PERMUTATION TESTS AND OUTGROUPS

Abstract — Commonly used permutation tail probability (PTP) and topology dependent permutation tail probability (T-PTP) tests incorporate an inappropriate treatment of designated outgroup taxa, and for that reason are biased either for (PTP) or for or against (T-PTP) rejection of the null hypothesis. A modified test is proposed, in which this source of bias is eliminated.     

The future of phylogeny reconstruction

A new approach to phylogenetic analysis, parsimony jackknifing, uses simple parsimony calculations combined with resampling of characters to arrive at a tree comprising well-supported groups. This is usually much the same as the consensus of most-parsimonious trees found from extensive multiple-tree calculations, but the new method is thousands of times faster, allowing analysis of much larger data matrices, and also provides information on the strength of support for different groups. Jackknife frequencies provide a more reliable assessment of support than do alternative methods, notably "confidence probability" (CP) and T-PTP testing.     

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.     

When Are Random Data Not Random,or Is the PTP Test Useful?

Recently, empirical evidence was presented that the permutation tail probability (PTP) test has extremely low discriminatory power when assessing character covariance in phylogenetic data based on bootstrap measures of confidence. Here we are concerned with the problem of using one statistical approach, especially when applied to empirical data, to judge the performance of another. Applying an appropriate statistical approach, we statistically demonstrated that the PTP test is extremely weak in detecting the absence of character covariation. In addition, we show that PTP is highly dependent on the number of terminals and the proportion of character states in phylogenetic matrices. In conclusion, we advocate the use of simulation studies when testing the performance of statistical tools applied to phylogenetic data.     

Is the PTP Test Useful?

We show empirically that the PTP test has very little discriminatory power, with highly significant PTP test probabilities often being associated with parsimony data that produce trees with low confidence (as measured by bootstrapping) and resolution. Because of this, we argue that the PTP test is useful only in the following, very limited way: if a data set fails the PTP test, it should not be used in a phylogenetic analysis. More conservative methods of measuring confidence such as the bootstrap or decay index are preferable.     

Taxon names as paradigms: the structure of nomenclatural revolutions

In the present paper I argue that the two systems of phylogenetic nomenclature hitherto proposed represent, in a generalized sense, two different philosophies for how science develops and progresses. The phylogenetic system of definition initially proposed by de Queiroz and Gauthier [Syst. Zool. 39 (1990) 307], and later labeled PSD, is typically Popperian in the sense that science progresses toward truth by an accumulation of knowledge. Phylogenetic definitions of taxon names are assumed to adapt automatically to each new hypothesis of phylogeny, thereby reflecting better and better hypotheses. The phylogenetic system of reference proposed by Härlin [Zool. Scr. 27 (1998a) 381], on the other hand, is more Kuhnian, because it is built on the idea that successive hypotheses are incommensurable (and thus not cumulative) and that taxon names might be equalled with low‐level paradigms.     

Phylogenetic relationships of the family Axinellidae (Porifera: Demospongiae) using morphological and molecular data

