Finding Optimal Ingroup Topologies and Convexities When the Choice of Outgroups Is Not Obvious

Considerable confusion remains among theoreticians and practicioners of phylogenetic science on the use of outgroup taxa. Here, we show that, despite claims to the contrary, details of the optimal ingroup topology can be changed by switching outgroup taxa. This has serious implications for phylogenetic accuracy. We delineate between the process of outgroup selection and the various possible processes involved in using an outgroup taxon after one has been selected. Criteria are needed for the determination that particular outgroup taxa do not reduce the accuracy of evolutionary tree topologies and inferred character state transformations. We compare previous results from a sensitivity bootstrap analysis of the mitochondrial cytochromebphylogenetic relationships among whales to the results of a Bremer support sensitivity analysis and of a recently developed application of RASA theory to the question of putative outgroup taxon plesiomorphy content.     

Mitochondrial genomes in the Hymenoptera and their utility as phylogenetic markers

Abstract.  In this study, we assessed the ability of mitochondrial genome sequences to recover a test phylogeny of five hymenopteran taxa from which phylogenetic relationships are well accepted. Our analyses indicated that the test phylogeny was well recovered in all nucleotide Bayesian analyses when all the available holometabolan (i.e. outgroup) taxa were included, but only in Bayesian analyses excluding third codon positions when only the hymenopteran representatives and a single outgroup were included. This result suggests that taxon sampling of the outgroup might be as important as taxon sampling of the ingroup when recovering hymenopteran phylogenetic relationships using whole mitochondrial genomes. Parsimony analyses were more sensitive to both taxon sampling and the analytical model than Bayesian analyses, and analyses using the protein dataset did not recover the test phylogeny. In general, mitochondrial genomes did not resolve the position of the Hymenoptera within the Holometabola with confidence, suggesting that an increased taxon sampling, both within the Holometabola and among outgroups, is necessary.     

2 Influence of mixed host populations on success of the parasitic dinoflagellate Amoebophrya

Proper taxon sampling is one of the greatest challenges to understanding phylogenetic relationships, perhaps as important as choice of optimality criterion or data type. This has been demonstrated in diatoms where centric diatoms may either be strongly supported as monophyletic or paraphyletic when analyzing SSU rDNA sequences using the same optimality criterion. The effect of ingroup and outgroup taxon sampling on relationships of diatoms is explored for diatoms as a whole and for the order Thalassiosirales. In the latter case, SSU rDNA and rbcL sequence data result in phylogenetic relationships that appear to be strongly incongruent with morphology and broadly incongruent with the fossil record. For example, Cyclotella stelligera Cleve & Grunow behaves like a rogue taxon, jumping from place to place throughout the tree. Morphological data place C. stelligera near the base of the freshwater group as sister to the extinct genus Mesodictyon Theriot and Bradbury, suggesting that it is an old, long branch that might be expected to "misbehave" in poorly sampled trees. Cyclotella stelligera and C. bodanica Grunow delimit the diameter of morphological diversity in Cyclotella , so increased sampling of intermediate taxa will be critical to resolving this part of the tree. Morphology is sampled for a much greater number of taxa and many transitional states of putative synapomorphies seem to suggest a robust morphological hypothesis. The Thalassiosirales are unstable with regards to taxon sampling in the genetic data, suggesting that perhaps the morphological hypothesis is (for now) preferable.     

1 Taxon sampling and inferences about diatom phylogeny

Proper taxon sampling is one of the greatest challenges to understanding phylogenetic relationships, perhaps as important as choice of optimality criterion or data type. This has been demonstrated in diatoms where centric diatoms may either be strongly supported as monophyletic or paraphyletic when analyzing SSU rDNA sequences using the same optimality criterion. The effect of ingroup and outgroup taxon sampling on relationships of diatoms is explored for diatoms as a whole and for the order Thalassiosirales. In the latter case, SSU rDNA and rbcL sequence data result in phylogenetic relationships that appear to be strongly incongruent with morphology and broadly incongruent with the fossil record. For example, Cyclotella stelligera Cleve & Grunow behaves like a rogue taxon, jumping from place to place throughout the tree. Morphological data place C. stelligera near the base of the freshwater group as sister to the extinct genus Mesodictyon Theriot and Bradbury, suggesting that it is an old, long branch that might be expected to “misbehave” in poorly sampled trees. Cyclotella stelligera and C. bodanica Grunow delimit the diameter of morphological diversity in Cyclotella, so increased sampling of intermediate taxa will be critical to resolving this part of the tree. Morphology is sampled for a much greater number of taxa and many transitional states of putative synapomorphies seem to suggest a robust morphological hypothesis. The Thalassiosirales are unstable with regards to taxon sampling in the genetic data, suggesting that perhaps the morphological hypothesis is (for now) preferable.     

