nucleotide substitution and the error intrinsic to the tree construction method itself.

Biological Evolution↗

PubMed1989

Effectiveness of measures requiring and not requiring prior sequence alignment for estimating the dissimilarity of natural sequences.

Various measures of sequence dissimilarity have been evaluated by how well the additive least squares estimation of edges (branch lengths) of an unrooted evolutionary tree fit the observed pairwise dissimilarity measures and by how consistent the trees are for different data sets derived from the same set of sequences. This evaluation provided sensitive discrimination among dissimilarity measures and among possible trees. Dissimilarity measures not requiring prior sequence alignment did about as well as did the traditional mismatch counts requiring prior sequence alignment. Application of Jukes-Cantor correction to singlet mismatch counts worsened the results. Measures not requiring alignment had the advantage of being applicable to sequences too different to be critically alignable. Two different measures of pairwise dissimilarity not requiring alignment have been used: (1) multiplet distribution distance (MDD), the square of the Euclidean distance between vectors of the fractions of base signlets (or doublets, or triplets, or ...) in the respective sequences, and (2) complements of long words (CLW), the count of bases not occurring in significantly long common words. MDD was applicable to sequences more different than was CLW (noncoding), but the latter often gave better results where both measures were available (coding). MDD results were improved by using longer mutliplets and, if the sequences were coding, by using the larger amino acid and codon alphabets rather than the nucleotide alphabet. The additive least squares method could be used to provide a reasonable consensus of different trees for the same set of species (or related genes).

Animals↗

PubMed2004

Should we be worried about long-branch attraction in real data sets? Investigations using metazoan 18S rDNA.

Although long-branch attraction (LBA) is frequently cited as the cause of anomalous phylogenetic groupings, few examples of LBA involving real sequence data are known. We have found several cases of probable LBA by analyzing subsamples from an alignment of 18S rDNA sequences for 133 metazoans. In one example, maximum parsimony analysis of sequences from two rotifers, a ctenophore, and a polychaete annelid resulted in strong support for a tree grouping two "long-branch taxa" (a rotifer and the ctenophore). Maximum-likelihood analysis of the same sequences yielded strong support for a more biologically reasonable "rotifer monophyly" tree. Attempts to break up long branches for problematic subsamples through increased taxon sampling reduced, but did not eliminate, LBA problems. Exhaustive analyses of all quartets for a subset of 50 sequences were performed in order to compare the performance of maximum likelihood, equal-weights parsimony, and two additional variants of parsimony; these methods do differ substantially in their rates of failure to recover trees consistent with well established, but highly unresolved phylogenies. Power analyses using simulations suggest that some incorrect inferences by maximum parsimony are due to statistical inconsistency and that when estimates of central branch lengths for certain quartets are very low, maximum-likelihood analyses have difficulty recovering accepted phylogenies even with large amounts of data. These examples demonstrate that LBA problems can occur in real data sets, and they provide an opportunity to investigate causes of incorrect inferences.

Animals↗

PubMed2002

Whole-tree methods for detecting differential diversification rates.

Prolific cladogenesis, adaptive radiation, species selection, key innovations, and mass extinctions are a few examples of biological phenomena that lead to differential diversification among lineages. Central to the study of differential diversification rates is the ability to distinguish chance variation from that which requires deterministic explanation. To detect diversification rate variation among lineages, we propose a number of methods that incorporate information on the topological distribution of species diversity from all internal nodes of a phylogenetic tree. These whole-tree methods (M(Pi), M(Sigma), and M(R)) are explicitly connected to a null model of random diversification--the equal-rates Markov (ERM) random branching model--and an alternative model of differential diversification: M(Pi) is based on the product of individual nodal ERM probabilities; M(Sigma) is based on the sum of individual nodal ERM probabilities, and M(R) is based on a transformation of ERM probabilities that corresponds to a formalized system that orders trees by their relative symmetry. These methods have been implemented in a freely available computer program, SYMMETREE, to detect clades with variable diversification rates, thereby allowing the study of biological processes correlated with and possibly causal to shifts in diversification rate. Application of these methods to several published phylogenies demonstrates their ability to contend with relatively large, incompletely resolved trees. These topology-based methods do not require estimates of relative branch lengths, which should facilitate the analysis of phylogenies, such as supertrees, for which such data are unreliable or unavailable.