Alvarez, B., Crisp, M.D., Driver, F., Hooper, J.N.A. & Van Soest, R.W.M. (2000). Phylogenetic relationships of the family Axinellidae (Porifera: Demospongiae) using morphological and molecular data. —Zoologica Scripta, 29, 169–198. Twenty‐seven species of marine sponges belonging to Axinellidae and related groups (Halichondriidae, Dictyonellidae, Agelasida) were selected to test the monophyly of Axinellidae and investigate their phylogenetic relationships using parsimony and maximum likelihood methods. Partial 28S rDNA sequences, including the D3 domain, and traditional morphological characters (mainly skeletal ones) were used independently to construct phylogenetic trees. Sequences were aligned using the appropriate model of secondary structure of the RNA and compared to that produced by the multiple sequence alignment program, ClustalW. The alignment using secondary structure constraints produced a better estimate of the phylogeny and was demonstrated to be an effective and objective method. Results of the cladistic analyses of the molecular and morphological data sets were not fully congruent; the morphological data suggest that Axinellidae is monophyletic, however, the molecular data suggest that it is nonmonophyletic. The single most‐parsimonious tree derived from the molecular data showed that species of Axinella (except A. polypoides) are united in a clade that is more closely related to members of Agelasida than to other species of Axinellidae; the remaining members of Axinellidae form a monophyletic group that is closely related to the families Dictyonellidae and Halichondriidae. The consensus tree of 20 most‐parsimonious trees from the morphological analysis, on the other hand, showed that all the sampled species of Axinellidae belong to a monophyletic group which is closely related to the species of Dictyonellidae and Halichondriidae. Only two branches were identical in both cladograms, the one uniting the species of Ptilocaulis and Reniochalina and the one with the species of Dictyonellidae. The robustness of the molecular and morphological trees (or parts of the trees), was tested using bootstrap, jack‐knife, PTP and T‐PTP tests. The results of the PTP test were significant indicating significant cladistic structure in both data sets. The bootstrap and jack‐knife values indicate that the molecular tree is in general better supported than the morphological one. The lack of morphological characters and the homoplastic nature of some may explain the weak support of the morphological tree. A T‐PTP test of nonmonophyly showed that the nonmonophyly of Axinellidae, as indicated by the results of the molecular analysis, is not significant; however, a T‐PTP test of monophyly of Axinellidae, as indicated by the morphological tree, produced significant results. This indicates that the monophyly of Axinellidae based on morphological data cannot be rejected; the family however, cannot be defined in terms of a unique diagnostic character common to all members of the ingroup. Tests of heterogeneity (reciprocal T‐PTP and partition homogeneity test) indicated that the data partitions are heterogeneous, which could be due to sampling errors (in either data set) or differences in the underlying phylogenies; therefore data were not combined in a single analysis. Further, both data sets are unequally sized (95 informative molecular characters vs. 16 informative morphological characters), which means that the molecular signal could swamp the morphological signal if the data is combined. Nonmonophyly of Axinellidae is supported by chemical and genetic evidence available in the literature and DNA sequences data of axinellid species from New Zealand. However, this needs to be confirmed using independent evidence from different genes (or gene regions), biochemistry, histology or cell ultrastructure. Therefore, no changes to the taxonomic position of the family in the higher classification are proposed at this stage.     

Frigatebirds, Tropicbirds, and Ciconiida: Excesses of Confidence Probability

Because it is based on a significance test that takes the shape of the tree as given, the Rzhetsky/Nei Confidence Probability (CP) can attribute high "confidence" to groups with little or even literally no support. CP further overestimates confidence in that it takes no account of reliability of alignment, and it shows instability in that drastic changes in results can be produced by small changes in data. Instability can arise when alignment is uncertain, since different alignment strategies can lead to slightly different matrices. Parsimony jackknifing offers a more reliable and stable way of assessing support. To take ambiguities of alignment into account with parsimony jackknifing, we suggest "consensus" and "average" methods of summarizing jackknife results from several alignments. Reanalyzing 12S and 16S rRNA data on pelecaniform birds, we find that CP has overestimated support for the Ciconiida, for placing frigatebirds with condors, and for placing tropicbirds with cormorants.     

Radical instability and spurious branch support by likelihood when applied to matrices with non-random distributions of missing data

Non-random distributions of missing data are a general problem for likelihood-based statistical analyses, including those in a phylogenetic context. Extensive non-randomly distributed missing data are particularly problematic in supermatrix analyses that include many terminals and/or loci. It has been widely reported that missing data can lead to loss of resolution, but only very rarely create misleading or otherwise unsupported results in a parsimony context. Yet this does not hold for all parametric-based analyses because of their assumption of homogeneity across characters and lineages, which can lead to both long-branch attraction and long-branch repulsion. Contrived examples were used to demonstrate that non-random distributions of missing data, even without rate heterogeneity among characters and a well fitting model, can provide misleading likelihood-based topologies and branch-support values that are radically unstable based on slight modifications to character sampling. The same can occur despite complete absence of parsimony-informative characters. Otherwise unsupported resolution and high branch support for these clades were found to occur frequently in 22 empirical examples derived from a published supermatrix. Partitioning characters based on the distribution of missing data helped to decrease, but did not eliminate, these artifacts. These artifacts were exacerbated by low quality tree searches, particularly when holding only a single optimal tree that must be fully resolved.     

