Weighting against homoplasy improves phylogenetic analysis of morphological data sets

The problem of character weighting in cladistic analysis is revisited. The finding that, in large molecular data sets, removal of third positions (with more homoplasy) decreases the number of well supported groups has been interpreted by some authors as indicating that weighting methods are unjustified. Two arguments against that interpretation are advanced. Characters that collectively determine few well‐supported groups may be highly reliable when taken individually (as shown by specific examples), so that inferring greater reliability for sets of characters that lead to an increase in jackknife frequencies may not always be warranted. But even if changes in jackknife frequencies can be used to infer reliability, we demonstrate that jackknife frequencies in large molecular data sets are actually improved when downweighting characters according to their homoplasy but using properly rescaled functions (instead of the very strong standard functions, or the extreme of inclusion/exclusion); this further weakens the argument that downweighting homoplastic characters is undesirable. Last, we show that downweighting characters according to their homoplasy (using standard homoplasy‐weighting methods) on 70 morphological data sets (with 50–170 taxa), produces clear increases in jackknife frequencies. The results obtained under homoplasy weighting also appear more stable than results under equal weights: adding either taxa or characters, when weighting against homoplasy, produced results more similar to original analyses (i.e., with larger numbers of groups that continue being supported after addition of taxa or characters), with similar or lower error rates (i.e., proportion of groups recovered that subsequently turn out to be incorrect). Therefore, the same argument that had been advanced against homoplasy weighting in the case of large molecular data sets is an argument in favor of such weighting in the case of morphological data sets. © The Willi Hennig Society 2008.     

Implied weighting and its utility in palaeontological datasets: a study using modelled phylogenetic matrices

Implied weighting, a method for phylogenetic inference that actively seeks to downweight supposed homoplasy, has in recent years begun to be widely utilized in palaeontological datasets. Given the method's purported ability at handling widespread homoplasy/convergence, we investigate the effects of implied weighting on modelled phylogenetic data. We generated 100 character matrices consisting of 55 characters each using a Markov Chain morphology model of evolution based on a known phylogenetic tree. Rates of character evolution in these datasets were variable and generated by pulling from a gamma distribution for each character in the matrix. These matrices were then analysed under equal weighting and four settings of implied weights (k = 1, 3, 5, and 10). Our results show that implied weighting is inconsistent in its ability to retrieve a known phylogenetic tree. Equally weighted analyses are found to generally be more conservative, retrieving higher frequency of polytomies but being less likely to generate erroneous topologies. Implied weighting is found to generally resolve polytomies while also propagating errors, resulting in an increase in both correctly and incorrectly resolved nodes with a tendency towards higher rates of error compared to equal weighting. Our results suggest that equal weights may be a preferable method for parsimony analysis.     

The impact of missing data on real morphological phylogenies: influence of the number and distribution of missing entries

Here we explore the effect of missing data in phylogenetic analyses using a large number of real morphological matrices. Different percentages and patterns of missing entries were added to each matrix, and their influence was evaluated by comparing the accuracy and error of most parsimonious trees. The relationships between accuracy and error and different parameters (e.g. the number of taxa and characters, homoplasy, support) were also evaluated. Our findings, based on real matrices, agree with the simulation studies, i.e. the negative effect increases with the percentage of missing entries, and decreases with the addition of more characters. This indicates that the main problem is the lack of information, not just the presence of missing data per se. Accuracy varies with different distribution patterns of missing entries; the worst case is when missing data are concentrated in a few taxa, while the best is when the missing entries are restricted to just a few characters. The results expand our knowledge of the missing data problem, corroborate many of the findings previously published using simulations, and could be useful for empirical or theoretical studies. © The Willi Hennig Society 2009.     

Misleading results of likelihood‐based phylogenetic analyses in the presence of missing data

The amount of missing data in many contemporary phylogenetic analyses has substantially increased relative to previous norms, particularly in supermatrix studies that compile characters from multiple previous analyses. In such cases the missing data are non‐randomly distributed and usually present in all partitions (i.e. groups of characters) sampled. Parametric methods often provide greater resolution and support than parsimony in such cases, yet this may be caused by extrapolation of branch lengths from one partition to another. In this study I use contrived and simulated examples to demonstrate that likelihood, even when applied to simple matrices with little or no homoplasy, homogeneous evolution across groups of characters, perfect model fit, and hundreds or thousands of variable characters, can provide strong support for incorrect topologies when the matrices have non‐random distributions of missing data distributed across all partitions. I do so using a systematic exploration of alternative seven‐taxon tree topologies and distributions of missing data in two partitions to demonstrate that these likelihood‐based artefacts may occur frequently and are not shared by parsimony. I also demonstrate that Bayesian Markov chain Monte Carlo analysis is more robust to these artefacts than is likelihood. © The Willi Hennig Society 2011.     

