Parallel tion in the context of character analysis

For the establishment of polarity of character transformation prior to phylogenetic analysis, various logical and biological criteria are discussed; some are rejected on grounds of liability to systematic error, circularity or unwarranted assumptions aboutParallel tion is used as a non-polar term, with forward and reverse to indicate polarity. A computer program for the detection of parallel tion is described which takes taxa in groups of four. The characters, with two derived: two primitive states or three derived: one primitive state, are listed according to the distribution of states over the four taxa. To each of the 15 phylogenies there corresponds a compatible pair of character patterns. Discordant 2: 2 patterns are unconditionally incompatible (Le Quesne test failure), discordant 3: 1 patterns are incompatible conditional upon correct scoring of polarity. For any putative phylogeny the concordant and discordant characters are identified. In cases of competing alternatives these character sets have to be weighed against one another. Character weighting is discussed; it is argued that it is the individual character transformation which should be weighted, in each direction separately.     

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.     

Testing character correlation using pairwise comparisons on a phylogeny

In comparative biology, pairwise comparisons of species or genes (terminal taxa) are used to detect character associations. For instance, if pairs of species contrasting in the state of a particular character are examined, the member of a pair with a particular state might be more likely than the other member to show a particular state in a second character. Pairs are chosen so as to be phylogenetically separate, that is, the path between members of a pair, along the branches of the tree, does not touch the path of any other pair. On a given phylogenetic tree, pairs must be chosen carefully to achieve the maximum possible number of pairs while maintaining phylogenetic separation. Many alternative sets of pairs may have this maximum number. Algorithms are developed that find all taxon pairings that maximize the number of pairs without constraint, or with the constraint that members of each pair have contrasting states in a binary character, or that they have contrasting states in two binary characters. The comparisons chosen by these algorithms, although phylogenetically separate on the tree, are not necessarily statistically independent.     

IN SEARCH OF HOMOPLASTIC TENDENCIES: STATISTICAL INFERENCE OF TOPOLOGICAL PATTERNS IN HOMOPLASY

The “tendency” for homoplasy to appear in closely related taxa has been widely discussed but rarely quantified. This paper proposes statistical tests that examine the topological distribution of homoplasy within characters in phylogenies. They test whether character changes are localized (confined to some subtree), or clustered (occur in proximity to each other), relative to two null models of character evolution. Null Model I assumes that the observed number of character changes are dispersed randomly among the internodes of the tree, whereas Model II weights the probability that an internode contains a change by the length of that internode—estimated by the total number of character changes along that internode. Localization is measured by the largest furthest-neighbor distance between changes, clustering by the mean nearest neighbor distance. Distances are measured either by the number of intervening branches or the number of intervening character changes. Analyses of four cladistic data sets from the literature reveal very few characters that exhibit significant levels of clustering or localization—no more than would be expected by chance. In every data set a majority of characters exhibited at least weak tendencies, but in only one data set was there a significant excess of such characters. The present findings do not provide compelling evidence for the existence of “tendencies” in homoplasy, at least among characters used to reconstruct phylogenies. They should be sought elsewhere, in cladistic analyses of larger scope, probably among a class of characters defined a priori on a structural or functional basis.     

PATTERNS OF VARIATION IN LEVELS OF HOMOPLASY

Patterns of variation in levels of homoplasy were explored through statistical analyses of standardized consistency indexes. Data were obtained from 60 recent cladistic analyses of a wide variety of organisms based on several different kinds of characters. Consistency index is highly correlated with the number of taxa included in an analysis, with homoplasy increasing as the number of taxa increases. This observation is compatible with a simple model of character evolution in which 1) the probability of character-state change increases with the total number of branches in a tree and 2) the number of possible states of a character is limited. Consistency index does not show a significant relationship to the number of characters utilized in an analysis or to the taxonomic rank of the terminal taxa. When the relationship between consistency index and number of taxa is taken into account, there is no significant difference between plant and animal data sets in the amount of homoplasy. Likewise, the level of homoplasy in morphological and molecular data sets does not appear to differ significantly, although there are still too few molecular studies to be confident of this result. Future comparisons of consistency indexes, including studies along the lines established here, must take into account the influence of the number of taxa on homoplasy.     

A formula for maximum possible steps in multistate characters: isolating matrix parameter effects on measures of evolutionary convergence

To identify a biological signal in the distribution of homoplasy, it is first necessary to isolate non-biological factors affecting its measurement. The number of states per character in a phylogenetic data matrix may indicate evolutionary flexibility and, consequently, the likelihood of recurrent evolution. However, we show here that the number of states per character limits the maximum number of steps that may be inferred using parsimony. A formula is provided for the maximum number of steps that may be taken by a character with a given number of states and taxa. We show that as more character states are included the maximum proportion of steps that can be attributed to homoplasy falls, and the greatest amount of homoplasy measurable with the consistency index declines.
© The Willi Hennig Society 2009.     