外群选择对隧蜂科（膜翅目：蜜蜂总科）系统重建的影响

外群用于给树附根和推断祖先性状状态。通常,来自内群的姐妹群中的多个分类单元被共同选择作为外群。为了在经验上验证这一方法, 我们采用了3种外群选择策略： 姐妹群中的单一分类单元, 姐妹群中的多个分类单元和连续姐妹群中的多个分类单元。以隧蜂科（膜翅目： 蜜蜂总科）的系统发育重建为例, 我们评估了这3种策略对树拓扑结构的影响, 包括最大似然树、 最大简约树和贝叶斯树。初步结果表明： 相比其他两种策略, 采用姐妹群中的多个分类单元作为外群更有利于系统发育重建得到现已被广泛认可的隧蜂科系统发育关系; 相比最大似然法和贝叶斯法, 虽然隧蜂科系统发育关系没有被很好地解决, 但最大简约法在不同外群选择策略下得到了较为一致的拓扑结构     

Relationships among the major lineages of Dictyoptera: the effect of outgroup selection on dictyopteran tree topology

Abstract Dictyoptera, comprising Blattaria, Isoptera, and Mantodea, are diverse in appearance and life history, and are strongly supported as monophyletic. We downloaded COII, 16S, 18S, and 28S sequences of 39 dictyopteran species from GenBank. Ribosomal RNA sequences were aligned manually with reference to secondary structure. We included morphological data (maximum of 175 characters) for 12 of these taxa and for an additional 15 dictyopteran taxa (for which we had only morphological data). We had two datasets, a 59‐taxon dataset with five outgroup taxa, from Phasmatodea (2 taxa), Mantophasmatodea (1 taxon), Embioptera (1 taxon), and Grylloblattodea (1 taxon), and a 62‐taxon dataset with three additional outgroup taxa from Plecoptera (1 taxon), Dermaptera (1 taxon) and Orthoptera (1 taxon). We analysed the combined molecular?morphological dataset using the doublet and MK models in Mr Bayes , and using a parsimony heuristic search in paup . Within the monophyletic Mantodea, Mantoida is recovered as sister to the rest of Mantodea, followed by Chaeteessa; the monophyly of most of the more derived families as defined currently is not supported. We recovered novel phylogenetic hypotheses about the taxa within Blattodea (following Hennig, containing Isoptera). Unique to our study, one Bayesian analysis places Polyphagoidea as sister to all other Dictyoptera; other analyses and/or the addition of certain orthopteran sequences, however, place Polyphagoidea more deeply within Dictyoptera. Isoptera falls within the cockroaches, sister to the genus Cryptocercus. Separate parsimony analyses of independent gene fragments suggest that gene selection is an important factor in tree reconstruction. When we varied the ingroup taxa and/or outgroup taxa, the internal dictyopteran relationships differed in the position of several taxa of interest, including Cryptocercus, Polyphaga, Periplaneta and Supella. This provides further evidence that the choice of both outgroup and ingroup taxa greatly affects tree topology.     

Phylogenetics of Chondrichthyes and the problem of rooting phylogenies with distant outgroups

Erroneous estimates of ingroup relationships can be caused by attributes in the outgroup chosen to root the tree. Phylogenetic analyses of DNA sequences frequently yield incorrect estimates of ingroup relationships when the outgroup used to "root" the tree is highly divergent from the ingroup. This is especially the case when the outgroup has a different base composition than the ingroup. Unfortunately, in many instances, alternative less divergent outgroups are not available. In such cases, investigators must either target genes with attributes that minimize the problem (slowly evolving genes with stationary base compositions--which are often not ideal for estimating relationships among the more closely related ingroup taxa) or use inference models that are explicitly tailored to deal with an attenuated historical signal with a superimposed non-stationary base composition. In this paper we explore the problem both empirically and through simulation. For the empirical component we looked at the phylogenetic relationships among elasmobranch fishes (sharks and rays), a group whose closest living outgroup, the holocephalan Ghost fishes, are separated from the elasmobranchs by more than 100 million years of evolution. We compiled a data set for analysis comprising 10 single-copy nuclear protein-coding genes (12,096 bp) for representatives of the major lineages within elasmobranchs and holocephalans. For the simulation, we used an evolutionary model on a fixed tree topology to generate DNA sequence data sets which varied both in their distance to the outgroup, and in their base compositional difference between ingroup and outgroup. Results from both the empirical data set and the simulation, support the idea that deviation from base compositional stationarity, in conjunction with distance from the root can act in concert to compromise accuracy of estimated relationships within the ingroup. We tested several approaches to mitigate such problems. We found, that excluding genes with overall faster rates and heterogeneous base compositions, while the least sophisticated of the methods evaluated, seemed to be the most effective.     