Relationships within Cornales and circumscription of Cornaceae-matK and rbcL sequence data and effects of outgroups and long branches

Phylogenetic relationships in Cornales were assessed using sequences rbcL and matK. Various combinations of outgroups were assessed for their suitability and the effects of long branches and outgroups on tree topology were examined using RASA 2.4 prior to conducting phylogenetic analyses. RASA identified several potentially problematic taxa having long branches in individual data sets that may have obscured phylogenetic signal, but when data sets were combined RASA no longer detected long branch problems. t(RASA) provides a more conservative measurement for phylogenetic signal than the PTP and skewness tests. The separate matK and rbcL sequence data sets were measured as not containing phylogenetic signal by RASA, but PTP and skewness tests suggested the reverse [corrected]. Nonetheless, the matK and rbcL sequence data sets suggested relationships within Cornales largely congruent with those suggested by the combined matK-rbcL sequence data set that contains significant phylogenetic signal as measured by t(RASA), PTP, and skewness tests. Our analyses also showed that a taxon having a long branch on the tree may not be identified as a "long-branched" taxon by RASA. The long branches identified by RASA had little effect on the arrangement of other taxa in the tree, but the placements of the long-branched taxa themselves were often problematic. Removing the long-branched taxa from analyses generally increased bootstrap support, often substantially. Use of non-optimal outgroups (as identified by RASA) decreased phylogenetic resolution in parsimony analyses and suggested different relationships in maximum likelihood analyses, although usually weakly supported clades (less than 50% support) were impacted. Our results do not recommend using t(RASA) as a sole criterion to discard data or taxa in phylogenetic analyses, but t(RASA) and the taxon variance ratio obtained from RASA may be useful as a guide for improved phylogenetic analyses. Results of parsimony and ML analyses of the sequence data using optimal outgroups suggested by RASA revealed four major clades within Cornales: (1) Curtisia-Grubbia, (2) Cornus-Alangium, (3) Nyssa-Camptotheca-Davidia-Mastixia-Diplopanax, and (4) Hydrangeaceae-Loasaceae, with clades (2) and (3) forming a monophyletic group sister to clade (4) and clade (1) sister to the remainder of Cornales. However, there was not strong bootstrap support for relationships among the major clades. The placement of Hydrostachys could not be reliably determined, although most analyses place the genus within Hydrangeaceae; ML analyses, for example, placed the genus as the sister of Hydrangeeae. Our results supported a Cornales including the systematically problematic Hydrostachys, a Cornaceae consisting of Cornus and Alangium, a Nyssaceae consisting of Nyssa and Camptotheca, a monogeneric Davidiaceae, a Mastixiaceae consisting of Mastixia and Diplopanax, and an expanded Grubbiaceae consisting of Grubbia and Curtisia, and two larger families, Hydrangeaceae and Loasaceae.     

Rejecting "the given" in systematics

How morphology and systematics come together through morphological analysis, homology hypotheses and phylogenetic analysis is a topic of continuing debate. Some contemporary approaches reject biological evaluation of morphological characters and fall back on an atheoretical and putatively objective (but, in fact, phenetic) approach that defers to the test of congruence for homology assessment. We note persistent trends toward an uncritical empiricism (where evidence is believed to be immediately “given” in putatively theory‐free observation) and instrumentalism (where hypotheses of primary homology become mere instruments with little or no empirical foundation for choosing among competing phylogenetic hypotheses). We suggest that this situation is partly a consequence of the fact that the test of congruence and the related concept of total evidence have been inappropriately tied to a Popperian philosophy in modern systematics. Total evidence is a classical principle of inductive inference and does not imply a deductive test of homology. The test of congruence by itself is based philosophically on a coherence theory of truth (coherentism in epistemology), which is unconcerned with empirical foundation. We therefore argue that coherence of character statements (congruence of characters) is a necessary, but not a sufficient, condition to support or refute hypotheses of homology or phylogenetic relationship. There should be at least some causal grounding for homology hypotheses beyond mere congruence. Such causal grounding may be achieved, for example, through empirical investigations of comparative anatomy, developmental biology, functional morphology and secondary structure. © The Willi Hennig Society 2006.     

Phylogenetic ANOVA: Group‐clade aggregation,biological challenges,and a refined permutation procedure

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.     

