A likelihood approach to character weighting and what it tells us about parsimony and compatibility

The statistical framework of maximum likelihood estimation is used to examine character weighting in inferring phylogenies. A simple probabilistic model of evolution is used, in which each character evolves independently among two states, and different lineages evolve independently. When different characters have different known probabilities of change, all sufficiently small, the proper maximum likelihood method of estimating phylogenies is a weighted parsimony method in which the weights are logarithmically related to the rates of change. When rates of change are taken extremely small, the weights become more equal and unweighted parsimony methods are obtained.
When it is known that a few characters have very high rates of change and the rest very low rates, but it is not known which characters are the ones having the high rates, the maximum likelihood criterion supports use of compatibility methods. By varying the fraction of characters believed to have high rates of change one obtains a 'threshold method' whose behavior depends on the value of a parameter. By altering this parameter the method changes smoothly from being a parsimony method to being a compatibility method. This provides us with a spectrum of intermediates between these methods. These intermediate methods may be of use in analysing real data.     

Probabilistic methods outperform parsimony in the phylogenetic analysis of data simulated without a probabilistic model

To understand patterns and processes of the diversification of life, we require an accurate understanding of taxon interrelationships. Recent studies have suggested that analyses of morphological character data using the Bayesian and maximum likelihood Mk model provide phylogenies of higher accuracy compared to parsimony methods. This has proved controversial, particularly studies simulating morphology‐data under Markov models that assume shared branch lengths for characters, as it is claimed this leads to bias favouring the Bayesian or maximum likelihood Mk model over parsimony models which do not explicitly make this assumption. We avoid these potential issues by employing a simulation protocol in which character states are randomly assigned to tips, but datasets are constrained to an empirically realistic distribution of homoplasy as measured by the consistency index. Datasets were analysed with equal weights and implied weights parsimony, and the maximum likelihood and Bayesian Mk model. We find that consistent (low homoplasy) datasets render method choice largely irrelevant, as all methods perform well with high consistency (low homoplasy) datasets, but the largest discrepancies in accuracy occur with low consistency datasets (high homoplasy). In such cases, the Bayesian Mk model is significantly more accurate than alternative models and implied weights parsimony never significantly outperforms the Bayesian Mk model. When poorly supported branches are collapsed, the Bayesian Mk model recovers trees with higher resolution compared to other methods. As it is not possible to assess homoplasy independently of a tree estimate, the Bayesian Mk model emerges as the most reliable approach for categorical morphological analyses.     

A Bayesian perspective on a non-parsimonious parsimony model

Several stochastic models of character change, when implemented in a maximum likelihood framework, are known to give a correspondence between the maximum parsimony method and the method of maximum likelihood. One such model has an independently estimated branch-length parameter for each site and each branch of the phylogenetic tree. This model--the no-common-mechanism model--has many parameters, and, in fact, the number of parameters increases as fast as the alignment is extended. We take a Bayesian approach to the no-common-mechanism model and place independent gamma prior probability distributions on the branch-length parameters. We are able to analytically integrate over the branch lengths, and this allowed us to implement an efficient Markov chain Monte Carlo method for exploring the space of phylogenetic trees. We were able to reliably estimate the posterior probabilities of clades for phylogenetic trees of up to 500 sequences. However, the Bayesian approach to the problem, at least as implemented here with an independent prior on the length of each branch, does not tame the behavior of the branch-length parameters. The integrated likelihood appears to be a simple rescaling of the parsimony score for a tree, and the marginal posterior probability distribution of the length of a branch is dependent upon how the maximum parsimony method reconstructs the characters at the interior nodes of the tree. The method we describe, however, is of potential importance in the analysis of morphological character data and also for improving the behavior of Markov chain Monte Carlo methods implemented for models in which sites share a common branch-length parameter.     

Distinguishing Felsenstein Zone from Farris Zone Using Neural Networks

Maximum likelihood and maximum parsimony are two key methods for phylogenetic tree reconstruction. Under certain conditions, each of these two methods can perform more or less efficiently, resulting in unresolved or disputed phylogenies. We show that a neural network can distinguish between four-taxon alignments that were evolved under conditions susceptible to either long-branch attraction or long-branch repulsion. When likelihood and parsimony methods are discordant, the neural network can provide insight as to which tree reconstruction method is best suited to the alignment. When applied to the contentious case of Strepsiptera evolution, our method shows robust support for the current scientific view, that is, it places Strepsiptera with beetles, distant from flies.     