Inferring the accumulation of morphological disparity in epiphyllous liverworts

Phylogenetic studies of lineages growing in extreme environments have frequently recovered evidence not only of high level of homoplasy but also of discordance of morphological disparity and species diversity. It has been suggested that this divergence may be caused by developmental constraints and/or natural selection. Here we explored these hypotheses by inferring the phenotypic evolution of the derived liverwort genus Cololejeunea. These liverworts occur preferentially on the surface of leaves or other aerial parts of vascular plants growing in wet forests. The evolution of 12 morphological characters was studied using a phylogenetic framework comprising 70 species of Cololejeunea. The phylogeny was reconstructed using DNA sequences of one nuclear and two plastid regions and enabled the inference of the evolution of the studied morphological characters by determining the frequency of homoplasy. Mantel tests were used to test for correlations of morphological disparity?×?species diversity and morphological disparity?×?epiphytism. The phylogenetic informativeness of each binary character was estimated by the D metric of the Fritz and Purvis test, and the relationship between each character and epiphytism was inferred by Pearson’s coefficient. We evaluated the morphospace occupation using principal coordinate analyses. Our results not only recovered high levels of homoplasy but also weak correlations of morphological disparity and species diversity. Morphological disparity was not linked to epiphytism, although positive or negative relationships between some characters and epiphytism were found. The Brownian model of character evolution was not rejected for the studied morphological disparity in Cololejeunea with the exception of asexual propagules. The observations support the prediction that iterative evolution in a well-defined morphospace may result in rampant homoplasy and the observed divergence of disparity and diversity.     

Inferring and testing hypotheses of cladistic character dependence by using character compatibility

The notion that two characters evolve independently is of interest for two reasons. First, theories of biological integration often predict that change in one character requires complementary change in another. Second, character independence is a basic assumption of most phylogenetic inference methods, and dependent characters might confound attempts at phylogenetic inference. Previously proposed tests of correlated character evolution require a model phylogeny and therefore assume that nonphylogenetic correlation has a negligible effect on initial tree construction. This paper develops "tree-free" methods for testing the independence of cladistic characters. These methods can test the character independence model as a hypothesis before phylogeny reconstruction, or can be used simply to test for correlated evolution. We first develop an approach for visualizing suites of correlated characters by using character compatibility. Two characters are compatible if they can be used to construct a tree without homoplasy. The approach is based on the examination of mutual compatibilities between characters. The number of times two characters i and j share compatibility with a third character is calculated, and a pairwise shared compatibility matrix is constructed. From this matrix, an association matrix analogous to a dissimilarity matrix is derived. Eigenvector analyses of this association matrix reveal suites of characters with similar compatibility patterns. A priori character subsets can be tested for significant correlation on these axes. Monte Carlo tests are performed to determine the expected distribution of mutual compatibilities, given various criteria from the original data set. These simulated distributions are then used to test whether the observed amounts of nonphylogenetic correlation in character suites can be attributed to chance alone. We have applied these methods to published morphological data for caecilian amphibians. The analyses corroborate instances of dependent evolution hypothesized by previous workers and also identify novel partitions. Phylogenetic analysis is performed after reducing correlated suites to single characters. The resulting cladogram has greater topological resolution and implies appreciably less change among the remaining characters than does a tree derived from the raw data matrix.     

Speciational Evolution: a Phylogenetic Test With Allozymes in Sceloporus (Reptilia)

Abstract— The potential role of speciation in accelerating evolutionary divergence remains controversial. Earlier tests based on genetic and morphologic distances which indicated an absence of speciational evolution rely on problematic assumptions. We provide a phylogenetic test in which amounts of discrete character change relative to an outgroup are compared between sister taxa. Although this test is constrained by a need to assume similar extinction rates in groups compared, it provides conceptual improvements regarding monophyly, equal age of taxa, and distribution of homoplasy. Based on analysis of 68 informative allozyme characters for 19 lizard species in the genus Sceloporus , significant speciational evolution and punctuational change is, at least, a viable explanation for the distribution of observed character changes.     

