A unifying theory for methods of systematic analysis

A unifying theory for systematic analysis states that a number of methods should be used jointly to cope with various kinds of data; also that groups should be as consistent as possible, be made with least information loss, and where needed, be polythetic. A test of relationship, homogeneity, can use various kinds of data. It can take account of the internal variation of aggregate items such as genera. It can give due emphasis to smaller clusters that have likely important contexts of external items. It helps in analysing trends, cores and hazes in dendrograms. A proposed detector for formal groups can be based on measures of isolation, identifiability and inclusiveness. Non-mathematical, inter-item reaction tests such as hybridization and serology can also be used in grouping. All relationship data are used polythetically to reveal natural groups. This leads to a unified informational concept for taxa. This is more useful than the biological species concept that is restricted to inter-breeding data. All the methods appear to be analogues of the powerful human grouping instinct. The resulting compatibility is important as precise methods are needed mainly when the data are too complex for the mind to use reliably. Cladograms can be made by self-graded deweighting of homogeneity and agglomerative clustering. Unlike classical cladistics this can reveal any polythetic group. Finding the derived states for making cladograms is often much too hypothetical for a fully cladistic approach to be properly precise. Instead, where the evidence is weak, a milder strength of graded deweighting is used for the cladistic properties, which help to show relationships along with the others. Axiomatic failures of other classes of grouping methods are discussed. Unavoidable remnants of instinctive processing lower the precision of all the methods. The Uniter computer program, based on the theory, is tested with finely graded values of artificially ‘evolved’ items and with coarsely coded cladistic data. The results show that with natural data, the program should act as a fairly sensitive probe of past evolutionary branching. Another test shows how specimens from species complexes can be grouped and how distinctions between groups are analysed.     

A generalized taxon concept

A generalized taxon concept (GTC) is proposed with a method for revealing and ranking difficult taxa at any level in the taxonomic hierarchy. The method is based on cluster quality, denned jointly by die compactness of a cluster's contents and its isolation from its informational neighbours. The cluster contents are individuals in die case of species and at higher levels, taxa from the rank below. A standard, quality threshold value is obtained from clustering accepted taxa in the informational region. If the quality value of a problem cluster lies at or above the threshold it is accepted as a taxon and ranked with others at the current level. If it lies below, and is likely to be informationally useful, it may be accepted as a sub-taxon such as a subgenus or subfamily. Provision is made for coarsely scored data. The clustering is mainly based on homogeneity, where possible with a rapid, fuzzily cladistic de-weighting of symplesiomorphies by self-graded factors. The strengms of inter-item reactions such as breeding and DNA-DNA hybridization may also be used. The method is agglomerative so that it can rapidly reveal polythetic groups which may be riddled with exceptional property states caused by long exposure to natural selective forces. All this fits the evolutionary oudook of the GTC, which sees taxa as fuzzy clusters of populations and lineages sharing much of a genetic memory, moulded by a unique history of evolution and extinction. Practical problems of memods based on mis and other taxon concepts are briefly compared. The GTC's approach offers important refinements that could be valuable in helping to speed up urgent surveys of biodiversity, especially in the moist tropics.     

Towards an inclusive philosophy for phylogenetic inference

We defend and expand on our earlier proposal for an inclusive philosophical framework for phylogenetics, based on an interpretation of Popperian corroboration that is decoupled from the popular falsificationist interpretation of Popperian philosophy. Any phylogenetic inference method can provide Popperian "evidence" or "test statements" based on the method's goodness-of-fit values for different tree hypotheses. Corroboration, or the severity of that test, requires that the evidence is improbable without the hypothesis, given only background knowledge that includes elements of chance. This framework contrasts with attempted Popperian justifications for cladistic parsimony--in which evidence is the data, background knowledge is restricted to descent with modification, and "corroboration," as a by-product of nonfalsification, is to be measured by cladistic parsimony. Recognition that cladistic "corroboration" reflects only goodness-of-fit, not corroboration/severity, makes it clear that standard cladistic prohibitions, such as restrictions on the evolutionary models to be included in "background knowledge," have no philosophical status. The capacity to assess Popperian corroboration neither justifies nor excludes any phylogenetic method, but it does provide a framework in phylogenetics for learning from errors--cases where apparent good evidence is probable even without the hypothesis. We explore these issues in the context of corroboration assessments applied to likelihood methods and to a new form of parsimony. These different forms of evidence and corroboration assessment point also to a new way to combine evidence--not at the level of overall fit, but at the level of overall corroboration/severity. We conclude that progress in an inclusive phylogenetics will be well served by the rejection of cladistic philosophy.     