Animals↗

PubMed2004

Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation.

Currently available methods for model selection used in phylogenetic analysis are based on an initial fixed-tree topology. Once a model is picked based on this topology, a rigorous search of the tree space is run under that model to find the maximum-likelihood estimate of the tree (topology and branch lengths) and the maximum-likelihood estimates of the model parameters. In this paper, we propose two extensions to the decision-theoretic (DT) approach that relax the fixed-topology restriction. We also relax the fixed-topology restriction for the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) methods. We compare the performance of the different methods (the relaxed, restricted, and the likelihood-ratio test [LRT]) using simulated data. This comparison is done by evaluating the relative complexity of the models resulting from each method and by comparing the performance of the chosen models in estimating the true tree. We also compare the methods relative to one another by measuring the closeness of the estimated trees corresponding to the different chosen models under these methods. We show that varying the topology does not have a major impact on model choice. We also show that the outcome of the two proposed extensions is identical and is comparable to that of the BIC, Extended-BIC, and DT. Hence, using the simpler methods in choosing a model for analyzing the data is more computationally feasible, with results comparable to the more computationally intensive methods. Another outcome of this study is that earlier conclusions about the DT approach are reinforced. That is, LRT, Extended-AIC, and AIC result in more complicated models that do not contribute to the performance of the phylogenetic inference, yet cause a significant increase in the time required for data analysis.

Computational Biology↗

PubMed1998

Population differentiation through mutation and drift--a comparison of genetic identity measures.

Different genetic identity or distance measures are compared that consider allelic variation within and between populations. Particularily we analyse those suggested by Nei (IS, DS), Rogers (DR), Reynolds, Weir and Cockerham (D theta), Nei, Tajima and Tateno (DA), Tomiuk and Loeschcke (ITL, DTL) and Goldstein et al. ((delta mu)2). The simulations focus on the influence of non-equilibrium conditions on the stability of these measures. The degree of homozygosity of an ancestral population before it splits into two sister populations is most important for the stability of the different estimates of genetic identity. If populations are not close to their equilibrium homozygosity, a considerable bias can occur and, thereby, provide very misleading estimates of the time span since divergence. The ITL-measure based on estimates of ancestral alleles is more robust than other measures of genetic identity, especially for large population sizes and high mutation rates. For the infinite allele model, the analysis shows that more precise estimates of the frequency of ancestral alleles can greatly improve the reliability of the estimate of genetic identity in the case of ITL. For the stepwise mutation model, the TL-measure combines the attributes of the DA- and (delta mu)2-measures. The TL-measure is efficient for the construction of the correct tree topology of related populations as well as for the estimation of the branch length when protein or microsatellite data are analysed.

Alleles↗

PubMed1994

A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates.

Using simulated data, we compared five methods of phylogenetic tree estimation: parsimony, compatibility, maximum likelihood, Fitch-Margoliash, and neighbor joining. For each combination of substitution rates and sequence length, 100 data sets were generated for each of 50 trees, for a total of 5,000 replications per condition. Accuracy was measured by two measures of the distance between the true tree and the estimate of the tree, one measure sensitive to accuracy of branch lengths and the other not. The distance-matrix methods (Fitch-Margoliash and neighbor joining) performed best when they were constrained from estimating negative branch lengths; all comparisons with other methods used this constraint. Parsimony and compatibility had similar results, with compatibility generally inferior; Fitch-Margoliash and neighbor joining had similar results, with neighbor joining generally slightly inferior. Maximum likelihood was the most successful method overall, although for short sequences Fitch-Margoliash and neighbor joining were sometimes better. Bias of the estimates was inferred by measuring whether the independent estimates of a tree for different data sets were closer to the true tree than to each other. Parsimony and compatibility had particular difficulty with inaccuracy and bias when substitution rates varied among different branches. When rates of evolution varied among different sites, all methods showed signs of inaccuracy and bias.

Algorithms↗