MACROEVOLUTIONARY PATTERNS OF MORPHOLOGICAL DIVERSIFICATION AMONG PARASITIC FLATWORMS (PLATYHELMINTHES: CERCOMERIA)

Patterns of parasite morphological diversification were investigated using a morphological data base for the parasitic platyhelminths comprising 1,459 characters analyzed using phylogenetic systematic methods. Only 10.8% of the 1,882 character transformations are losses, casting doubt on views that parasites are secondarily simplified and exhibit degenerate evolution. Chi-squared analysis indicates that character loss in the Digenea and Monogenea occurs in proportion to total change and is disproportionately lower within the Eucestoda. In the Digenea fewer female characters and more male characters have been lost than expected by the total number of characters in that group, and more male and more nonreproductive characters have been lost in proportion to their distribution across groups. In the Monogenea fewer nonreproductive and more larval characters have been lost than expected within the group, and female character loss is high relative to other groups. In the Eucestoda fewer female and more larval characters have been lost than expected within the group, whereas loss of male and nonreproductive character is low, and loss of larval characters is high, compared to the other groups. Patterns of character loss result partially from characters that show repeated (homoplasious) loss in different groups. High consistency index and low homoplasy slope ratio values indicate that the parasitic platyhelminths show unusually low levels of homoplasy, casting doubt on views that parasite morphology is unusually adaptively plastic. Homoplasy within the monogeneans occurs in proportion to overall character change, is slightly higher than expected in the digeneans, and is much lower than expected within the eucestodes. Homoplasy occurs less often than expected in larval characters, and more often than expected in nonreproductive characters in the Digenea. Monogeneans show more homoplasy than expected for larval characters both within and among groups. Eucestodes show fewer homoplasious male and nonreproductive, and more homoplasious larval, characters than expected within the group, and higher homoplasy in larval characters and lower homoplasy in female and nonreproductive characters among groups.     

Meta-analysis of character utility and phylogenetic information content in cladistic studies of ammonoids

While previous workers have argued persuasively that ammonoid workers should use cladistic approaches to reconstruct phylogeny, relatively few cladistic studies have been published to date. An essential yet challenging part of cladistic analysis is the selection of characters. Are certain types of characters more likely to show homoplasy? Are certain aspects of shell anatomy more likely to contain phylogenetically informative characters? Are datasets with more characters inherently better? To answer these questions, a meta-analysis of character data from published ammonoid phylogenies was performed. I compiled 14 datasets, published between 1989 and 2007, representing parsimony-based phylogenetic analyses of ammonoids. These studies defined a combined total of 323 characters, which were grouped into categories reflecting different aspects of anatomy: shell size and shape, ornament, suture, early ontogeny, body chamber and apertural modifications. Tree searches were re-run to determine overall tree statistics, parsimony permutation tail probability (PTP) tests were calculated to assess the phylogenetic information content of the matrices, and retention and rescaled consistency indices for each character were calculated. My analyses revealed that studies with higher character/taxon ratios did not necessarily produce trees with more information content and less homoplasy, as measured by retention or rescaled consistency indices, because additional characters were often parsimony-uninformative. Rather, studies with relatively few characters could produce high-quality trees if the characters were well-chosen and character states carefully defined. Characters related to the body chamber and adult aperture typically had retention indices of either 0 or 1, rarely in between, indicating that they either worked perfectly or not at all. Suture characters tended to have higher indices than shell shape or ornament characters, suggesting more phylogenetic information and less homoplasy in the suture line than in shell traits. These results should aid in the selection of characters for future cladistic studies of ammonoids.     

Within-Terminal Steps and Fit Calculation—A Warning to Pee-Wee Users

Because Pee-Wee (version 2.5.1 and earlier versions) treats all within-terminal steps (internal steps) as homoplasies, if the command "ccode = (space).;" is in effect, it reports incorrect, and consistently too low, fit values for characters having states that occur only within polymorphic terminals (WPTO states). For matrices with WPTO states, this property of Pee-Wee may bias tree search in favour of characters having fewer WPTO states, other things being equal. Contrary to the intended purpose of the Goloboff criterion, Pee-Wee may even, in certain cases involving WPTO states, assign higher weight (fit) to characters with more homoplasy and therefore resolve character conflict in favour of less reliable characters.     

Measuring Topological Congruence by Extending Character Techniques

A measure of topological congruence which is an extension of the Mickevich–Farris character incongruence metric ( i.e. , ILD; Mickevich and Farris, 1981) is proposed. Group inclusion characters (1 = member of a clade; 0 = not a member) are constructed for each topology to be considered. The sets of characters derived from the topologies are then compared for character incongruence due to data set combination. Each homoplasy signifies a disagreement among topological statements. The value is normalized for potential maximum incongruence to adjust values for unresolved topologies. This measure is compared to other topological and character congruence techniques and explored in test data.     