Outgroup sampling in phylogenetics: Severity of test and successive outgroup expansion

Outgroup sampling is a fundamental step in the design of phylogenetic analyses, independent of optimality criterion, taxonomic group, or source of evidence. Studies have demonstrated the efficient analysis of many thousands of terminals, all of which could be included in any empirical investigation, yet outgroup samples typically include only a small number of terminals. Most discussion of outgroup sampling centers on employing “correct” or “appropriate” outgroup terminals to increase “accuracy” or “reliability” by preventing “errors” such as long branch attraction and “incorrect” ingroup rooting. As an alternative, I develop a theory of outgroup sampling grounded in the logic of scientific discovery, whereby the objective is to test nested hypotheses of ingroup topology and character‐state transformation as severely as possible by incorporating outgroup terminals in unconstrained, simultaneous analysis, using background knowledge to select the terminals that have the greatest chance of refuting those hypotheses. This framework provides a logical basis for selecting outgroup taxa but does not provide grounds for limiting the outgroup sample, given that, ceteris paribus, testability and explanatory power increase with the inclusion of additional terminals. Therefore, I propose the ancillary procedure of successively expanding the outgroup sample until ingroup hypotheses become stable (insensitive) to increased sampling, with each expansion guided by the scientific objectives of outgroup sampling. This is a heuristic procedure that does not prevent more outgroup terminals from being sampled or guarantee that ingroup hypotheses will remain insensitive to further outgroup expansion, and it has no bearing on the objective support of a given hypothesis. Nevertheless, it provides an objective, empirical basis for limiting outgroup sampling in a given research cycle. I illustrate this procedure by examining the effect of successive outgroup expansion on the relationships among the poison frog genera Adelphobates, Dendrobates, and Oophaga.     

Limitations of relative apparent synapomorphy analysis (RASA) for measuring phylogenetic signal.

In this paper we use hypothetical and empirical data matrices to evaluate the ability of relative apparent synapomorphy analysis (RASA) to measure phylogenetic signal, select outgroups, and identify terminals subject to long-branch attraction. In all cases, except for equal character-state frequencies, RASA indicated extraordinarily high levels of phylogenetic information for hypothetical data matrices that are uninformative regarding relationships among the terminals. Yet, regardless of the number of characters or character-state frequencies, RASA failed to detect phylogenetic signal for hypothetical matrices with strong phylogenetic signal. In our empirical example, RASA indicated increasing phylogenetic signal for matrices for which the strict consensus of the most parsimonious trees is increasingly poorly resolved, clades are increasingly poorly supported, and for which many relationships are in conflict with more widely sampled analyses. RASA is an ineffective approach to identify outgroup terminal(s) with the most plesiomorphic character states for the ingroup. Our hypothetical example demonstrated that RASA preferred outgroup terminals with increasing numbers of convergent character states with ingroup terminals, and rejected the outgroup terminal with all plesiomorphic character states. Our empirical example demonstrated that RASA, in all three cases examined, selected an ingroup terminal, rather than an outgroup terminal, as the best outgroup. In no case was one of the two outgroup terminals even close to being considered the optimal outgroup by RASA. RASA is an ineffective means of identifying problematic long-branch terminals. In our hypothetical example, RASA indicated a terminal as being a problematic long-branch terminal in spite of the terminal being on a zero-length branch and having no possibility of undergoing long-branch attraction with another terminal. RASA also failed to identify actual problematic long-branch terminals that did undergo long-branch attraction, but only after following Lyons-Weiler and Hoelzer's (1997) three-step process to identify and remove terminals subject to long-branch attraction. We conclude that RASA should not be used for any of these purposes.     