Phylogenetic signal in AFLP data sets

AFLP markers provide a potential source of phylogenetic information for molecular systematic studies. However, there are properties of restriction fragment data that limit phylogenetic interpretation of AFLPs. These are (a) possible nonindependence of fragments, (b) problems of homology assignment of fragments, (c) asymmetry in the probability of losing and gaining fragments, and (d) problems in distinguishing heterozygote from homozygote bands. In the present study, AFLP data sets of Lactuca s.l. were examined for the presence of phylogenetic signal. An indication of this signal was provided by carrying out tree length distribution skewness (g1) tests, permutation tail probability (PTP) tests, and relative apparent synapomorphy analysis (RASA). A measure of the support for internal branches in the optimal parsimony tree (MPT) was made using bootstrap, jackknife, and decay analysis. Finally, the extent of congruence in MPTs for AFLP and internal transcribed spacer (ITS)-1 data sets for the same taxa was made using the partition homogeneity test (PHT) and the Templeton test. These analytical studies suggested the presence of phylogenetic signal in the AFLP data sets, although some incongruence was found between AFLP and ITS MPTs. An extensive literature survey undertaken indicated that authors report a general congruence of AFLP and ITS tree topologies across a wide range of taxonomic groups, suggesting that the present results and conclusions have a general bearing. In these earlier studies and those for Lactuca s.l., AFLP markers have been found to be informative at somewhat lower taxonomic levels than ITS sequences. Tentative estimates are suggested for the levels of ITS sequence divergence over which AFLP profiles are likely to be phylogenetically informative.     

Grebes and flamingos: standards of evidence,adjudication of disputes,and societal politics in avian systematics

The recent proposal of a sister‐group relationship between the Neoavian grebes (Podicipedidae) and flamingos (Phoenicopteridae) is chronicled, and morphological evidence claimed to be supportive of the grouping is examined. The hypothesis arose from an exiguous amalgam of molecular inferences, advanced in part by a pervasive, unsupported superiority conferred upon sequence data, and adopted by several societal committees on avian classification. Morphological characters marshalled specifically to support the hypothesis were found to be erroneous, and associated phylogenetic analyses, where given, were ambiguous. A combined analysis of large data sets for morphology and RAG‐1 sequences found flamingos and storks to be sister groups but with reduced support. This example illustrates problems attending the synthesis of contradictory evidence and evaluation of unprecedented hypotheses, and reveals the informality by which revisions are adopted. Procedures for rational synthesis of evidence are needed for progress during this challenging but promising period of diversified phylogenetics, without which disputes will be dominated increasingly by polarized, intransigent prejudice regarding methods and data.© The Willi Hennig Society 2010.     

The Australian Aborigines and the Human Past

Indifference to events which may actually have taken place between the Dreamtime and European contact is commonly held to be a salient feature of traditional Aboriginal thought. This contention contains a significant element of truth but it may have been exaggerated by some anthropologists. Structural-functionalist emphases on myth as charter led not only to the rejection of historical interpretations of Aboriginal myths which were ill-considered and naïve, but also to an excessive neglect of potentially fruitful attempts to extract from myths clues about post-Dreamtime experiences. This neglect has unduly strengthened the view that Aboriginal thought is entirely sui generis and that its supposed indifference to human history is an inescapable cultural attribute of Aboriginality. A sketch is offered for a reappraisal of the significance of Aboriginal myths for Aboriginal history.     

Phylogenetic Classification at Generic Level in the Absence of Distinct Phylogenetic Patterns of Phenotypical Variation: A Case Study in Graphidaceae (Ascomycota)

Molecular phylogenies often reveal that taxa circumscribed by phenotypical characters are not monophyletic. While re-examination of phenotypical characters often identifies the presence of characters characterizing clades, there is a growing number of studies that fail to identify diagnostic characters, especially in organismal groups lacking complex morphologies. Taxonomists then can either merge the groups or split taxa into smaller entities. Due to the nature of binomial nomenclature, this decision is of special importance at the generic level. Here we propose a new approach to choose among classification alternatives using a combination of morphology-based phylogenetic binning and a multiresponse permutation procedure to test for morphological differences among clades. We illustrate the use of this method in the tribe Thelotremateae focusing on the genus Chapsa, a group of lichenized fungi in which our phylogenetic estimate is in conflict with traditional classification and the morphological and chemical characters do not show a clear phylogenetic pattern. We generated 75 new DNA sequences of mitochondrial SSU rDNA, nuclear LSU rDNA and the protein-coding RPB2. This data set was used to infer phylogenetic estimates using maximum likelihood and Bayesian approaches. The genus Chapsa was found to be polyphyletic, forming four well-supported clades, three of which clustering into one unsupported clade, and the other, supported clade forming two supported subclades. While these clades cannot be readily separated morphologically, the combined binning/multiresponse permutation procedure showed that accepting the four clades as different genera each reflects the phenotypical pattern significantly better than accepting two genera (or five genera if splitting the first clade). Another species within the Thelotremateae, Thelotrema petractoides, a unique taxon with carbonized excipulum resembling Schizotrema, was shown to fall outside Thelotrema. Consequently, the new genera Astrochapsa, Crutarndina, Pseudochapsa, and Pseudotopeliopsis are described here and 39 new combinations are proposed.     

