Partitioned likelihood support and the evaluation of data set conflict

In simultaneous analyses of multiple data partitions, the trees relevant when measuring support for a clade are the optimal tree, and the best tree lacking the clade (i.e., the most reasonable alternative). The parsimony-based method of partitioned branch support (PBS) "forces" each data set to arbitrate between the two relevant trees. This value is the amount each data set contributes to clade support in the combined analysis, and can be very different to support apparent in separate analyses. The approach used in PBS can also be employed in likelihood: a simultaneous analysis of all data retrieves the maximum likelihood tree, and the best tree without the clade of interest is also found. Each data set is fitted to the two trees and the log-likelihood difference calculated, giving "partitioned likelihood support" (PLS) for each data set. These calculations can be performed regardless of the complexity of the ML model adopted. The significance of PLS can be evaluated using a variety of resampling methods, such as the Kishino-Hasegawa test, the Shimodiara-Hasegawa test, or likelihood weights, although the appropriateness and assumptions of these tests remains debated.     

Exploring the effects of phylogenetic uncertainty and consensus trees on stratigraphic consistency scores: a new program and a standardized method

The stratigraphic record of first appearances provides an independent source of data for evaluating and comparing phylogenetic hypotheses that include taxa with fossil histories. However, no standardized method exists for calculating these metrics for polytomous phylogenies, restricting their applicability. Previously proposed methods insufficiently deal with this problem because they skew or restrict the resulting scores. To resolve this issue, we propose a standardized method for treating polytomies when calculating these metrics: the Comprehensive Polytomy approach (ComPoly). This approach accurately describes how phylogenetic uncertainty, indicated by polytomies, affects stratigraphic consistency scores. We also present a new program suite (Assistance with Stratigraphic Consistency Calculations) that incorporates the ComPoly approach and simplifies the calculation of absolute temporal stratigraphic consistency metrics. This study also demonstrates that stratigraphic consistency scores calculated from strict consensus trees can be overly inclusive and those calculated from less‐than‐strict consensus trees inaccurately describe the phylogenetic signal present in the source most‐parsimonious trees (MPTs). Therefore, stratigraphic consistency scores should be calculated directly from the source MPTs whenever possible to ensure their accuracy. Finally, we offer recommendations for standardizing comparisons between molecular divergence dates and the stratigraphic record of first appearances, a promising new application of these methods. © The Willi Hennig Society 2010.     

Introgression explains incongruence between nuclear and chloroplast DNA-based phylogenies in Allium section Cepa

Phylogenetic relationships between species of Allium section Cepa and A. rqylei (section Rhizirideum) have been inferred from nuclear DNA variation (RAPDs; nDNA dataset) and from morphological, pollen epidermis texture, chromosomal and chemical variation (supranuclear dataset). These sets were complemented with data, taken from the literature, on cpDNA variation and crossability. The trees produced with the supranuclear, nDNA and cpDNA datasets were compared by using the topology of the most parsimonious tree of one dataset as the constraint for the construction of a most parsimonious tree of another dataset. The accuracy of the trees were evaluated by calculating several Consistency and Incongruence Indices. The constrained tree of supranuclear-nDNA datasets showed the highest index values. The tree topologies of the supranuclear and cpDNA datasets were the least similar. The cpDNA tree and crossability dendrograms were identical. The most important difference between the nDNA-supranuclear trees and the cpDNA-crossability trees pertains to the position of Allium roylei , which is much closer to the clade A. cepa/A. vavilovii in the cpDNA tree than in the nDNA tree. This difference is considered to be the result of chloroplast capture from one species to another after an introgression event. A shorter distance between species inferred from a cpDNA tree than from a nDNA or comparable tree might be indicative for the level of crossability.     

