Artifacts of Coding Amino Acids and Other Composite Characters for Phylogenetic Analysis

A phylogenetic analysis can be no better than the characters on which it is based. Just as it is inappropriate to code character states of individual characters as separate presence/absence characters, it is inappropriate to combine independent characters because not all information in the data is being utilized. Composite characters link otherwise discernible states from different characters together to form new character states. There are two related problems with this coding. First, there is a loss of hierarchic information between the reductive and composite characters when unordered states are used. Second, the linking of separate characters that occurs during the construction of composite character states can create putative synapomorphies that were not present in the separate characters. For amino acid characters, the problem may occur whenever more than one position of a codon is variable among the terminals sampled. Groups that are resolved as paraphyletic with reductive coding may be resolved as monophyletic with composite coding. The artificial character states indicated by the amino acid characters are unlikely to be congruent with the true gene tree.     

Homology and errors

A recent review of the homology concept in cladistics is critiqued in light of the historical literature. Homology as a notion relevant to the recognition of clades remains equivalent to synapomorphy. Some symplesiomorphies are “homologies” inasmuch as they represent synapomorphies of more inclusive taxa; others are complementary character states that do not imply any shared evolutionary history among the taxa that exhibit the state. Undirected character‐state change (as characters optimized on an unrooted tree) is a necessary but not sufficient test of homology, because the addition of a root may alter parsimonious reconstructions. Primary and secondary homology are defended as realistic representations of discovery procedures in comparative biology, recognizable even in Direct Optimization. The epistemological relationship between homology as evidence and common ancestry as explanation is again emphasized. An alternative definition of homology is proposed. © The Willi Hennig Society 2012.     

How to identify (as opposed to define) a homoplasy: examples from fossil and living great apes

There is much debate on the definitions of homoplasy and homology, and on how to spot them among character states used in a phylogenetic analysis. Many advocate what I call a "processual approach," in which information on genetics, development, function, or other criteria help a priori in identifying two character states as homologous or homoplastic. I argue that the processes represented by these criteria are insufficiently known for most organisms and most characters to be reliably used to identify homoplasies and homologies. Instead, while not foolproof, phylogeny should be the ultimate test for homology. Character states are assumed to be homologous a priori because this is falsifiable and because their initial inclusion in the character-state analysis is based on the assumption that they may be phylogenetically informative. If they fall out as symplesiomorphies or synapomorphies in a phylogenetic analysis, their status as homologies remains unfalsified. If they fall out as homoplasies, having evolved independently in more than one clade, their status as homologous is falsified, and a homoplasy is identified. The character-state transformation series, functional morphology, finer levels of morphological comparison, and the distribution and correlation of characters all help to explain the presence of homoplasies in a given phylogeny. Explaining these homoplasies, and not ignoring them as "noise," should be as much a goal of phylogenetic analysis as the production of a phylogeny. Examples from the fossil record of Miocene hominoids are given to illustrate the advantages of a process-informs-pattern-recognition-after-the-fact approach to understanding the evolution of character states.     

EVOLUTIONARY CHARACTER ANALYSIS: TRACING CHARACTER CHANGE ON A CLADOGRAM

Abstract— There has been little formal discussion concerning character analysis in cladistics, even though characters and their character state trees are central to phylogenetic analyses. We refer to this field as Evolutionary Character Analysis. This paper defines the components of evolutionary character analysis: character state trees, transmodal characters, cladogram characters, attribute and character phylogenies; and the use of these components in phylogenetic inference and evolutionary studies. Character state trees and their effect on cladogram construction are discussed. A new method for numerically coding complex character state trees is described that further reduces the number of variables required to describe them. This method, ordinal coding, reduces the size of data matrices, and facilitates retrieval of state codes. This paper advocates the use of both biological evidence and evidence internal to the cladogram itself to construct character state trees (CSTs). We discuss general models of character evolution (morphocline analysis, Fitch minimum mutation model, etc.) and their role in forming CSTs. Character state trees formed with theories of character evolution are referred to as transmodal characters. These transmodal characters are contrasted with cladogram characters (Mickevich, 1982), and the place of each in a phylogenetic analysis is discussed. The method for determining cladogram characters is detailed with more complicated examples than found in previous publications. We advocate testing transmodal characters by comparing them with the resultant cladogram characters. This comparison involves transformation series analysis (TSA; Mickevich, 1982) which is viewed as an extension of reciprocal illumination. The TSA procedure and its place in hypothesis testing are reviewed. Tracing the evolution of characters interests both systematists and non-systematists alike. When character state trees (transmodal characters) are optimized on pre-existing phylogenies, character phylogenies and attribute phylogenies result. Attributes are defined as a feature that may or may not be homologous (i.e., ecological categories, plant hosts, etc.). We provide two illustrations of this approach, one involving the evolution of the anuran ear and another involving the coevolution of the butterfly Heliconius and its hostplants. Finally, the components of phylogenetic character analysis can be used to test more general evolutionary theories such as the biogenetic law and vicariance biogeography.     