A likelihood approach to estimating phylogeny from discrete morphological character data

Evolutionary biologists have adopted simple likelihood models for purposes of estimating ancestral states and evaluating character independence on specified phylogenies; however, for purposes of estimating phylogenies by using discrete morphological data, maximum parsimony remains the only option. This paper explores the possibility of using standard, well-behaved Markov models for estimating morphological phylogenies (including branch lengths) under the likelihood criterion. An important modification of standard Markov models involves making the likelihood conditional on characters being variable, because constant characters are absent in morphological data sets. Without this modification, branch lengths are often overestimated, resulting in potentially serious biases in tree topology selection. Several new avenues of research are opened by an explicitly model-based approach to phylogenetic analysis of discrete morphological data, including combined-data likelihood analyses (morphology + sequence data), likelihood ratio tests, and Bayesian analyses.     

Computational complexity of inferring phylogenies from chromosome inversion data

In systematics, parsimony methods construct phylogenies, or evolutionary trees, in which characters evolve with the least evolutionary change. The chromosome inversion, or polymorphism, parsimony criterion is used when each character of a population may exhibit homozygous or heterozygous states, but when the heterozygous state must evolve uniquely. Variations of the criterion concern whether or not the ancestral states of characters are specified. We establish that problems of inferring phylogenies by these criteria are NP-complete and thus are so difficult computationally that efficient optimal algorithms for them are unlikely to exist.     

Stochastic mapping of morphological characters

Many questions in evolutionary biology are best addressed by comparing traits in different species. Often such studies involve mapping characters on phylogenetic trees. Mapping characters on trees allows the nature, number, and timing of the transformations to be identified. The parsimony method is the only method available for mapping morphological characters on phylogenies. Although the parsimony method often makes reasonable reconstructions of the history of a character, it has a number of limitations. These limitations include the inability to consider more than a single change along a branch on a tree and the uncoupling of evolutionary time from amount of character change. We extended a method described by Nielsen (2002, Syst. Biol. 51:729-739) to the mapping of morphological characters under continuous-time Markov models and demonstrate here the utility of the method for mapping characters on trees and for identifying character correlation.     

Inference of phylogenetic relationships among key angiosperm lineages using a compatibility method on a molecular data set

Phylogenetic relationships among the five key angiosperm lineages,Ceratophyllum,Chloranthaceae,eudicots,magnoliids,and monocots,have resisted resolution despite several large-scale analyses sampling taxa and characters extensively and using various analytical methods.Meanwhile,compatibility methods,which were explored together with parsimony and likelihood methods during the early development stage of phylogenetics.have been greatly under-appreciated and not been used to analyze the massive amount of sequence data to reconstruct thye basal angiosperm phylogeny.In this study,we used a compatibility method on a data set of eight genes (mitochondrial atp1,matR,and nad5,plastid atpB,marK,rbcL,and rpoC2,and nuclear 18S rDNA)gathered in an earlier study.We selected two sets of characters that are compatible with more of the other characters than a random character would be with at probabilities of pM＜0.1 and p＜0.5 respectively.The resulting data matrices were subjected to parsimony and likelihood bootstrap analyses.Our unrooted parsimony analyses showed that Ceratophyllum was immediately related to eudicots,this larger lineage was immediately related to magnoliids,and monocots were closely related to Chloranthaceae.All these relationships received 76%-96% bootstrap support.A likelihood analysis of the 8 gene pM＜0.5 compatible site matrix recovered the same topology but with low support.Likelihood analyses of other compatible site matrices produced different topologies that were all weakly supported.The topology reconstructed in the parsimony analyses agrees with the one recovered in the previous study using both parsimony and likelihood methods when no character was eliminated.Parts of this topology have also been recovered in several earlier studies.Hence,this topology plausibly reflects the true relationships among the five key angiosperm lineages.     