HOMOPLASY AND THE CHOICE AMONG CLADOGRAMS

Abstract Cladistic data are more decisive when the possible trees differ more in tree length. When all the possible dichotomous trees have the same length, no one tree is better supported than the others, and the data are completely undecisive . From a rule for recursively generating undecisive matrices for different numbers of taxa, formulas to calculate consistency, rescaled consistency and retention indices in undecisive matrices are derived. The least decisive matrices are not the matrices with the lowest possible consistency, rescaled consistency or retention indices (on the most parsimonious trees); those statistics do not directly vary with decisiveness. Decisiveness can be measured with a newly proposed statistic, DD = − S )/( − S ) (where S = length of the most parsimonious cladogram, = mean length of all the possible cladograms for the data set and M = observed variation). For any data set, can be calculated exactly with simple formulas; it depends on the types of characters present, and not on their congruence. Despite some recent assertions to the contrary, the consistency index is an appropriate measure of homoplasy (= deviation from hierarchy). The retention index seems more appropriate for comparing the fit of different trees for the same data set.     

Conodonts Meet Cladistics: Recovering Relationships and Assessing the Completeness of the Conodont Fossil Record

A numerical cladistic analysis of the conodont family Palmatolepidae has been undertaken to determine the applicability of the technique to group-wide systematic revision. Results suggest a new hypothesis of relationships that is considerably more parsimonious than trees compatible with existing hypotheses of relationships, or trees that are even loosely constrained stratigraphically. This may occur either because the fossil record is incomplete, because taxon sampling for the cladistic analysis is low, or because the most parsimonious trees approximate the true tree less well than do stratigraphically-constrained trees (or because of a combination of these factors). Although more taxa and more characters would be preferable in choosing between these possibilities, the tree derived solely from morphological data is adopted. Thus, stratigraphic data can be used to test hypotheses of relationships and construct phylogenies; hypotheses of relationships can be used to test the completeness of the conodont fossil record. Existing schemes of classification within the Palmatolepidae are rejected because most groups within them are either polyphyletic or paraphyletic. A new scheme is presented. Character changes suggest correlated, progressive and mosaic evolution within the Palmatolepidae. Parsimony analysis of partitioned datasets indicates that more phylogenetic information can be recovered from S rather than P or M element positions, although data from all three positional groups are preferable to data from just one. Thus, multielement taxonomy is essential to the resolution of conodont interrelationships.     

Computationally difficult parsimony problems in phylogenetic systematics

A basic problem in phylogenetic systematics is to construct an evolutionary hypothesis, or phylogenetic tree, from available data for a set of operational taxonomic units (OTUs). Associated with the edges of such trees are weights that usually are interpreted as lengths. Methods proposed for constructing phylogenetic trees attempt to select from among the myriad alternatives a tree that optimizes in some sense the fit of tree topology and edge lengths with the original data. One optimization criterion seeks a most parsimonious tree in which the sum of edge lengths is a minimum. Researchers have failed to develop efficient algorithms to compute optimal solutions for important variations of the parsimonious tree construction problem. Recently Graham & Foulds (1982) proved that a special case of the problem is NP-complete, thus making it unlikely that the computational problem for this case can be solved efficiently. I describe three other parsimonious tree construction problems and prove that they, too, are NP-complete.     

Non-hereditary Maximum Parsimony trees

In this paper, we investigate a conjecture by Arndt von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This conjecture deals with the question whether Maximum Parsimony trees are hereditary. The conjecture suggests that a Maximum Parsimony tree for a particular (DNA) alignment necessarily has subtrees of all possible sizes which are most parsimonious for the corresponding subalignments. We answer the conjecture affirmatively for binary alignments on 5 taxa but also show how to construct examples for which Maximum Parsimony trees are not hereditary. Apart from showing that a most parsimonious tree cannot generally be reduced to a most parsimonious tree on fewer taxa, we also show that compatible most parsimonious quartets do not have to provide a most parsimonious supertree. Last, we show that our results can be generalized to Maximum Likelihood for certain nucleotide substitution models.     

Rooting with Multiple Outgroups: Consensus Versus Parsimony

Using outgroup(s) is the most frequent method to root trees. Rooting through unconstrained simultaneous analysis of several outgroups is a favoured option because it serves as a test of the supposed monophyly of the ingroup. When contradiction occurs among the characters of the outgroups, the branching pattern of basal nodes of the rooted tree is dependent on the order of the outgroups listed in the data matrix, that is, on the prime outgroup (even in the case of exhaustive search). Different equally parsimonious rooted trees (=cladograms) can be obtained by permutation of prime outgroups. An alternative to a common implicit practice (select one outgroup to orientate the tree) is that the accepted cladogram is the strict consensus of the different equally parsimonious rooted trees. The consensus tree is less parsimonious but is not hampered with extra assumption such as the choice of one outgroup (or more) among the initial number of outgroup terminals. It also does not show sister-group relations that are ambiguously resolved or not resolved at all.     