Complex clines: the predictivity of complicated patterns of geographic variation portrayed by multivariate analysis

The stability of complex patterns of geographic variation was investigated by assessing the congruence between multivariate ordinations derived from randomly chosen real characters. Two series of populations were analysed representing two situations with complex patterns of geographic variation. The first, a ‘Eurasian’ series of populations, showed a strongly structured hierarchical pattern, the second, an ‘eastern’ series of populations, showed a more subtle complex pattern of smooth clines and steps. The characters were selected from a total of 81 (Eurasian) or 61 (eastern) within-population independent characters from six different systems. The congruence between ordinations of the geographical populations was measured by the rotational fit statistic, R². Three procedures were used to compare ordinations based on from two to up to 80 characters randomly chosen to give: A, completely independent character sets; B, subsets compared to the total set; and C, potentially overlapping sets. All three procedures showed that congruence between the ordinations was asymptotic in relation to character number. This relationship was described by one of two mathematical models (procedure B did not result in a hyperbolic model as found with simple patterns of geographic variation). Generally speaking, once a sufficient number of characters are used, the complex patterns of geographic variation are stable, reliable and predictive and not substantially influenced by character choice. The strongly structured hierarchical pattern required 15 or so characters to achieve reliability whilst the more subtle patterns required 20 or so characters. However, the addition of further characters does improve reliability in both cases. The greater percentage of variance portrayed by three-dimensional ordinations compared to two-dimensional ordinations is achieved at the cost of lower congruence when a sufficient number of characters are used. If case studies of geographic variation were to adopt these procedures (preferably using completely independent character sets; procedure A) the reliability of their results would be indicated).     

A method for measuring support for synapomorphy using character state distributions on phylogenetic trees

Synapomorphies are fundamental to phylogenetic systematics as they offer empirical evidence of monophyletic groups. However, no method exists to directly measure synapomorphy. Here, we propose a method that quantifies synapomorphy using the pattern of character state distribution over a cladogram separately for each character and for each clade. We define a fully synapomorphic character state as one shared by all of a clade’s terminal taxa and at the same time completely absent from all terminal taxa outside that clade. The extent to which this condition is met corresponds to the support for the character state being synapomorphic or, in short, support for synapomorphy. It is calculated as the probability of randomly selecting, by multi‐stage sampling following the topology of the tree, two terminals from inside a clade sharing the same character state and one terminal from outside the clade bearing a different character state. The method is independent of tree inference and free of transformational assumptions, and so can be applied to any tree and used for any type of discrete character. By measuring synapomorphy, the method offers a potential tool for determining diagnostic character states for taxa on different hierarchical levels, for evaluating alternative systems of character coding, and for evaluating clade support. We show how the method differs from ancestral character state reconstruction methods and goodness‐of‐fit indices. We demonstrate the behaviour of our method with several hypothetical scenarios and its potential use with two real‐life examples.     

A COMPARISON OF TWO METHODS TO STUDY CORRELATED DISCRETE CHARACTERS ON PHYLOGENETIC TREES

Abstract — We use a simulation approach to study two methods proposed for the analysis of correlated discrete characters on cladograms, the concentrated changes test (CCT) and the contingent states test (CST). Both of these consider the case where there is an independent and a dependent character and assign probabilities to various events in the dependent character given one or the other state of the independent character. The CCT gives different results for symmetric and asymmetric cladograms. In the latter case, the proportion of branches reconstructed as having the derived state has less influence on the resulting probabilities. The CST is only sensitive to the proportion of derived branches, regardless of whether the tree is symmetric or asymmetric. The CCT calculates probabilities by considering character state reconstructions which are not allowed by parsimony algorithms, thereby increasing the probability of rejecting a true null hypothesis (type I error rate). We discuss some alternative questions that could be studied using these tests and also derive equations for calculating the number of possible events in the dependent character for unresolved parts of the phylogeny.     