Mapping characters on a tree with or without the outgroups

A character of special interest in evolutionary studies is usually optimized on a phylogenetic tree, with or without the outgroups employed in that analysis. Both practices are never justified and look like arbitrary choices. Focusing on one example, we draw the conclusion that authors retain or remove outgroups depending on the way these outgroups sample the diversity of states of the character(s) of special interest. The topology without outgroups is often used by authors when different outgroup taxa non‐exhaustively sample the different states of the character of interest outside of the ingroup. This can make the analysis incoherent, because its different steps are not based on the same data matrix (outgroups are removed in the last step). It can provide several incoherent and possibly different patterns for a same character of interest, one issuing from the first step of phylogeny construction and the other resulting from the a posteriori optimization on the truncated topology. Phylogenetic analyses should be designed to minimize this problem, selecting outgroup and ingroup taxa whose diversity of character states is needed for reconstructing the evolutionary history of the character of interest. © The Willi Hennig Society 2004.     

The interrelationships of all major groups of Platyhelminthes: phylogenetic evidence from morphology and molecules

We used a data matrix of 65 morphological characters from 25 ingroup and 6 outgroup taxa, and an alignment comprising complete 18S rDNA sequences from 82 species of parasitic and free-living Platyhelminthes and from 19 species of lower invertebrates to analyse phylogenetic relationships of various platyhelminth taxa. Of the 1358 unambiguously alignablc molecular positions, 995 were variable and 757 were phylogenctically informative (parsimony criterion); complete 18S rDNA sequences ranged in length from 1755 to 2873 bp. Main conclusions are: Ncodermata are monophylctic, and the Trematoda, Monogenca and Cestoda within them are monophylctic as well. The sister group of the Ncodermata is all the other Ncoophora; the Kalyptorhynchia, Typhloplanida, Dalyelliida and Tcmnocephalida form one clade, and the last three another. Monophyly of the Seriata is rejected, but Polycladida/ Macrostomida/Haplopharyngida are monophylctic, as arc the last two taxa. As a consequence, validity of the taxon Trepaxonemata is rejected. Further studies must show the correct position of the Acocla and Nemertodermatida. It is stressed that morphological and molecular data in some respects lead to contradictory results, for instance concerning the position of the Fecampiidac/ Urastoma/Ichthyophaga and the relative position of the Lccithoepitheliata. Denser sampling of taxa for molecular data, complementary sequences from independent genes, and inclusion of additional morphological data are necessary to resolve these contradictions.     

Taxon influence index: assessing taxon-induced incongruities in phylogenetic inference

Understanding the evolutionary history of species is at the core of molecular evolution and is done using several inference methods. The critical issue is to quantify the uncertainty of the inference. The posterior probabilities in Bayesian phylogenetic inference and the bootstrap values in frequentist approaches measure the variability of the estimates due to the sampling of sites from genes and the sampling of genes from genomes. However, they do not measure the uncertainty due to taxon sampling. Taxa that experienced molecular homoplasy, recent selection, a spur of evolution, and so forth may disrupt the inference and cause incongruences in the estimated phylogeny. We define a taxon influence index to assess the influence of each taxon on the phylogeny. We found that although most taxa have a weak influence on the phylogeny, a small fraction of influential taxa strongly alter it even in clades only loosely related to them. We conclude that highly influential taxa should be given special attention and sampling them more thoroughly can lead to more dependable phylogenies.     

Selected characters of the copulatory organs in the land planarian family Bipaliidae and their taxonomic significance (Tricladida: Terricola)

Preliminary analysis was made of 76 species in the monotypic family Bipaliidae, for which the copulatory apparatus has been described. Four characters from the copulatory organs were selected: profile of the female organ (three character states), approachment of the ovovitelline ducts to the female organ (two states), shape of the penial papilla (two states), and shape of the male antrum wall (three states). Data were scored for five preliminary ingroup taxa, viz., the restricted genus Placocephalus, and four other a priori defined subgroups within the family, viz., the genus Bipalium sensu stricto and three other informal taxonomic groupings. An artificial outgroup taxon was constructed on the basis of character states generalized from the Geoplanidae subfamilies Caenoplaninae, Pelmatoplaninae and Rhynchodemidae subfamily Microplaninae. Analysis of the data matrix resulted in a single most parsimonious tree with the following topology: (outgroup (Placocephalus (Bipalium, group A (group B1, group B2)))). This revised version was published online in July 2006 with corrections to the Cover Date.     