A data based parsimony method of cophylogenetic analysis

Phylogenies of closely interacting groups, such as hosts and parasites, are seldom completely congruent. Incongruence can arise from biologically meaningful differences in the histories of the two groups, or can be generated by artifactual differences that are merely the result of incorrect phylogenies with weakly supported nodes. We present a method that distinguishes between these sources of incongruence and identifies lineages that are responsible for significant differences between phylogenies. We use the logic of conditional combination in that we first test for statistically significant incongruence using the partition homogeneity test. Then we remove all possible combinations of taxa until a non-significant result of this test is achieved. Finally, we construct a 'combined evidence' phylogeny and then reposition the incongruent taxa. This method produces trees for final comparison using reconciliation methods, but it includes only as many incongruence events as can be statistically justified from the data sets. We apply this method to a host–parasite (gopher–louse) data set and identify many fewer incongruence events than do topology based analyses alone. Our method is broadly applicable to comparisons of phylogenies of interacting taxa, such as hosts and parasites, or mutualists. The method should also be useful for other problems involving comparisons of phylogenies, such as multiple gene trees or cladistic biogeography.     

Scoring clustering solutions by their biological relevance

MOTIVATION: A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering gene expression data into homogeneous groups was shown to be instrumental in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on clustering algorithms for gene expression analysis, very few works addressed the systematic comparison and evaluation of clustering results. Typically, different clustering algorithms yield different clustering solutions on the same data, and there is no agreed upon guideline for choosing among them. RESULTS: We developed a novel statistically based method for assessing a clustering solution according to prior biological knowledge. Our method can be used to compare different clustering solutions or to optimize the parameters of a clustering algorithm. The method is based on projecting vectors of biological attributes of the clustered elements onto the real line, such that the ratio of between-groups and within-group variance estimators is maximized. The projected data are then scored using a non-parametric analysis of variance test, and the score's confidence is evaluated. We validate our approach using simulated data and show that our scoring method outperforms several extant methods, including the separation to homogeneity ratio and the silhouette measure. We apply our method to evaluate results of several clustering methods on yeast cell-cycle gene expression data. AVAILABILITY: The software is available from the authors upon request.     

Incorporating single-locus tests into haplotype cladistic analysis in case-control studies

In case-control studies, genetic associations for complex diseases may be probed either with single-locus tests or with haplotype-based tests. Although there are different views on the relative merits and preferences of the two test strategies, haplotype-based analyses are generally believed to be more powerful to detect genes with modest effects. However, a main drawback of haplotype-based association tests is the large number of distinct haplotypes, which increases the degrees of freedom for corresponding test statistics and thus reduces the statistical power. To decrease the degrees of freedom and enhance the efficiency and power of haplotype analysis, we propose an improved haplotype clustering method that is based on the haplotype cladistic analysis developed by Durrant et al. In our method, we attempt to combine the strengths of single-locus analysis and haplotype-based analysis into one single test framework. Novel in our method is that we develop a more informative haplotype similarity measurement by using p-values obtained from single-locus association tests to construct a measure of weight, which to some extent incorporates the information of disease outcomes. The weights are then used in computation of similarity measures to construct distance metrics between haplotype pairs in haplotype cladistic analysis. To assess our proposed new method, we performed simulation analyses to compare the relative performances of (1) conventional haplotype-based analysis using original haplotype, (2) single-locus allele-based analysis, (3) original haplotype cladistic analysis (CLADHC) by Durrant et al., and (4) our weighted haplotype cladistic analysis method, under different scenarios. Our weighted cladistic analysis method shows an increased statistical power and robustness, compared with the methods of haplotype cladistic analysis, single-locus test, and the traditional haplotype-based analyses. The real data analyses also show that our proposed method has practical significance in the human genetics field.     

A simple method for the analysis of clustered binary data.