THE PHYLOGENETIC RELATIONSHIPS AMONG REQUIEM AND HAMMERHEAD SHARKS: INFERRING PHYLOGENY WHEN THOUSANDS OF EQUALLY MOST PARSIMONIOUS TREES RESULT

Abstract— Protein variation among 37 species of carcharhiniform sharks was examined at 17 presumed loci. Evolutionary trees were inferred from these data using both cladistic character and a distance Wagner analysis. Initial cladistic character analysis resulted in more than 30 000 equally parsimonious tree arrangements. Randomization tests designed to evaluate the phylogenetic information content of the data suggest the data are highly significantly different from random in spite of the large number of parsimonious trees produced. Different starting seed trees were found to influence the kind of tree topologies discovered by the heuristic branch swapping algorithm used. The trees generated during the early phases of branch swapping on a single seed tree were found to be topologically similar to those generated throughout the course of branch swapping. Successive weighting increased the frequency and the consistency with which certain clades were found during the course of branch swapping, causing the semi-strict consensus to be more resolved. Successive weighting also appeared resilient to the bias associated with the choice of initial seed tree causing analyses seeded with different trees to converge on identical final character weights and the same semi-strict consensus tree.
The summary cladistic character analysis and the distance Wagner analysis both support the monophyly of two major clades, the genus Rhizoprionodon and the genus Sphyrna. . The distance Wagner analysis also supports the monophyly of the genus Carcharhinus . However, the cladistic analysis suggests that Carcharhinus is a paraphyletic group that includes the blue shark Prionace glauca .     

THE EFFECT OF ORDERED CHARACTERS ON PHYLOGENETIC RECONSTRUCTION

Abstract Morphological structures are likely to undergo more than a single change during the course of evolution. As a result, multistate characters are common in systematic studies and must be dealt with. Particularly interesting is the question of whether or not multistate characters should be treated as ordered (additive) or unordered (non-additive). In accepting a particular hypothesis of order, numerous others are necessarily rejected. We review some of the criteria often used to order character states and the underlying assumptions inherent in these criteria.
The effects that ordered multistate characters can have on phylogenetic reconstruction are examined using 27 data sets. It has been suggested that hypotheses of character state order are more informative then hypotheses of unorder and may restrict the number of equally parsimonious trees as well as increase tree resolution. Our results indicate that ordered characters can produce more, equal or less equally parsimonious trees and can increase, decrease or have no effect on tree resolution. The effect on tree resolution can be a simple gain in resolution or a dramatic change in sister-taxa relationships. In cases where several outgroups are included in the data matrix, hypotheses of order can change character polarities by altering outgroup topology. Ordered characters result in a different topology from unordered characters only when the hierarchy of the cladogram disagrees with the investigator's a priori hypothesis of order. If the best criterion for assessing character evolution is congruence with other characters, the practice of ordering multistate characters is inappropriate.     

Mitochondrial DNA phylogeography of the polytypic North American rat snake (Elaphe obsoleta): a critique of the subspecies concept

Subspecies have been considered artificial subdivisions of species, pattern classes, or incipient species. However, with more data and modern phylogenetic techniques, some subspecies may be found to represent true species. Mitochondrial DNA analysis of the polytypic snake, Elaphe obsoleta, yields well-supported clades that do not conform to any of the currently accepted subspecies. Complete nucleotide sequences of the cytochrome b gene and the mitochondrial control region produced robust maximum-parsimony and maximum-likelihood trees that do not differ statistically. Both trees were significantly shorter than a most parsimonious tree in which each subspecies was constrained to be monophyletic. Thus, the subspecies of E. obsoleta do not represent distinct genetic lineages. Instead, the evidence points to three well-supported mitochondrial DNA clades confined to particular geographic areas in the eastern United States. This research underscores the potential problems of recognizing subspecies based on one or a few characters.     