EFFECT OF TAXON SAMPLING,CHARACTER WEIGHTING,AND COMBINED DATA ON THE INTERPRETATION OF RELATIONSHIPS AMONG THE HETEROKONT ALGAE1

Nuclear ribosomal small subunit and chloroplast rbcL sequence data for heterokont algae and potential outgroup taxa were analyzed separately and together using maximum parsimony. A series of taxon sampling and character weighting experiments was performed. Traditional classes (e.g. diatoms, Phaeophyceae, etc.) were monophyletic in most analyses of either data set and in analyses of combined data. Relationships among classes and of heterokont algae to outgroup taxa were sensitive to taxon sampling. Bootstrap (BS) values were not always predictive of stability of nodes in taxon sampling experiments or between analyses of different data sets. Reweighting sites by the rescaled consistency index artificially inflates BS values in the analysis of rbcL data. Inclusion of the third codon position from rbcL enhanced signal despite the superficial appearance of mutational saturation. Incongruence between data sets was largely due to placement of a few problematic taxa, and so data were combined. BS values for the combined analysis were much higher than for analyses of each data set alone, although combining data did not improve support for heterokont monophyly.     

A review of long-branch attraction

The history of long‐branch attraction, and in particular methods suggested to detect and avoid the artifact to date, is reviewed. Methods suggested to avoid LBA‐artifacts include excluding long‐branch taxa, excluding faster evolving third codon positions, using inference methods less sensitive to LBA such as likelihood, the Aguinaldo et al. approach, sampling more taxa to break up long branches and sampling more characters especially of another kind, and the pros and cons of these are discussed. Methods suggested to detect LBA are numerous and include methodological disconcordance, RASA, separate partition analyses, parametric simulation, random outgroup sequences, long‐branch extraction, split decomposition and spectral analysis. Less than 10 years ago it was doubted if LBA occurred in real datasets. Today, examples are numerous in the literature and it is argued that the development of methods to deal with the problem is warranted. A 16 kbp dataset of placental mammals and a morphological and molecular combined dataset of gall waSPS are used to illustrate the particularly common problem of LBA of problematic ingroup taxa to outgroups. The preferred methods of separate partition analysis, methodological disconcordance, and long branch extraction are used to demonstrate detection methods. It is argued that since outgroup taxa almost always represent long branches and are as such a hazard towards misplacing long branched ingroup taxa, phylogenetic analyses should always be run with and without the outgroups included. This will detect whether only the outgroup roots the ingroup or if it simultaneously alters the ingroup topology, in which case previous studies have shown that the latter is most often the worse. Apart from that LBA to outgroups is the major and most common problem; scanning the literature also detected the ill advised comfort of high support values from thousands of characters, but very few taxa, in the age of genomics. Taxon sampling is crucial for an accurate phylogenetic estimate and trust cannot be put on whole mitochondrial or chloroplast genome studies with only a few taxa, despite their high support values. The placental mammal example demonstrates that parsimony analysis will be prone to LBA by the attraction of the tenrec to the distant marsupial outgroups. In addition, the murid rodents, creating the classic “the guinea‐pig is not a rodent” hypothesis in 1996, are also shown to be attracted to the outgroup by nuclear genes, although including the morphological evidence for rodents and Glires overcomes the artifact. The gall wasp example illustrates that Bayesian analyses with a partition‐specific GTR + Γ + I model give a conflicting resolution of clades, with a posterior probability of 1.0 when comparing ingroup alone versus outgroup rooted topologies, and this is due to long‐branch attraction to the outgroup. © The Willi Hennig Society 2005.     

Phylogenetic representativeness: a new method for evaluating taxon sampling in evolutionary studies

Background  

Taxon sampling is a major concern in phylogenetic studies. Incomplete, biased, or improper taxon sampling can lead to misleading results in reconstructing evolutionary relationships. Several theoretical methods are available to optimize taxon choice in phylogenetic analyses. However, most involve some knowledge about the genetic relationships of the group of interest (i.e., the ingroup), or even a well-established phylogeny itself; these data are not always available in general phylogenetic applications.     

Rooting phylogenetic trees with distant outgroups: a case study from the commelinoid monocots