Hidden likelihood support in genomic data: can forty-five wrongs make a right?

Combined analysis of multiple phylogenetic data sets can reveal emergent character support that is not evident in separate analyses of individual data sets. Previous parsimony analyses have shown that this hidden support often accounts for a large percentage of the overall phylogenetic signal in cladistic studies. Here, reanalysis of a large comparative genomic data set for yeast (genus Saccharomyces) demonstrates that hidden support can be an important factor in maximum likelihood analyses of multiple data sets as well. Emergent signal in a concatenation of 106 genes was responsible for up to 64% of the likelihood support at a particular node (the difference in log likelihood scores between optimal topologies that included and excluded a supported clade). A grouping of four yeast species (S. cerevisiae, S. paradoxus, S. mikatae, and S. kudriavzevii) was robustly supported by combined analysis of all 106 genes, but separate analyses of individual genes suggested numerous conflicts. Forty-eight genes strictly contradicted S. cerevisiae + S. paradoxus + S. mikatae + S. kudriavzevii in separate analyses, but combined likelihood analyses that included up to 45 of the "wrong" data sets supported this group. Extensive hidden support also emerged in a combined likelihood analysis of 41 genes that each recovered the exact same topology in separate analyses of the individual genes. These results show that isolated analyses of individual data sets can mask congruence and distort interpretations of clade stability, even in strictly model-based phylogenetic methods. Consensus and supertree procedures that ignore hidden phylogenetic signals are, at best, incomplete.     

The evolution of ecologically important characters in Heliconius butterflies (Lepidoptera: Nymphalidae): a cladistic review

The biology of Heliconius butterflies has provided a rich source of data to test theories of ecological genetics, coevolution and community ecology. Many putatively adaptive characters have been discussed with reference to a phylogenetic hypothesis based on a variety of morphological and life-history traits interpreted from an evolutionary taxonomic perspective. Here, alternate interpretations of characters on the traditional tree and a more recent mitochondrial DNA cladogram with a substantially different topology are compared and contrasted. It is shown that many characters ostensibly providing support for the traditional phylogenetic hypothesis are almost equally parsimoniously distributed and in some cases more parsimoniously distributed on the mtDNA tree than on the tree inferred from those characters. Discussion of alternate evolutionary scenarios based on the mDNA-based topology is presented for pupal mating, pollen feeding, foodplant coevolution, and other ecologically significant features.     

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.

     

Homology as a parsimony problem: a dynamic homology approach for morphological data

The primary data used to reconstruct phylogenies comes organized in the conceptual grid of homology correspondences, and the construction of this theory‐rich grid depends in part on knowledge of relationships. This situation is not satisfactory as a conceptual system, because the evidence is not clearly delimited from the results. I explore the testing of alternative hypotheses of morphological correspondences in a quantitative cladistic context. The varying homology assessments implied by classical criteria of homology (topological equivalence, or position and connections; composition of structures, or commonality in details of construction) can be expressed as regular characters in a cladistic analysis. Doing so provides adequate transformation costs for changes in schemas of correspondences. Correspondences imply evolutionary transformations, and multiple schemas of correspondences can be compared according to the evolutionary transformations that they imply. The method is used to test the correspondences in sclerites of the male copulatory organs of spiders of the subfamily Amaurobioidinae (Arachnida, Araneae, Anyphaenidae). The correspondences of three sclerites are tested, in a data set of 93 species having one, two or three sclerites, using a simultaneous analysis of all the morphological characters. Most parsimonious trees are identified together with the correspondences they imply. Once the correspondences are integrated in the phylogenetic analysis, it is easy to evaluate the robustness of trees or decay in optimality after changes in anatomical interpretations. A Bremer support for anatomical interpretations is proposed, calculated as the increase in tree length when the specific interpretation is not used. © The Willi Hennig Society 2007.