A simple method for comparing independent groups of clustered binary data with group-specific covariates is proposed. It is based on the concepts of design effect and effective sample size widely used in sample surveys, and assumes no specific models for the intracluster correlations. It can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing. The method is applied to a variety of problems involving clustered binary data: testing homogeneity of proportions, estimating dose-response models and testing for trend in proportions, and performing the Mantel-Haenszel chi-squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance. Illustrative applications of the method are also presented.     

Rapid initial clustering of large data sets

Summary Multivariate analysis of plant community data has three goals: summarization of redundancy, identification of outliers, and elueidation of relationships. The first two are handled conveniently by initial fast clustering, and the third by subsequent ordination and hierarchical clustering, and perhaps table arrangement.Initial clustering algorithms should achieve withincluster homogeneity and require minimal computer resources. However, algorithmic uniqueness and a hierarchy are not needed. Computing time should be proportional to the amount of data, with no higher dependencies on the number of samples. A method is presented here meeting these requirements, called composite clustering and implemented in a FORTRAN program called COMPCLUS. The computer time required for COMPCLUS clustering is on the order of the time required merely to read the data, regardless of the number of samples.Several large field data sets were analyzed effectively by using COMPCLUS to reduce redundancy and identify outliers, and then ordinating the resulting composite clusters by detrended correspondence analysis (DECORANA). Various clusterings of the same data set can be compared using a percent mutual matches (PMM) index, and a matrix of such values can be ordinated for simultaneous comparison of a number of clusterings.This paper benefited at many points from discussions with Mark O. Hill and Robert H. Whittaker. Mark Hill suggested condensed data storage. This work was done under a National Science Foundation grant to Robert Whittaker. I also appreciate technical assistance from Timothy F. Mason and Steven B. Singer.     

Text mining biomedical literature for discovering gene-to-gene relationships: a comparative study of algorithms

Partitioning closely related genes into clusters has become an important element of practically all statistical analyses of microarray data. A number of computer algorithms have been developed for this task. Although these algorithms have demonstrated their usefulness for gene clustering, some basic problems remain. This paper describes our work on extracting functional keywords from MEDLINE for a set of genes that are isolated for further study from microarray experiments based on their differential expression patterns. The sharing of functional keywords among genes is used as a basis for clustering in a new approach called BEA-PARTITION in this paper. Functional keywords associated with genes were extracted from MEDLINE abstracts. We modified the Bond Energy Algorithm (BEA), which is widely accepted in psychology and database design but is virtually unknown in bioinformatics, to cluster genes by functional keyword associations. The results showed that BEA-PARTITION and hierarchical clustering algorithm outperformed k-means clustering and self-organizing map by correctly assigning 25 of 26 genes in a test set of four known gene groups. To evaluate the effectiveness of BEA-PARTITION for clustering genes identified by microarray profiles, 44 yeast genes that are differentially expressed during the cell cycle and have been widely studied in the literature were used as a second test set. Using established measures of cluster quality, the results produced by BEA-PARTITION had higher purity, lower entropy, and higher mutual information than those produced by k-means and self-organizing map. Whereas BEA-PARTITION and the hierarchical clustering produced similar quality of clusters, BEA-PARTITION provides clear cluster boundaries compared to the hierarchical clustering. BEA-PARTITION is simple to implement and provides a powerful approach to clustering genes or to any clustering problem where starting matrices are available from experimental observations.     

COULD A CLADOGRAM THIS SHORT HAVE ARISEN BY CHANCE ALONE?: ON PERMUTATION TESTS FOR CLADISTIC STRUCTURE

Abstract Absolute criteria for evaluating cladistic analyses are useful, not only because cladistic algorithms impose structure, but also because applications of cladistic results demand some assessment of the degree of corroboration of the cladogram. Here, a means of quantitative evaluation is presented based on tree length. The length of the most-parsimonious tree reflects the degree to which the observed characters co-vary such that a single tree topology can explain shared character states among the taxa. This “cladistic covariation” can be quantified by comparing the length of the most parsimonious tree for the observed data set to that found for data sets with random covariation of characters. A random data set is defined as one in which the original number of characters and their character states are maintained, but for each character, the states are randomly reassigned to the taxa. The cladistic permutation tail probability, PTP, is defined as the estimate of the proportion of times that a tree can be found as short or shorter than the original tree. Significant cladistic covariation exists if the PTP is less than a prescribed value, for example, 0.05. In case studies based on molecular and morphological data sets, application of the PTP shows that:

• 1 In the comparison of four different molecular data sets for orders of mammals, the sequence data set for alpha hemoglobin does not have significant cladistic covariation, while that for alpha crystallin is highly significant. However, when each data set was reduced to the 11 common taxa in order to standardize comparison, reduced levels of cladistic covariation, with no clear superiority of the alpha crystallin data, were found. Morphological data for these 11 taxa had a highly significant PTP, producing a tree roughly congruent with those for the three molecular sets with marginal or significant PTP values. Merging of all data sets, with the exclusion of the poorly structured alpha hemoglobin data, produced a data set with a significant PTP, and provides an estimate of the phylogenetic relationships among these 11 orders of mammals.
• 2 In an analysis of lactalbumin and lysozyme DNA sequence data for four taxa, purine-pyrimidine coding yields a data set with significant cladistic covariation, while other codings fail. The data for codon position 3 taken alone exhibit the strongest cladistic covariation.
• 3 A data set based on flavonoids in taxa of Polygonum initially yields a significant PTP; however, deletion of identically scored taxa leaves no significant cladistic covariation.
• 4 For mitochondrial DNA data on population genome types for four species of the crested newt, there is significant cladistic covariation for the set of all genome types, and among the five mtDNA genome types within one of the species. However, a conditional PTP test that assumes species monophyly shows that no significant cladistic covariation exists among the fur species for these data.
• 5 In an application of the test to a group of freshwater insects, as preliminary to biological monitoring, individual subsets of the taxonomic data representing larval, pupal, and adult stages had non-significant PTPs, while the complete data set showed significant cladistic structure.

     

Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees

MOTIVATION: Gene expression data clustering provides a powerful tool for studying functional relationships of genes in a biological process. Identifying correlated expression patterns of genes represents the basic challenge in this clustering problem. RESULTS: This paper describes a new framework for representing a set of multi-dimensional gene expression data as a Minimum Spanning Tree (MST), a concept from the graph theory. A key property of this representation is that each cluster of the expression data corresponds to one subtree of the MST, which rigorously converts a multi-dimensional clustering problem to a tree partitioning problem. We have demonstrated that though the inter-data relationship is greatly simplified in the MST representation, no essential information is lost for the purpose of clustering. Two key advantages in representing a set of multi-dimensional data as an MST are: (1) the simple structure of a tree facilitates efficient implementations of rigorous clustering algorithms, which otherwise are highly computationally challenging; and (2) as an MST-based clustering does not depend on detailed geometric shape of a cluster, it can overcome many of the problems faced by classical clustering algorithms. Based on the MST representation, we have developed a number of rigorous and efficient clustering algorithms, including two with guaranteed global optimality. We have implemented these algorithms as a computer software EXpression data Clustering Analysis and VisualizATiOn Resource (EXCAVATOR). To demonstrate its effectiveness, we have tested it on three data sets, i.e. expression data from yeast Saccharomyces cerevisiae, expression data in response of human fibroblasts to serum, and Arabidopsis expression data in response to chitin elicitation. The test results are highly encouraging. AVAILABILITY: EXCAVATOR is available on request from the authors.     

3-D clustering: a tool for high throughput docking

This report describes a computer program for clustering docking poses based on their 3-dimensional (3D) coordinates as well as on their chemical structures. This is chiefly intended for reducing a set of hits coming from high throughput docking, since the capacity to prepare and biologically test such molecules is generally far more limited than the capacity to generate such hits. The advantage of clustering molecules based on 3D, rather than 2D, criteria is that small variations on a scaffold may bring about different binding modes for molecules that would not be predicted by 2D similarity alone. The program does a pose-by-pose/atom-by-atom comparison of a set of docking hits (poses), scoring both spatial and chemical similarity. Using these pair-wise similarities, the whole set is clustered based on a user-supplied similarity threshold. An output coordinate file is created that mirrors the input coordinate file, but contains two new properties: a cluster number and similarity to the cluster center. Poses in this output file can easily be sorted by cluster and displayed together for visual inspection with any standard molecular viewing program, and decisions made about which molecule should be selected for biological testing as the best representative of this group of similar molecules with similar binding modes.     