Semi-strict supertrees

A method to calculate semi‐strict supertrees is proposed. The semi‐strict supertrees are calculated by creating the matrix that represents all the groups in the source trees (as done in already existing techniques), and then finding the trees determined by the ultra‐clique. The ultra‐clique is defined as the set of characters where each possible subset is compatible with each possible subset from the entire matrix. Finding the ultra‐clique is computationally complex (since in most cases many of the characters have missing entries), but a heuristic method yields reliable results. When the trees have no conflict, or when there are only two trees, the method produces the exact result for any ordering of the input trees and any ordering of the groups within them; when there are more than two trees and they have conflict, a single ordering or sequence can create some spurious groups, but doing multiple sequences eliminates the spurious groups. The method uses only state set operations, and is thus easily implemented in computer programs. Unlike any existing type of supertree, semi‐strict supertrees display all the groups, and only those groups, that are implied by at least some combination of the input trees and contradicted by none. The idea that supertrees should take into account the number of occurences of a given group, so as to retain some groups even in the case of conflict, is discussed; it is argued that a conceptual equivalent of the majority rule consensus is not possible when the sets of taxa differ among trees. Also, when pruning taxa from a set of trees, the supertree can display groups that contradict the consensus for the entire trees, suggesting that supertrees for matrices with very dissimilar sets of taxa should be interpreted with caution. If (for any valid reason) the data cannot be combined in a single matrix, it is advisable that the taxon sets in the matrices be as similar as possible.     

Combined phylogenetic analysis of the subclass Marchantiidae (Marchantiophyta): towards a robustly diagnosed classification

The most extensive combined phylogenetic analyses of the subclass Marchantiidae yet undertaken was conducted on the basis of morphological and molecular data. The morphological data comprised 126 characters and 56 species. Taxonomic sampling included 35 ingroup species with all genera and orders of Marchantiidae sampled, and 21 outgroup species with two genera of Blasiidae (Marchantiopsida), 15 species of Jungermanniopsida (the three subclasses represented) and the three genera of Haplomitriopsida. Takakia ceratophylla (Bryophyta) was employed to root the trees. Character sampling involved 92 gametophytic and 34 sporophytic traits, supplemented with ten continuous characters. Molecular data included 11 molecular markers: one nuclear ribosomal (26S), three mitochondrial genes (nad1, nad5, rps3) and seven chloroplast regions (atpB, psbT‐psbH, rbcL, ITS, rpoC1, rps4, psbA). Searches were performed under extended implied weighting, weighting the character blocks against the average homoplasy. Clade stability was assessed across three additional weighting schemes (implied weighting corrected for missing entries, standard implied weighting and equal weighting) in three datasets (molecular, morphological and combined). The contribution from different biological phases regarding node recovery and diagnosis was evaluated. Our results agree with many of the previous studies but cast doubt on some relationships, mainly at the family and interfamily level. The combined analyses underlined the fact that, by combining data, taxonomic enhancements could be achieved regarding taxon delimitation and quality of diagnosis. Support values for many clades of previous molecular studies were improved by the addition of morphological data. The long‐held assumption that morphology may render spurious or low‐quality results in this taxonomic group is challenged. The morphological trends previously proposed are re‐evaluated in light of the new phylogenetic scheme.     