Reconstructing phylogenies from allozyme data: comparing method performance with congruence

Allozyme data are widely used to infer the phylogenies of populations and closely-related species. Numerous parsimony, distance, and likelihood methods have been proposed for phylogenetic analysis of these data; the relative merits of these methods have been debated vigorously, but their accuracy has not been well explored. In this study, I compare the performance of 13 phylogenetic methods (six parsimony, six distance, and continuous maximum likelihood) by applying a congruence approach to eight allozyme data sets from the literature. Clades are identified that are supported by multiple data sets other than allozymes (e.g. morphology, DNA sequences), and the ability of different methods to recover these 'known' clades is compared. The results suggest that (1) distance and likelihood methods generally outperform parsimony methods, (2) methods that utilize frequency data tend to perform well, and (3) continuous maximum likelihood is among the most accurate methods, and appears to be robust to violations of its assumptions. These results are in agreement with those from recent simulation studies, and help provide a basis for empirical workers to choose among the many methods available for analysing allozyme characters.     

The limitations of ancestral state reconstruction and the evolution of the ascus in the Lecanorales (lichenized Ascomycota)

Ancestral state reconstructions of morphological or ecological traits on molecular phylogenies are becoming increasingly frequent. They rely on constancy of character state change rates over trees, a correlation between neutral genetic change and phenotypic change, as well as on adequate likelihood models and (for Bayesian methods) prior distributions. This investigation explored the outcomes of a variety of methods for reconstructing discrete ancestral state in the ascus apex of the Lecanorales, a group containing the majority of lichen-forming ascomycetes. Evolution of this character complex has been highly controversial in lichen systematics for more than two decades. The phylogeny was estimated using Bayesian Markov chain Monte Carlo inference on DNA sequence alignments of three genes (small subunit of the mitochondrial rDNA, large subunit of the nuclear rDNA, and largest subunit of RNA polymerase II). We designed a novel method for assessing the suitable number of discrete gamma categories, which relies on the effect on phylogeny estimates rather than on likelihoods. Ancestral state reconstructions were performed using maximum parsimony and maximum likelihood on a posterior tree sample as well as two fully Bayesian methods. Resulting reconstructions were often strikingly different depending on the method used; different methods often assign high confidence to different states at a given node. The two fully Bayesian methods disagree about the most probable reconstruction in about half of the nodes, even when similar likelihood models and similar priors are used. We suggest that similar studies should use several methods, awaiting an improved understanding of the statistical properties of the methods. A Lecanora-type ascus may have been ancestral in the Lecanorales. State transformations counts, obtained using stochastic mapping, indicate that the number of state changes is 12 to 24, which is considerably greater than the minimum three changes needed to explain the four observed ascus apex types. Apparently, the ascus in the Lecanorales is far more apt to change than has been recognized. Phylogeny corresponds well with morphology, although it partly contradicts currently used delimitations of the Crocyniaceae, Haematommataceae, Lecanoraceae, Megalariaceae, Mycoblastaceae, Pilocarpaceae, Psoraceae, Ramalinaceae, Scoliciosporaceae, and Squamarinaceae.     

Corroboration versus "Strongest Evidence"

Background knowledge comprises accepted (well-corroborated) theories and results. Such theories are taken to be true for the purpose of interpreting evidence when assessing the corroboration of a hypothesis currently in question. Accordingly, background knowledge does not properly include rejected theories, false assumptions, or null models. In particular, regarding a model of random character distribution as "background knowledge" would rule out corroboration of phylogenetic hypotheses, since it would make character data irrelevant to inferring phylogeny. The presence of homoplasy is not grounds for treating characters as if they were randomly distributed, since characters can show strong phylogenetic structure even when they show homoplasy. This means that clique (compatibility) analysis is unjustified, since that method depends crucially on the assumption that characters showing any homoplasy at all are unrelated to phylogeny. Although likelihood does not measure corroboration, corroboration is closely connected to likelihood: for given evidence and background, the most likely trees are also best corroborated. Most parsimonious trees are best corroborated; the apparent clash between parsimony and likelihood is an artifact of the use of unrealistic models in most "maximum likelihood" methods.     

CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP

The recently-developed statistical method known as the “bootstrap” can be used to place confidence intervals on phylogenies. It involves resampling points from one's own data, with replacement, to create a series of bootstrap samples of the same size as the original data. Each of these is analyzed, and the variation among the resulting estimates taken to indicate the size of the error involved in making estimates from the original data. In the case of phylogenies, it is argued that the proper method of resampling is to keep all of the original species while sampling characters with replacement, under the assumption that the characters have been independently drawn by the systematist and have evolved independently. Majority-rule consensus trees can be used to construct a phylogeny showing all of the inferred monophyletic groups that occurred in a majority of the bootstrap samples. If a group shows up 95% of the time or more, the evidence for it is taken to be statistically significant. Existing computer programs can be used to analyze different bootstrap samples by using weights on the characters, the weight of a character being how many times it was drawn in bootstrap sampling. When all characters are perfectly compatible, as envisioned by Hennig, bootstrap sampling becomes unnecessary; the bootstrap method would show significant evidence for a group if it is defined by three or more characters.     

THE ACCURACY OF PHYLOGENETIC ESTIMATION USING THE NEIGHBOR-JOINING METHOD

We studied the factors affecting the accuracy of the neighbor-joining (NJ) method for estimating phylogenies by simulating character change under different evolutionary models applied to twenty different 8-OTU tree topologies that varied widely with respect to tree imbalance and stemminess. The models incorporated three evolutionary rates—constant, varying among lineages, varying among characters—and three evolutionary contexts concerning patterns of character change relative to speciation events—phyletic, speciational, and punctuational. All combinations of the rate and context models were studied. In addition, three different absolute rates of change were investigated. To measure the accuracy, the strict consensus index was computed between the estimated tree and the tree topology along which the data had been generated. The results were analyzed by analysis of variance and compared to a previous study that evaluated UPGMA clustering and maximum parsimony (MP) as phylogenetic estimation techniques. We found evolutionary context and tree imbalance to be the most important factors affecting the accuracy of the NJ method. NJ was more accurate than UPGMA or MP in terms of the average strict consensus index over all treatments. However, no one method was more accurate than the other two for all combinations of treatments. Higher absolute rate of change generally resulted in higher accuracy for all three methods.     

Evolution of micromorphological and chemical characters in the lichen-forming fungal family Pertusariaceae

Micromorphological characters of the fruiting bodies, such as ascus-type and hymenial amyloidity, and secondary chemistry have been widely employed as key characters in Ascomycota classification. However, the evolution of these characters has yet not been studied using molecular phylogenies. We have used a combined Bayesian and maximum likelihood based approach to trace character evolution on a tree inferred from a combined analysis of nuclear and mitochondrial ribosomal DNA sequences. The maximum likelihood aspect overcomes simplifications inherent in maximum parsimony methods, whereas the Markov chain Monte Carlo aspect renders results independent of any particular phylogenetic tree. The results indicate that the evolution of the two chemical characters is quite different, being stable once developed for the medullary lecanoric acid, whereas the cortical chlorinated xanthones appear to have been lost several times. The current ascus-types and the amyloidity of the hymenial gel in Pertusariaceae appear to have been developed within the family. The basal ascus-type of pertusarialean fungi remains unknown.  © 2006 The Linnean Society of London, Biological Journal of the Linnean Society , 2006, 89 , 615–626.     

Efficacy or convenience? Model‐based approaches to phylogeny estimation using morphological data

Model‐based approaches (e.g. maximum likelihood, Bayesian inference) are widely used with molecular data, where they might be more appropriate than maximum parsimony for estimating phylogenies under various models of molecular evolution. Recently, there has been an increase in the application of model‐based approaches with morphological (mainly fossil) data; however, there is some doubt as to the effectiveness of the model of morphological evolution. The input parameters (prior probabilities) for the model are unclear, particularly when concerned with unobserved character states. Despite this, some systematists are suggesting superiority of these model‐based methods over maximum parsimony based on, for example, increased resolution or, in the current study, the preferred phylogenetic placement of an iconic taxon. Here, we revisit a recently published analysis implying such superiority and document the discrepancies between parsimony‐based and model‐based approaches to phylogeny estimation. We find that although some taxa are shifted back to their “traditional” phylogenetic placement, other clades are disturbed. The model‐based phylogenies are better resolved; however, due to the lack of an appropriate model of morphological evolution, the increase in resolving power is probably not meaningful. Similarly, some of the preferred phylogenetic positions of taxa, particularly of labile taxa such as Archaeopteryx, are based solely on analyses employing maximum parsimony as the optimality criterion. Poor resolution and labile taxa indicate a need for further examination of the morphology and not a change in method.     