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.     

Parallelism,parsimony, and the phytogeny of the lemuridae

In spite of the increasing popularity of cladistic methods in studies of primate systematics, few authors have investigated the effects of parallel evolution when such methods are applied to empirical data. To counter the effects of parallelism, cladistic techniques rely on the principle of evolutionary parsimony. When parsimony procedures are used to reconstruct the phylogeny of the Lemuridae, nine highly parsimonious phylogenies can be deduced. Further choice among these competing hypotheses of relationship is determined by the extent to which one embraces the parsimony principle. The phylogeny obtained by the most rigorous adherence to the parsimony principle is one which is wholly consistent with traditional evolutionary classifications of the Lemuridae. Moderate levels of parallelism can lead to the generation of several plausible, alternative phylogenetic hypotheses; less than 25% of the characters analyzed here need have evolved in parallel, yet they are largely responsible for the ambiguity of the nine different lemurid phylogenies. This suggests that phylogeny reconstructions based entirely on cladistic methods do not provide a suitable basis for the construction of classifications for groups such as the order Primates, where the degree of parallelism is likely to be quite high.     

A botanical critique of cladism

Clade versus grade is an old question in taxonomy, going back as far as Darwin himself. Taxonomists have long believed that both must be taken into account in the formation of a general-purpose system. Recently clade has been elevated to a position of total dominance by a group of taxonomists who take their inspiration from Willi Hennig. Mayr has dubbed this approach cladism, and its exponents cladists. Cladistic theory is being vigorously developed and propounded by Hennig’s disputatious disciples, and much of the present-day theory would scarcely be recognized by the founder. I here address myself to what I consider the core features of present-day cladism. The essential distinctive feature of cladism, and its fatal flaw, is that a group is considered to be monophyletic, and thus taxonomically acceptable, only if it includesall the descendants from the most recent common ancestor. The traditional taxonomic view has been that a group can still be considered monophyletic (and thus taxonomically acceptable) after some of its more divergent branches have been trimmed off. This simple and seemingly innocuous difference has profound consequences to the taxonomic system. In Hennigian classification, organisms are ranked entirely on the basis of recency of common descent, that is, on the basis of the sequence of dichotomies in the inferred phylogeny. Theamount of divergence scarcely enters into the picture. This procedure represents an effort to capture taxonomy for a narrowly limited special purpose, at the expense of the important and necessary function of providing a general-purpose system that can be used by all who are concerned with similarities and differences among organisms. The first corollary of the Hennigian concept of phylogenetic taxonomy is that no existing taxon can be ancestral to any other existing taxon. The descendant must be included in the same taxon as its ancestor. At the level of species this is palpably false. The ancestral species often continues to exist for an indefinite time after giving rise to one or more descendants. At the higher taxonomic levels adherence to the principle often requires excessive lumping or excessive splitting to avoid paraphyletic groups (i.e., groups that do not include all of their own descendants), and it forbids the taxonomic recognition of many conceptually useful groups. Neither the prokaryotes nor the dicotyledons form a cladistically acceptable taxon, since both are paraphyletic. The prokaryotes are putatively ancestral to the eukaryotes, and the dicotyledons are putatively ancestral to the monocotyledons. Many other traditional and readily recognizable taxa would have to be abandoned, without being replaced by conceptually useful groups. Fossils present a special problem, because the whole concept of cladistic classification depends on the absence of taxa at the branch points of the cladogram. Presumably all of these branch points were at some time in the past represented by actual taxa, which under cladistic theory can neither be assigned to one of their descendants nor treated as paraphyletic taxa. The difficulty is mitigated somewhat by the gaps in the known fossil record. Once it is admitted that paraphyletic as well as holophyletic groups are taxonomically acceptable, there is much value in cladistic methodology. Formal outgroup comparison for the establisment of polarity, and the emphasis on synapomorphies in the construction of a cladogram can both be usefully incorporated into taxonomic theory and practice. These require no revolution in taxonomic thought. There are unresolved problems, however, in how to gather and manipulate the data, and how to interpret the cladogram produced by computers. In any complex group, the computer may produce several or many cladograms of equal or nearly equal parsimony. This is particularly true in angiosperms, among which the extensive evolutionary parallelism casts doubt on the importance of parsimony and may lead to the production of hundreds of such cladograms for a single group. Despite the claims of objectivity and repeatability in cladistic taxonomy, the necessity for some subjective decisions remains. The Wagner groundplan-divergence method has most of the advantages of formal cladism without the most important disadvantages. Wagner accepts paraphyletic taxa in principle, and he casts a wider net for data bearing on the polarity of characters. In complex groups consisting of many taxa, however, both methods retain a strong subjective component in the computer manipulation and in the degree of reliance on absolute parsimony.     