ANOTHER MONOPHYLY INDEX: REVISITING THE JACKKNIFE

Abstract — Randomization routines have quickly gained wide usage in phylogenetic systematies. Introduced a decade ago, the jackknife has rarely been applied in cladistic methodology. This data resampling technique was re-investigated here as a means to discover the effect that taxon removal may have on the stability of the results obtained from parsimony analyses. This study shows that the removal of even a single taxon in an analysis can cause a solution of relatively few multiple equally parsimonious trees in an inclusive matrix to result in hundreds of equally parsimonious trees with the single removal of a taxon. On the other hand, removal of other taxa can stabilize the results to fewer trees. An index of clade stability, the Jackknife Monophyly Index (JMI) is developed which, like the bootstrap, applies a value to each clade according to its frequency of occurrence in jackknife pseudoreplicates. Unlike the bootstrap and earlier application of the jackknife, alternative suboptimal hypotheses are not forwarded by this method. Only those clades in the most parsimonious tree(s) are given JMI values. The behaviour of this index is investigated both in relation to a hypothetical and a real data set, as well as how it performs in comparison to the bootstrap. The JMI is found to not be influenced by uninformative characters or relative synapomorphy number, unlike the bootstrap.     

Molecular systematics of Iridaceae: evidence from four plastid DNA regions

Iridaceae are one of the largest families of Lilianae and probably also among the best studied of monocotyledons. To further evaluate generic, tribal, and subfamilial relationships we have produced four plastid DNA data sets for 57 genera of Iridaceae plus outgroups: rps4, rbcL (both protein-coding genes), the trnL intron, and the trnL-F intergenic spacer. All four matrices produce similar although not identical trees, and we thus analyzed them in a combined analysis, which produced a highly resolved and well-supported topology, in spite of the fact that the partition homogeneity test indicated strong incongruence. In each of the individual trees, some genera or groups of genera are misplaced relative to morphological cladistic studies, but the combined analysis produced a pattern much more similar to these previous ideas of relationships. In the combined tree, all subfamilies were resolved as monophyletic, except Nivenioideae that formed a grade in which Ixioideae were embedded. Achlorophyllous Geosiris (sometimes referred to Geosiridaceae or Burmanniaceae) fell within the nivenioid grade. Most of the tribes were monophyletic, and Isophysis (Tasmanian) was sister to the rest of the family; Diplarrhena (Australian) fell in a well-supported position as sister to Irideae/Sisyrinchieae/Tigridieae/Mariceae (i.e., Iridoideae); Bobartia of Sisyrinchieae is supported as a member of Irideae. The paraphyly of Nivenioideae is suspicious due to extremely high levels of sequence divergence, and when they were constrained to be monophyletic the resulting trees were only slightly less parsimonious (<1.0%). However, this subfamily also lacks clear morphological synapomorphies and is highly heterogeneous, so it is difficult to develop a strong case on nonmolecular grounds for their monophyly.     

Comparison of the Cladograms Produced by Li's Method and Farris' Method

In order to avoid producing many equally most parsimonious trees, Li (1990) developed a new cladistic method, the Median Elimination Series (MES), to construct a single cladogram for a given data set. However, we found that Li's method can produce more than one tree if two or more taxa have the same advancement index (which is the total number of apomorphies for a taxon in a given data set), because there is no objective method to decide which taxon should be connected first and different orders of connection can produce different trees. Li claimed that the result produced by his method did not apply the principle of simplicity (parsimony). Nevertheless, Zhang (1991) recognised that Li's method actually accepted the principle of parsimony. Here we demonstrated that Li's method also can produce the minimum-length trees. We conclude that Li's method could produce more than one tree and the tree(s) may be the minimum-length possible. However, the length of tree(s) depends on the order of connection of the taxa. The major problems in using Li's methodare discussed.     