Testing and weighting characters

Published justifications for weighting characters in parsimony analyses vary tremendously. Some authors argue for weighting a posteriori, some for a priori, and especially those authors that rely on a falsificationist approach to systematics argue for non-weighting. To find a decision, while following the falsificationist approach, one first has to investigate the necessary conditions for the possibility of phylogenetic research to establish an empirical science sensu Popper. A concept of phylogenetic homology together with the criterion of identity is proposed, which refers to the genealogical relations between individual organisms. From this concept a differentiation of the terms character and character state is proposed, defining each character as a single epistemological argument for the reconstruction of a unique transformation event. Synapomorphy is distinguished from homology by referring to the relationship between species instead of individual organisms, thus the set of all synapomorphies constitutes a subset of the set of all homologies. By examining the structure of characteristics during character analysis and hypothesizing specific types of transformations responsible for having caused them, a specific degree of severity is assigned to each identity test. It thus provides a specific degree of corroboration for every hypothesis that successfully passed this test. Since the congruence criterion tests hypotheses of synapomorphy against each other on grounds of their degree of corroboration gained from the identity test, these different degrees of corroboration determine the specific weights given to characters and character state transformations before the cladistic analysis. This provides a reasonable justification for an a priori weighting scheme within a falsificationist approach to phylogeny. It also demonstrates the indispensable necessity of its application.     

Strong character incongruence and character choice in phylogeny of sea stars of the Asterinidae

Abstract. Historically, characters from early animal development have been a potentially rich source of phylogenetic information, but many traits associated with the gametes and larval stages of animals with complex life cycles are widely suspected to have evolved frequent convergent similarities. Such convergences will confound true phylogenetic relationships. We compared phylogenetic inferences based on early life history traits with those from mitochondrial DNA sequences for sea stars in the genera Asterina, Cryptasterina , and Patiriella (Valvatida: Asterinidae). Analysis of these two character sets produced phylogenies that shared few clades. We quantified the degree of homoplasy in each character set when mapped onto the phylogeny inferred from the alternative characters. The incongruence between early life history and nucleotide characters implies more homoplasy in the life history character set. We suggest that the early life history traits in this case are most likely to be misleading as phylogenetic characters because simple adaptive models predict convergence in early life histories. We show that adding early life history characters may slightly improve a phylogeny based on nucleotide sequences, but adding nucleotide characters may be critically important to improving inferences from phylogenies based on early life history characters.     

THE NATURE OF CLADISTIC DATA

Abstract— Cladistic data are the characters of organisms. Character is defined as a feature that can be evaluated as a variable with two or more mutually exclusive and ordered states. Cladistic characters must be treated as multistate variables, and coded as sequential numbers or in additive binary fashion. Any other interpretation and handling of cladistic data will introduce error into analysis. Character states cannot be treated independently as present or absent, i.e., as nominal variables, because redundancy is introduced into the data and information content is sacrificed. Non-additive binary coding demonstrates that treating cladistic variables as nominal data will lead to multiple, equally parsimonious solutions. Defining characters found universally in a group of organisms, but unknown outside those organisms have no alternative state that can be designated as absent. Absence, however, is valid as a character state if it can be shown to be apomorphic. When two or more character states occur within a taxon, that taxon must be coded as having an unknown state for that character, or the taxon must be split in two or more taxa. Continuously varying quantitative data are not suitable for cladistic analysis because there is no justifiable basis for recognizing discrete states among them. Quantitative data are questionable even when they exhibit mutually exclusive states because the states can be interpreted only in reference to an archetype, i.e., as implied homologies not subject to test.     

Optimal multiple testing and design in clinical trials

A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of power and how they relate to study goals, and also consider the requirements of type I error control and the nature of the procedures. This leads us to an explicit optimization problem with objective and constraints that describe its specific desiderata. We present a complete solution for deriving optimal procedures for two hypotheses, which have desired monotonicity properties, and are computationally simple. For some of the optimization formulations this yields optimal procedures that are identical to existing procedures, such as Hommel's procedure or the procedure of Bittman et al. (2009), while for other cases it yields completely novel and more powerful procedures than existing ones. We demonstrate the nature of our novel procedures and their improved power extensively in a simulation and on the APEX study (Cohen et al., 2016).     