Phylogeny of the genera of the parasitic wasps subfamily Doryctinae (Hymenoptera: Braconidae) based on morphological evidence

The evolutionary relationships among most (143 genera) of the currently recognized genera of the braconid wasp subfamily Doryctinae were investigated using maximum parsimony analysis, employing 100 characters from external morphology and four additional, less well‐studied character systems (male genitalia, ovipositor structure, venom apparatus and larval cephalic structure). We investigated the ‘performance’ of characters from external morphology and the other character systems and the effects of abundant missing entries by comparing the data decisiveness, retention and consistency indices of four different character partitions. The results indicate that the performances of the different partitions are not related to the proportions of missing entries, but instead are negatively correlated to their proportion of informative characters, suggesting that the morphological information in this group is subject to high levels of homoplasy. The external morphological partition is significantly incongruent with respect to a data set comprising the other character systems based on the ILD test. Analyses supported neither the monophyly of the large tribes Doryctini and Hecabolini, nor the monophyly of the Spathiini and Heterospilini. Relationships obtained from successive approximation weighting analysis for the complete data differ considerably from the currently accepted tribal and subtribal classifications. The only exceptions were the Ypsistocerini and the Ecphylini, whose recognized members were recovered in single clades. A close relationship between the Binaerini and Holcobraconini, and also Monarea, is consistently supported by venom apparatus and ovipositor structure characters but is not indicated by external morphological data. Low bootstrap values obtained for most of the recovered clades in all analyses do not allow us to propose a meaningful reclassification for the group at this time. A complete list of the recognized genera and their synonymies is given. © 2004 The Linnean Society of London, Zoological Journal of the Linnean Society, 2004, 142 , 369–404.     

Adult and early‐stage characters of Brassolini contain conflicting phylogenetic signal (Lepidoptera,Nymphalidae)

This study examines the contribution of early‐stages and adult characters to the reconstruction of the phylogeny of Brassolini butterflies. Parsimony analyses used both equal weights and implied weights, and a series of analyses were performed. First, we analysed adult and early‐stages partitions independently and in combination for a subset of 27 species; in these cases the matrices were mostly complete. Whereas the adult partition alone produced a topology that was well resolved and congruent with previous studies, the early‐stages partition produced a poorly resolved tree under equal weights. Furthermore, implied weights produced a well‐resolved early‐stages topology that differed significantly from the adult topology. When both partitions were combined for 27 species, implied weights yielded a topology that resembled the adult tree except for the positions of Bia and Penetes, but statistical node support was generally lower. This suggests that stochastic noise increased when early‐stage characters were added to the adult partition, but the combined partitions topology was not statistically different from that based on adult characters alone. Second, given that preserved early stages are not as readily available as adults, we analysed a matrix including 45 species in which early‐stage data were missing for 18 species, and compared the topology to that produced by the adult partition alone. Results were similar to the analyses including fewer species; the combined partitions tree was similar to that from the adult partition except for the position of Bia and Penetes. We compare our findings to other genus‐level phylogenetic studies within Lepidoptera that have also used early‐stages and adult characters.     

ESTIMATING CHARACTER WEIGHTS DURING TREE SEARCH

Abstract— A new method for weighting characters according to their homoplasy is proposed; the method is non-iterative and does not require independent estimations of weights. It is based on searching trees with maximum total fit, with character fits defined as a concave function of homoplasy. Then, when comparing trees, differences in steps occurring in characters which show more homoplasy on the trees are less influential. The reliability of the characters is estimated, during the analysis, as a logical implication of the trees being compared. The "fittest" trees imply that the characters are maximally reliable and, given character conflict, have fewer steps for the characters which fit the tree better. If other trees save steps in some characters, it will be at the expense of gaining them in characters with less homoplasy.     

The phylogeny of Hildoceratidae (Cephalopoda,Ammonitida) resolved by an integrated coding scheme of the conch

Ammonite phylogeny has mainly been established based on a stratigraphic approach, with cladistics underconsidered. The main arguments against the use of cladistics are the supposed large amount of homoplasy and the small number of characters. Resolving the phylogeny of the Hildoceratidae (Early Jurassic) is especially challenging because of its large diversity and disparity. Many forms that have not been determined as closely related in previous studies exhibit very similar shapes. Moreover, some groups are morphologically very different, adding difficulties to building a unique coding scheme at a low taxonomic resolution (i.e. species). Here we propose an integrated coding scheme of the peristome shape and the ornamentation, allowing an increased level of comparison. The shape of the peristome is used as a new reference to locate ornamental features and propose new homology hypotheses. In total, 105 taxa have been analysed for 47 characters. We code continuous characters by their means and ranges ± one standard deviation. We test two weighting schemes: equal weights standardized by unit range and implied weighting with several concavity constants. This work has led to redefinition of the phylogenetic inclusivenesses of all the hildoceratid subfamilies. The new coding scheme based on peristome shapes provides the fewest homoplastic characters. The schemes appear promising to improve phylogenetic analyses in ammonoids as well as molluscs as a whole by creating a general coding framework.     