Evolution of myrmecophytism in western Malesian Macaranga (Euphorbiaceae)

Plants inhabited by ants (myrmecophytes) have evolved in a diversity of tropical plant lineages. Macaranga includes approximately 300 paleotropical tree species; in western Malesia there are 26 myrmecophytic species that vary in morphological specializations for ant association. The origin and diversification of myrmecophytism in Macaranga was investigated using phylogenetic analyses of morphological and nuclear ITS DNA characters and studies of character evolution. Despite low ITS variation, the combined analysis resulted in a well-supported hypothesis of relationships. Mapping myrmecophytism on all most parsimonious trees resulting from the combined analysis indicated that the trait evolved independently between two and four times and was lost between one and three times (five changes). This hypothesis was robust when tested against trees constrained to have three or fewer evolutionary transformations, although increased taxon sampling for the ITS analysis is required to confirm this. Mapping morphological traits on the phylogeny indicated that myrmecophytism was not homologous among lineages; each independent origin involved a suite of different specializations for ant-plant association. There was no evidence that myrmecophytic traits underwent sequential change through evolution; self-hollowing domatia evolved independently from ant-excavated domatia, and different food-body production types evolved in different lineages. The multiple origins of myrmecophytism in Macaranga were restricted to one small, exclusively western Malesian lineage of an otherwise large and nonmyrmecophytic genus. Although the evolution of aggregated food-body production and the formation of domatia coincided with the evolution of myrmecophytism in all cases, several morphological, ecological, and biogeographic factors appear to have facilitated and constrained this radiation of ant-plants.     

Phylogenetic relationships of Holarctic Teleiodini (Lepidoptera: Gelechiidae) based on analysis of morphological and molecular data

Abstract Phylogenetic relationships of 25 genera of Holarctic Teleiodini (Gelechiidae) are postulated based on morphology and molecular characters, including CO‐I, CO‐II, and 28S genes. The phylogenetic analysis of the morphology matrix yielded four equal most‐parsimonious trees (length 330 steps, CI = 0.36, RI = 0.55) and a strict consensus tree (length 335 steps, CI = 0.36, RI = 0.54) with one polytomy and one trichotomy. The phylogenetic analysis of the combined morphology and CO‐I + CO‐II + 28S matrices yielded two equally most‐parsimonious trees (length 1184 steps, CI = 0.50, RI = 0.42) and a strict consensus tree (length 1187 steps, CI = 0.50, RI = 0.42) that reinforced results from the morphological analysis and resolved the one polytomy present in the morphology consensus tree. Teleiodini are defined as a monophyletic clade with a Bremer support value greater than 5 in the consensus tree based on morphological and molecular data. Twenty‐three clades of genera are defined with Bremer support values provided. An analysis of larval host‐plant preferences based on the consensus tree for combined data indicates derivation of feeding on woody hosts from genera feeding on herbaceous hosts and a single origin of feeding on coniferous hosts. An area cladogram indicates five independent origins of Nearctic genera from Holarctic ancestors and one origin from a Palearctic genus.     

POLYMORPHIC TAXA, MISSING VALUES AND CLADISTIC ANALYSIS

Abstract Missing values have been used in cladistic analyses when data are unavailable, inapplicable or sometimes when character states are variable within terminal taxa. The practice of scoring taxa as having "missing values" for polymorphic characters introduces errors into the calculation of cladogram lengths and consistency indices because some character change is hidden within terminals. Because these hidden character steps are not counted, the set of most parsimonious cladograms may differ from those that would be found if polymorphic taxa had been broken into monomorphic subunits. In some cases, the trees found when polymorphisms are scored as missing values may not include any of the most parsimonious trees found when the data are scored properly. Additionally, in some cases, polymorphic taxa may be found to be polyphyletic when broken into monomorphic subunits; this is undetected when polymorphisms are treated as missing. Because of these problems, terminal units in cladistic analysis should be based on unique, fixed combinations of characters. Polymorphic taxa should be subdivided into subunits that are monomorphic for each character used in the analysis. Disregarding errors in topology, the additional hidden steps in a cladogram in which polymorphisms are scored as missing can be calculated by a simple formula, based on the observation that if it is assumed that polymorphic terminals include all combinations of character states, 2 ^p − 1 additional steps are required for each taxon in which p polymorphic binary characters are scored as missing values. Thus, when several polymorphisms are scored as missing in the same taxon, very large errors can be introduced into the calculation of tree length.     