Comparative morphology and molecular phylogeny of aplanochytrids (Labyrinthulomycota)

Aplanochytrids comprise one of three major subgroups within the Labyrinthulomycota. We have surveyed the diversity of aplanochytrids and have discovered that most isolates are difficult to identify to species because of character plasticity and ambiguity. Ten isolates were studied using molecular phylogenies based on small subunit ribosomal gene sequences (SSU rDNA) and morphological characters derived from light microscopy, SEM and TEM (e.g., colony size, colony shape, colony pattern, agar penetration, cell shape, cell surface patterns, cell inclusion characteristics and ectoplasmic net morphology). Of these isolates, we could positively identify two of them to species, namely Aplanochytrium yorkensis (Perkins, 1973) Leander and Porter, 2000 and A. minuta (Watson and Raper, 1957) Leander and Porter, 2000. We used standardized conditions for growing aplanochytrid isolates in order to minimize environmentally induced phenotypic plasticity in our comparative studies of morphology. By mapping the morphological characters listed above onto a conservative phylogenetic topology derived from SSU rDNA sequences, we were able to identify several synapomorphies (e.g., gross colony characteristics and cell surface patterns) that serve as valuable taxonomic characters for the identification of species and specific clades of aplanochytrids.     

The evolution of the laterophysic connection with a revised phylogeny and taxonomy of butterflyfishes (Teleostei: Chaetodontidae)

The higher‐level relationships of butterflyfishes were examined using 37 morphological characters. This analysis combines characters derived from a histological study describing variation in the morphology of the laterophysic connection (an association between the swim bladder and the lateral‐line canals) with previously described morphological characters. The phylogenetic analysis resulted in four equally parsimonious trees that only differed in the placement of two of the 11 chaetodontid genera (Amphichaetodon and Forcipiger). We compare our analysis with previous hypotheses, present a new taxonomy consistent with the proposed cladistic relationships, and diagnose Chaetodon with five unreversed synapomorphies, including the evolution of characters composing the laterophysic connection. A new character‐based diagnosis of Chaetodon is provided and species are allocated accordingly; Chaetodon now includes the former Parachaetodon ocellatus and excludes the former subgenera Prognathodes and Roa. The evolution of the laterophysic connection is examined by optimizing character‐state transformations on the new hypothesis of relationships.     

Morphological character evolution in hepialid moths (Lepidoptera: Hepialidae) from New Zealand

Mapping morphological characters on a molecular-based phytogeny enabled examination of character evolution and an historical perspective into evolutionary processes, both of which are important aspects of systematic research and comparative biology. In this study, 63 morphological characters from hepialid moths in New Zealand were mapped on a phylogenetic tree reconstructed from mitochondrial DNA COI & II sequence data. Morphological characters hypothesized to be synapomorphies for the New Zealand 'Oxycanus' lineages and 'Oxycanus' lineage s.s. were confirmed to be homologous when mapped on the COI & II phytogeny. The direction of character state transformation was determined for five characters, with members of the Aenetus and Aoraia lineages exhibiting hypothesized ancestral states. Male genitalic characters were less homoplasious than other character partitions and covaried significandy with phytogeny.     

A COMPUTER ASSISTED ANALYSIS OF THE RELATIONSHIPS OF THE HIGHER CATEGORIES OF TURTLES

Abstract— A character matrix of 39 characters for 14 supregeneric categories of living and extinct turtles was examined using PAUP 2.41 and 3.0L. The Branch and Bound algorithm found a single most parsimonious cladogram of 55 steps, consistency index of 0.709, retention index of 0.848 and a rescaled consistency index of 0.601. The cladogram is identical to that proposed by Gaffney and Meylan (1988). The Pleurodira and Cryptodira are each shown to be monophyletic and are supported by synapomorphies involving complex structures of the basicranium and adductor musculature. These synapomorphies are judged to be relatively well-tested homologies. A paraphyletic Cryptodira occurs in 18% of 38 equally parsimonious trees 57 steps in length, but these trees are based on characters, such as absence of pterygoid teeth, that are susceptible to homoplasy in amniotes. We re-iterate the notion that it is better to choose fewer, well-analysed characters than large numbers of poorly analysed characters.     