The Usefulness of the Sting Apparatus in Phylogenetic Reconstructions in Vespids,with Emphasis on the Epiponini: More Support for the Single Origin of Eusociality in the Vespidae

This study aimed at testing the utility of characters derived from chitinous structures of the sting apparatus for elucidating relationships among the genera of Epiponini. The characters were obtained from the spiracular and quadrate plates, gonostylus, and sting. The data matrix was analyzed using parsimony with equal and implied weighting. Sting characters were also optimized on the tree of Wenzel & Carpenter (1994). Consensus of analysis using equal weights parsimony resulted in a tree with low resolution, but the use of implied weighting improved the results and a consensus tree with a better resolution was obtained. Implied weighting analysis showed an interesting result with Vespinae and Epiponini (the taxa that present the highest degree of sociality) together in a clade. The overall uniformity in morphology of sting apparatus and a possible influence of sociality on morphology could explain these results. The evolution of some characters is discussed.     

Successive Weighting and Polymorphic Terminals—A Warning to PAUP Users

The naïve user of PAUP 3.1.1 (and earlier versions) is warned about a shortcoming in the program's successive weighting facility. With matrices containing multistate terminals, PAUP, under the "polymorphism" interpretation, will assign higher weight to characters with more within-terminal steps, other things being equal, i.e. to characters with the largest amount of homoplasy. The shortcoming has been corrected in PAUP* version 4.0.     

Adaptation and functional integration in primate phylogenetics

In two areas of phylogenetics, contrary predictions have been developed and maintained for character analysis and weighting. With regard to adaptation, many have argued that adaptive characters are poorly suited to phylogenetic analysis because of a propensity for homoplasy, while others have argued that complex adaptive characters should be given high weight because homoplasy in complex characters is unlikely. Similarly, with regard to correlated sets of characters, one point of view is that such sets should be collapsed into a single character-a single piece of phylogenetic evidence. Another point of view is that a suite of correlated characters should be emphasized in phylogenetics, again because recurrence of detailed similarity in the same suite of features is unlikely. In this paper, I discuss the theoretical background of adaptation and functional integration with respect to phylogenetic systematics of primates. Several character examples are reviewed with regard to their functional morphology and phylogenetic signal: postorbital structures, tympanic morphology, fusion of the mandibular symphysis, the tooth comb, strepsirrhine talar morphology, and the prehensile tail. It is clear when considering characters such as these that some characters are synapomorphic of major clades and at the same time functionally important. This appears particularly to be the case when characters are integrated into a complex and maintained as stable configurations. Rather than being simply a problem in character analysis, processes of integration may help to explain the utility of phylogenetically informative characters. On the other hand, the character examples also highlight the difficulty in forming a priori predictions about a character's phylogenetic signal. Explanations of patterns of character evolution are often clade-specific, which does not allow for a simple framework of character selection and/or weighting.     

Quantification of homoplasy for nucleotide transitions and transversions and a reexamination of assumptions in weighted phylogenetic analysis

Nucleotide transitions are frequently down-weighted relative to transversions in phylogenetic analysis. This is based on the assumption that transitions, by virtue of their greater evolutionary rate, exhibit relatively more homoplasy and are therefore less reliable phylogenetic characters. Relative amounts of homoplastic and consistent transition and transversion changes in mitochondrial protein coding genes were determined from character-state reconstructions on a highly corroborated phylogeny of mammals. We found that although homoplasy was related to evolutionary rates and was greater for transitions, the absolute number of consistent transitions greatly exceeded the number of consistent transversions. Consequently, transitions provided substantially more useful phylogenetic information than transversions. These results suggest that down-weighting transitions may be unwarranted in many cases. This conclusion was supported by the fact that a range of transition: transversion weighting schemes applied to various mitochondrial genes and genomic partitions rarely provided improvement in phylogenetic estimates relative to equal weighting, and in some cases weighting transitions more heavily than transversions was most effective.     