Exhaustion of morphologic character states among fossil taxa

Frequencies of new character state derivations are analyzed for 56 fossil taxa. The hypothesis that new character states are added continuously throughout clade history can be rejected for 48 of these clades. Two alternative explanations are considered: finite states and ordered states. The former hypothesizes a limited number of states available to each character and is tested using rarefaction equations. The latter hypothesizes that there are limited possible descendant morphologies for any state, even if the character has infinite potential states. This is tested using power functions. The finite states hypothesis explains states: steps relationships significantly better than does the ordered states hypothesis in 14 cases; the converse is true for 14 other cases. Under either hypothesis, trilobite clades show appreciably more homoplasty after the same numbers of steps than do molluscs, echinoderms, or vertebrates. The prevalence of the exhaustion pattern among different taxonomic groups implies that worker biases are not to blame and instead implicates biological explanations such as intrinsic constraints or persistent selective trends. Regardless of the source of increased homoplasy, clades appear to exhaust their available character spaces. Nearly all examined taxa show significant increases in proportions of incompatible character pairs (i.e., those necessarily implying homoplasy) as progressively younger taxa are added to character matrices. Thus, a deterioration of hierarchical structure accompanies character state exhaustion. Exhaustion has several implications: (1) the basic premise of cladistic analyses (i.e., that maximum congruence reflects homology rather than homoplasy) becomes increasingly less sound as clades age; (2) sampling high proportions of taxa probably is needed for congruence to discern homoplasy from homology; (3) stratigraphic data might be necessary to discern congruent homoplasy from congruent homology; and (4) in many cases, character states appear to have evolved in ordered patterns.     

Corroboration versus "Strongest Evidence"

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

Convergence and parallelism: is a new life ahead of old concepts?

In comparative biology, character observations initially separate similar and dissimilar characters. Only similar characters are considered for phylogeny reconstruction; their homology is attested in a two‐step process, firstly a priori of phylogeny reconstruction by accurate similarity statements, and secondly a posteriori of phylogeny analysis by congruence with other characters. Any pattern of non‐homology is then a homoplasy, commonly, but vaguely, associated with “convergence”. In this logical scheme, there is no way to analyze characters which look similar, but cannot meet usual criteria for homology statements, i.e., false similarity detected a priori of phylogenetic analysis, even though such characters may represent evolutionarily significant patterns of character transformations. Because phylogenies are not only patterns of taxa relationships but also references for evolutionary studies, we propose to redefine the traditional concepts of parallelism and convergence to associate patterns of non‐homology with explicit theoretical contexts: homoplasy is restricted to non‐similarity detected a posteriori of phylogeny analysis and related to parallelism; non‐similarity detected a priori of phylogenetic analysis and necessarily described by different characters would then correspond to a convergence event s. str. We propose to characterize these characters as heterologous (heterology). Heterology and homoplasy correspond to different non‐similarity patterns and processes; they are also associated with different patterns of taxa relationships: homoplasy can occur only in non‐sister group taxa; no such limit exists for heterology. The usefulness of these terms and concepts is illustrated with patterns of acoustic evolution in ensiferan insects. © The Willi Hennig Society 2005.     

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.     

Trees within trees: genes and species, molecules and morphology

The construction and interpretation of gene trees is fundamental in molecular systematics. If the gene is defined in a historical (coalescent) sense, there can be multiple gene trees within the single contiguous set of nucleotides, and attempts to construct a single tree for such a sequence must deal with homoplasy created by conflict among divergent histories. On a larger scale, incongruence is expected among gene tree topologies at different loci of individuals within sexually reproducing species, and it has been suggested that this discordance can be used to delimit species. A practical concern for such topological methods is that polymorphisms may be maintained through numerous cladogenic events; this polymorphism problem is less of a concern for nontopological approaches to species delimitation using molecular data. Although a central theoretical concern in molecular systematics is discordance between a given gene tree and the true "species tree," the primary empirical problem faced in reconstructing taxic phylogeny is incongruence among the trees inferred from different sequences. Linkage relationships limit character independence and thus have important implications for handling multiple data sets in phylogenetic analysis, particularly at the species level, where incongruence among different historically associated loci is expected. Gene trees can also be reconstructed for loci that influence phenotypic characters, but there is at best a tenuous relationship between phenotypic homoplasy and homoplasy in such gene trees. Nevertheless, expression patterns and orthology relationships of genes involved in the expression of phenotypes can in theory provide criteria for homology assessment of morphological characters.