Weighted parsimony outperforms other methods of phylogenetic inference under models appropriate for morphology

One of the lasting controversies in phylogenetic inference is the degree to which specific evolutionary models should influence the choice of methods. Model‐based approaches to phylogenetic inference (likelihood, Bayesian) are defended on the premise that without explicit statistical models there is no science, and parsimony is defended on the grounds that it provides the best rationalization of the data, while refraining from assigning specific probabilities to trees or character‐state reconstructions. Authors who favour model‐based approaches often focus on the statistical properties of the methods and models themselves, but this is of only limited use in deciding the best method for phylogenetic inference—such decision also requires considering the conditions of evolution that prevail in nature. Another approach is to compare the performance of parsimony and model‐based methods in simulations, which traditionally have been used to defend the use of models of evolution for DNA sequences. Some recent papers, however, have promoted the use of model‐based approaches to phylogenetic inference for discrete morphological data as well. These papers simulated data under models already known to be unfavourable to parsimony, and modelled morphological evolution as if it evolved just like DNA, with probabilities of change for all characters changing in concert along tree branches. The present paper discusses these issues, showing that under reasonable and less restrictive models of evolution for discrete characters, equally weighted parsimony performs as well or better than model‐based methods, and that parsimony under implied weights clearly outperforms all other methods.     

A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates [published erratum appears in Mol Biol Evol 1995 May;12(3):525]

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.      

追溯山茱萸科植物的性状进化和生物地理学历史——方法选择的影响?

This study compares results on reconstructing the ancestral state of characters and ancestral areas of distribution in Cornaceae to gain insights into the impact of using different analytical methods. Ancestral character state reconstructions were compared among three methods (parsimony, maximum likelihood, and stochastic character mapping) using MESQUITE and a full Bayesian method in BAYESTRAITS and inferences of ancestral area distribution were compared between the parsimony-based dispersal-vicariance analysis (DIVA) and a newly developed maximum likelihood (ML) method. Results indicated that among the six inflorescence and fruit characters examined, "perfect" binary characters (no homoplasy, no polymorphism within terminals, and no missing data) are little affected by choice of method, while homoplasious characters and missing data are sensitive to methods used. Ancestral areas at deep nodes of the phylogeny are substantially different between DIVA and ML and strikingly different between analyses including and excluding fossils at three deepest nodes. These results, while raising caution in making conclusions on trait evolution and historical biogeography using conventional methods, demonstrate a limitation in our current understanding of character evolution and biogeography. The biogeographic history favored by the ML analyses including fossils suggested the origin and early radiation of Cornus likely occurred in the late Cretaceous and earliest Tertiary in Europe and intercontinental disjunctions in three lineages involved movements across the North Atlantic Land Bridge (BLB) in the early and mid Tertiary. This result is congruent with the role of NALB for post-Eocene migration and in connecting tropical floras in North America and Africa, and in eastern Asia and South America. However, alternative hypotheses with an origin in eastern Asia and early Trans-Beringia migrations of the genus cannot be ruled out.     

Stability of characters and construction of phylogenetic trees.

Parsimony methods infer phylogenetic trees by minimizing number of character changes required to explain observed character states. From the perspective of applicability of parsimony methods, it is important to assess whether the characters used to infer phylogeny are likely to provide a correct tree. We introduce a graph theoretical characterization that helps to assess whether given set of characters is appropriate to use with parsimony methods. Given a set of characters and a set of taxa, we construct a network called character overlap graph. We show that the character overlap graph for characters that are appropriate to use in parsimony methods is characterized by significant under-representation of subnetworks known as holes, and provide a validation for this observation. This characterization explains success in constructing evolutionary trees using parsimony method for some characters (e.g., protein domains) and lack of such success for other characters (e.g., introns). In the latter case, the understanding of obstacles to applying parsimony methods in a direct way has lead us to a new approach for detecting inconsistent and/or noisy data. Namely, we introduce the concept of stable characters which is similar but less restrictive than the well known concept of pairwise compatible characters. Application of this approach to introns produces the evolutionary tree consistent with the Coelomata hypothesis.