Is it better to add taxa or characters to a difficult phylogenetic problem?

The effects on phylogenetic accuracy of adding characters and/or taxa were explored using data generated by computer simulation. The conditions of this study were constrained but allowed for systematic investigation of certain parameters. The starting point for the study was a four-taxon tree in the "Felsenstein zone," representing a difficult phylogenetic problem with an extreme situation of long branch attraction. Taxa were added sequentially to this tree in a manner specifically designed to break up the long branches, and for each tree data matrices of different sizes were simulated. Phylogenetic trees were reconstructed from these data using the criteria of parsimony and maximum likelihood. Phylogenetic accuracy was measured in three ways: (1) proportion of trees that are completely correct, (2) proportion of correctly reconstructed branches in all trees, and (3) proportion of trees in which the original four-taxon statement is correctly reconstructed. Accuracy improved dramatically with the addition of taxa and much more slowly with the addition of characters. If taxa can be added to break up long branches, it is much more preferable to add taxa than characters.     

Phylogenetic relationships and generic delimitation in Inuleae subtribe Inulinae (Asteraceae) based on ITS and cpDNA sequence data

Phylogenetic relationships in Inuleae subtribe Inulinae (Asteraceae) were investigated. DNA sequence data from three chloroplast regions ( ndhF , trnL–F and psbA–trnH ) and the nuclear ribosomal internal transcribed spacer (ITS) region were analysed separately and in combination using parsimony and Bayesian inference. A total of 163 ingroup taxa were included, of which 60 were sampled for all four markers. Conflicts between chloroplast and nuclear data were assessed using partitioned Bremer support (PBS). Rather than averaging PBS over several trees from constrained searches, individual trees were considered by evaluating PBS ranges. Criteria to be used in the detection of a significant conflict between data partitions are proposed. Three nodes in the total data tree were found to encompass significant conflict that could result from ancient hybridization. Neither of the large, heterogeneous and widespread genera Inula and Pulicaria is monophyletic. A monophyletic group ("the Inula complex") that comprises all species of Inula includes also Telekia , Carpesium , Chrysophthalmum , Rhanteriopsis , Amblyocarpum , and Pentanema sensu stricto . Two species of Pentanema were found to be closer to Blumea (including Blumeopsis and Merrittia ) and Caesulia . The monophyletic " Pulicaria complex" includes all taxa with heteromorphic pappus. Within this group, Francoeuria is distinct from Pulicaria and merits recognition as a separate genus.
 © The Willi Hennig Society 2009.     

Fossils impact as hard as living taxa in parsimony analyses of morphology

Systematists disagree whether data from fossils should be included in parsimony analyses. In a handful of well-documented cases, the addition of fossil data radically overturns a hypothesis of relationships based on extant taxa alone. Fossils can break up long branches and preserve character combinations closer in time to deep splitting events. However, fossils usually require more interpretation than extant taxa, introducing greater potential for spurious codings. Moreover, because fossils often have more "missing" codings, they are frequently accused of increasing numbers of MPTs, frustrating resolution and reducing support. Despite the controversy, remarkably little is known about the effects of fossils more generally. Here we provide the first systematic study, investigating empirically the behavior of fossil and extant taxa in 45 published morphological data sets. First-order jackknifing is used to determine the effects that each terminal has on inferred relationships, on the number of MPTs, and on CI' and RI as measures of homoplasy. Bootstrap leaf stabilities provide a proxy for the contribution of individual taxa to the branch support in the rest of the tree. There is no significant difference in the impact of fossil versus extant taxa on relationships, numbers of MPTs, and CI' or RI. However, adding individual fossil taxa is more likely to reduce the total branch support of the tree than adding extant taxa. This must be weighed against the superior taxon sampling afforded by including judiciously coded fossils, providing data from otherwise unsampled regions of the tree. We therefore recommend that investigators should include fossils, in the absence of compelling and case specific reasons for their exclusion.