Phylogeny and classification of the Signiphoridae (Hymenoptera: Chalcidoidea)

Abstract. A data set consisting of twenty-eight anatomical characters scored for twenty-eight terminal taxa representing the world fauna of Signiphoridae was analysed using parsimony and compatibility methods. The Coccophaginae (Aphelinidae) and the Azotinae (Aphelinidae) were used as outgroups to establish polarity of character state changes. Relationships of Signiphoridae to other Chalcidoidea are discussed. Several multistate characters were treated in the parsimony analyses either as unordered or as ordered into transformation series using additive binary coding, which in some cases drastically reduced the number of equally parsimonious solutions. Monophyly of Signiphoridae is supported by seven synapomorphies. Four genera, Chartocerus, Thysanus, Clytina and Signiphora , are recognized within Signiphoridae based on synapomorphies. Rozanoviella syn.n . and Kerrichiella syn.n . are synonymized under Signiphora. Species of Signiphora are further assigned to four species groups, three of which are demonstrably monophyletic. Nine species or subspecies are transferred to Chartocerus from Signiphora ( australicus comb.n. , australiensis comb.n. , australiensis orbiculatus comb.n., beethoveni comb.n. , corvinus comb.n. , funeralis comb.n. , reticulata comb.n. , ruskini comb.n. , thusanoides comb.n.) , one species to Thysanus from Signiphora (melancholicus comb.n.) , and one species to Signiphora from Kerrichiella ( coleoptratus comb.n.) . A key to genera of Signiphoridae and species groups of Signiphora is presented. A diagnosis, relevant nomenclatural history, and a list of included species are given for each genus and species group, and the biology and distribution of each is summarized.     

Trilobite monophyly revisited

Fortey's and Whittington's recent refutation of Lauterbach's hypothesis of a paraphyletic Trilobita is supported. However, much of the character evidence raised by Fortey and Whittington to substantiate the monophyly of the Trilobita (including, inter alia, "Olenellinae”; and Agnostoidea) is ambiguous. Of seven proposed synapomorphies, only one (dorsal cuticle calcification) may be maintained at that node after testing within a cladistic framework. The other six characters are either constrained by calcification or define nodes up or down the cladogram. As positioned by Fortey's and Whittington's characters, Agnostoidea could be regarded either as the most primitive trilobites, or as being outside that clade. Lauterbach's support for an “olenelline"‐chelicerate clade is found to include interdependent characters which are reduced here to two testable derived similarities. Only one of these may conform to general criteria indicative of homology, such as detailed similarity and topology. It is, however, rejected on the basis of parsimony. We emphasize that resolution of the chelicerate‐"olenelline"‐trilobite three‐taxon problem must be based on recognition of homologies among each of these taxa. Nectaspida are excluded from Trilobita as defined by cuticle calcification, but as ingroup “Arachnata”; (sensu Lauterbach) they are important for determining character generality in this clade.     

The effects of increasing genetic distance on alignment of,and tree construction from,rDNA internal transcribed spacer sequences

We examined how alignment of internal transcribed spacers of rDNA in fungi and plants changes with increasing genetic distance by successive removal of sequences from each data set followed by realignment and phylogenetic analysis. Increasing genetic distance can negatively affect phylogenetic reconstruction in two ways. First, it may cause errors in the alignment and therefore the homology hypotheses of the sequence characters. Second, it may cause errors in the homology assessments of character states because of multiple hits on individual branches. These two causes of error in phylogenetic inference were distinguished from one another in our analysis. The errors in alignment caused by increasing genetic distance were primarily due to inserting too few gaps and inserting gaps at the wrong positions. Errors in tree resolution, topology, and/or branch-support values were more often caused by multiple hits than by misaligned positions. This suggests that increasing genetic distance negatively affects our primary homology assessments of character states more severely than our primary homology assessments of characters. We suggest that increasing taxon sampling with the aim of subdividing long branches is a strategy for obtaining reliable alignments.     

Multiple testing with discrete data: Proportion of true null hypotheses and two adaptive FDR procedures

We consider multiple testing with false discovery rate (FDR) control when p values have discrete and heterogeneous null distributions. We propose a new estimator of the proportion of true null hypotheses and demonstrate that it is less upwardly biased than Storey's estimator and two other estimators. The new estimator induces two adaptive procedures, that is, an adaptive Benjamini–Hochberg (BH) procedure and an adaptive Benjamini–Hochberg–Heyse (BHH) procedure. We prove that the adaptive BH (aBH) procedure is conservative nonasymptotically. Through simulation studies, we show that these procedures are usually more powerful than their nonadaptive counterparts and that the adaptive BHH procedure is usually more powerful than the aBH procedure and a procedure based on randomized p‐value. The adaptive procedures are applied to a study of HIV vaccine efficacy, where they identify more differentially polymorphic positions than the BH procedure at the same FDR level.