Phylogenetic rooting experiments demonstrate that two chloroplast genes from commelinoid monocot taxa that represent the closest living relatives of the pickerelweed family, Pontederiaceae, retain measurable signals regarding the position of that family's root. The rooting preferences of the chloroplast sequences were compared with those for artificial sequences that correspond to outgroups so divergent that their signal has been lost completely. These random sequences prefer the three longest branches in the unrooted ingroup topology and do not preferentially root on the branches favored by real outgroup sequences. However, the rooting behavior of the artificial sequences is not a simple function of branch length. The random outgroups preferentially root on long terminal ingroup branches, but many ingroup branches comparable in length to those favored by random sequences attract no or few hits. Nonterminal ingroup branches are generally avoided, regardless of their length. Comparisons of the ease of forcing sequences onto suboptimal roots indicate that real outgroups require a substantially greater rooting penalty than random outgroups for around half of the least-parsimonious candidate roots. Although this supports the existence of nonrandomized signal in the real outgroups, it also indicates that there is little power to choose among the optimal and nearly optimal rooting possibilities. A likelihood-based test rejects the hypothesis that all rootings of the subtree using real outgroup sequences are equally good explanations of the data and also eliminates around half of the least optimal candidate roots. Adding genes or outgroups can improve the ability to discriminate among different root locations. Rooting discriminatory power is shown to be stronger, in general, for more closely related outgroups and is highly correlated among different real outgroups, genes, and optimality criteria.     

An approximation to the phylogeny of Sclerotinia and related genera

Phylogenies are constructed based on nuclear ribosomal internal transcribed spacer (ITS) DNA sequences from an ingroup consisting of 50 isolates representing 24 species of the discomycete family Sclerotiniaceae and an outgroup consisting of five related taxa of the same family. The ingroup taxa are: three Botrytis spp., two Botryotinia spp., one Ciborinia sp., one Dumontinia sp., one Grovesinia sp., six Myriosclerotinia spp., nine Sclerotinia spp. and one Sclerotium sp. The outgroup taxa are: one Ciboria sp., one Encoelia sp. and three Monilinia spp. The type species is included for all taxa except for Ciborinia and Encoelia. Several of the included taxa are important plant pathogens. The resulting phytogenies are discussed with regard to morphology, life history and taxonomy. A suspected relationship between Sclerotinia borealis and S. tetraspora , and Myriosclerotinia is rejected, while a suspected relationship between Ciborinia ciborium and Myriosclerotinia is strongly supported. Sclerotinia ulmariae , previously synonymized with Dumontinia tuberosa , is reinstated as an independent species of Dumontinia. Two new combinations, Dumontinia ulmariae and Myriosclerotinia ciborium , are proposed. The imperfectly known taxon Sclerotium cepivorum seems most closely related to Dumontinia. We conclude that Dumontinia , and Myriosclerotinia , as currently conceived, are monophyletic, and that Botryotinia along with Botrytis anamorphs probably also constitute a monophyletic lineage. The genus Sclerotinia is probably polyphyletic and characterized by symplesiomorphies rather than synapomorphies. Two putatively new taxa, Sclerotinia sp. 1, and Sclerotinia sp.2 are most closely related to S. minor, S. sclerotiorum and S. trifoliorum , and to S. borealis , respectively.     

Head capsule characters in the Hymenoptera and their phylogenetic implications

The head capsule of a taxon sample of three outgroup and 86 ingroup taxa is examined for characters of possible phylogenetic significance within Hymenoptera. 21 morphological characters are illustrated and scored, and their character evolution explored by mapping them onto a phylogeny recently produced from a large morphological data set. Many of the characters are informative and display unambiguous changes. Most of the character support demonstrated is supportive at the superfamily or family level. In contrast, only few characters corroborate deeper nodes in the phylogeny of Hymenoptera.     

Hypothetical Ancestors and Rooting in Cladistic Analysis

Most hypothetical ancestors that are used to root trees in cladistic analyses summarize character-state information in one or more outgroup taxa. Nonetheless, hypothetical ancestors also provide a means of rooting trees using the ontogenetic and paleontological methods of polarizing character transformations, and for incorporating the inferences of more than one of these methods into a single analysis. However, the use of one hypothetical ancestor that combines inferences based on outgroup comparison with those based on other methods of polarizing character transformations to root a cladogram is invalid. Inferences regarding plesiomorphic character states based on outgroup comparison apply to the outgroup node, whereas inferences based on either the ontogenetic or paleontological method apply to the ingroup node. These inferences cannot be combined into a single hypothetical construct. A hypothetical ancestor based on outgroup information is included in the data matrix and used to root the resulting network; however, because this ancestor places potentially problematic constraints on the analysis, the use of actual outgroup taxa is preferable in most instances. Correct use of a hypothetical ancestor inferred with the ontogenetic and paleontological methods involves the Lundberg method in which the shortest ingroup network is rooted at the internode to which the hypothetical ancestor attaches most parsimoniously. Because inferences of polarity based on outgroup comparison cannot be combined directly with those based on other polarization methods, the synthesis of information from all three methods in a single tree must involve taxonomic congruence.