Automated statistical analysis of microbial enumeration by dilution series

Equations are formulated for the standard error and confidence interval for the MPN estimate of microbial density from a general dilution series. A statistical test of homogeneity is presented. This tests whether a handling error in the dilution series may have occurred which would invalidate the density estimate. The analysis may be automated using a Basic computer program which contains a fast algorithm for the solution of the general MPN equation. This allows the calculation of the MPN, standard error, 95% confidence interval and test statistic for any dilution series, with any degree of replication at each dilution level, with variable sample volumes at each dilution level, with variable dilution ratio between levels, and with any number of levels.     

Taxic and Transformational Homology: Different Ways of Seeing

Hypotheses of taxic homology are hypotheses of taxa (groups). Hypotheses of transformational homology are hypotheses of transformations between character states within the context of an explicit model of character evolution. Taxic and transformational homology are discussed with respect to secondary loss and reversal in the context of three-taxon statement analysis and standard cladistic analysis. We argue that it is important to distinguish complement relation homologies from those that we term paired homologues. This distinction means that the implementation of three-taxon statement analysis needs modification if all data are to be considered potentially informative. Modified three-taxon statement analysis and standard cladistic analysis yield different results for the example of character reversal provided by Kluge (1994) for both complement relation data and paired homologues. We argue that these different results reflect the different approaches of standard cladistic analysis and modified t.t.s. analysis. In the standard cladistic approach, absence, as secondary loss, can provide evidence for a group. This is because the standard cladistic approach implements a transformational view of homology. In the t.t.s approach discussed in this paper, absence can only be interpreted as secondary loss by congruence with other data; absence alone can never provide evidence for a group. In this respect, the modified t.t.s. approach is compatible with a taxic view of homology.     

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.     

CONGRUENCE BETWEEN SUPERPOSITIONAL AND PHYLOGENETIC PATTERNS: COMPARING CLADISTIC PATTERNS WITH FOSSIL RECORDS

Abstract— As the only direct evidence of past organismic history, the fossil record has always figured importantly in the reconstruction of phylogeny. But the incomplete nature of the fossil record has also been cited as a basis for claiming that fossils play only a secondary role in developing phylogenetic hypotheses that encompass extant taxa. The reliability of fossil data in such applications is a function of the degree of fit between superpositional relationships and the sequence of phylogenetic events. Thirty-eight vertebrate cases are examined for the fit between age data based on fossil first occurrences and phylogenetic results based on cladistic analysis. A general correspondence between superpositional and cladistic information is observed, although the degree of fit varies widely among cases. Horses, certain other ungulates, synapsids and basal archosaurs, which show very high correlations, are taxa characterized by an abundance of superpositional and cladistic data. Other groups, such as primates, show very poor correlations because certain major clades have either unreasonably short fossil durations or no fossil record at all. Correlations are also diminished when either fossil records or cladistic sequences are poorly resolved. In most cases, cladistic resolution was observed to exceed superpositional resolution. Correlations can be enhanced by more precise (e.g. radiometric) age dates, but these also place a high expectation on the fit between fossil first occurrence and cladistic results. Stratigraphic occurrence does not always provide a precise reflection of independently derived phylogenies, but the correspondence between age and cladistic information is remarkably high in a notable number of vertebrate examples.     

A FORTRAN program for testing trend and homogeneity in proportions

A FORTRAN program is provided for testing linear trend and homogeneity in proportions. Trend is evaluated by the Cochran-Armitage method and homogeneity is tested by an overall X2 test as well by multiple pairwise comparisons by the Fisher-Irwin exact method. The program should be easy to implement on any size of computer with a FORTRAN compiler.