Morphology,molecules and the phylogeny of Characidae (Teleostei,Characiformes)

This is the most comprehensive phylogenetic analysis of the Characidae to date and the first large-scale hypothesis of the family, combining myriad morphological data with molecular information. A total of 520 morphological characters were analysed herein, of which 98 are newly defined. Among the analysed taxa, 259 species were coded by examining specimens, three fossil species were coded from the literature, one species was coded almost completely from published figures, 122 were partially coded from the literature, and 88 were analysed exclusively from molecular data. The total number of species in the analysed dataset is 473. Analyses were made by parsimony under equal and extended implied weighting with a broad range of parameters. The final hypothesis was selected using a stability criterion that chooses among the most parsimonious trees of all searches. It was found by weighting molecular characters with the average homoplasy of entire partitions (markers). The resulting hypothesis is congruent with previous molecular-based phylogenies of the family. The Characidae are monophyletic, with four main clades: the Spintherobolinae new subfamily; an expanded Stethaprioninae including the Grundulini, Gymnocharacini, Rhoadsiini and Stethaprionini; the Stevardiinae; and a clade composed of the Aphyocharacinae, Characinae, Cheirodontinae, Exodontinae and Tetragonopterinae. Also, a stem Characidae was found, as formed by the Eocene–Oligocene genera †Bryconetes and †Paleotetra as successive sister groups of extant members of the family. A subfamilial classification is proposed, but deep changes in the systematics that are beyond the scope of this study are still needed to classify the Characidae into monophyletic genera.     

Support Weighting

Previous weighting methods—including compatibility weighting—have assumed that homoplasy indicates unreliability, but this assumption does not seem to hold for large molecular data matrices. Reliability can be better assessed by support weighting, which measures the degree to which the changes in a character (site) are concentrated in the supported branches of a tree. Jackknife resampling can be used to generate randomly selected suites of initial weights in successive support weighting, and this provides a way of assessing the stability of successive weighting results.     

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.     

Data Decisiveness, Missing Entries, and the DD Index

The decisiveness of a data set has been defined as the degree to which all possible dichotomous trees for that data set differ in length, and the DD statistic (the data decisiveness index) has been proposed to measure this degree. In this paper, we first discuss an exact nonre cursive formula for the length of indecisive datasets (DD = 0) that consist of informative binary characters in which no missing entries are allowed. Next, the concept of indecisive data sets is extended to data sets in which missing entries may be present. Last, indecisive data sets with missing entries are used as an aid to construct hypothetical data sets that single out some of the factors that influence the DD statistic. On the basis of these examples, it is concluded that the concept of data decisiveness is too elusive to be captured into a single and simple index such as DD.     

Comparing levels of homoplasy in the primate skeleton

Hard-tissue morphological characters (bones and teeth) are a primary source of information about the evolutionary history of primates. These tissues are commonly found as isolated elements in the fossil record and studied as three separate partitions: the dentition, the cranium, and the postcranium. The relative phylogenetic utility of characters from each partition is often called into question with respect to varying amounts of homoplasy. In this paper, the consistency index (CI) was used to measure levels of homoplasy in each data partition for a sample of fossil and living primates. Sources of bias in the collection and treatment of data and in the internal structure of the data set are addressed. These biases include number of taxa, number of characters, ordering of characters, amounts of polymorphically scored or missing data, and character-state distribution. The results of this study suggest that the levels of homoplasy are very similar, though the postcranial data may be slightly less homoplastic than either the dental or cranial data.     

Sampling diverse characters improves phylogenies: Craniodental and postcranial characters of vertebrates often imply different trees

Morphological cladograms of vertebrates are often inferred from greater numbers of characters describing the skull and teeth than from postcranial characters. This is either because the skull is believed to yield characters with a stronger phylogenetic signal (i.e., contain less homoplasy), because morphological variation therein is more readily atomized, or because craniodental material is more widely available (particularly in the palaeontological case). An analysis of 85 vertebrate datasets published between 2000 and 2013 confirms that craniodental characters are significantly more numerous than postcranial characters, but finds no evidence that levels of homoplasy differ in the two partitions. However, a new partition test, based on tree‐to‐tree distances (as measured by the Robinson Foulds metric) rather than tree length, reveals that relationships inferred from the partitions are significantly different about one time in three, much more often than expected. Such differences may reflect divergent selective pressures in different body regions, resulting in different localized patterns of homoplasy. Most systematists attempt to sample characters broadly across body regions, but this is not always possible. We conclude that trees inferred largely from either craniodental or postcranial characters in isolation may differ significantly from those that would result from a more holistic approach. We urge the latter.