Maximum Parsimony and the Skewness Test: A Simulation Study of the Limits of Applicability

The maximum parsimony (MP) method for inferring phylogenies is widely used, but little is known about its limitations in non-asymptotic situations. This study employs large-scale computations with simulated phylogenetic data to estimate the probability that MP succeeds in finding the true phylogeny for up to twelve taxa and 256 characters. The set of candidate phylogenies are taken to be unrooted binary trees; for each simulated data set, the tree lengths of all (2n − 5)!! candidates are computed to evaluate quantities related to the performance of MP, such as the probability of finding the true phylogeny, the probability that the tree with the shortest length is unique, the probability that the true phylogeny has the shortest tree length, and the expected inverse of the number of trees sharing the shortest length. The tree length distributions are also used to evaluate and extend the skewness test of Hillis for distinguishing between random and phylogenetic data. The results indicate, for example, that the critical point after which MP achieves a success probability of at least 0.9 is roughly around 128 characters. The skewness test is found to perform well on simulated data and the study extends its scope to up to twelve taxa.     

Noise

The proliferation of DNA sequence data has generated a concern about the effects of "noise" on phylogeny reconstruction. This concern has led to various recommendations for weighting schemes and for separating data types prior to analysis. A new technique is explored to examine directly how noise influences the stability of parsimony reconstruction. By appending purely random characters onto a matrix of pure signal, or by replacing characters in a matrix of signal by random states, one can measure the degree to which a matrix is robust against noise. Reconstructions were sensitive to tree topology and clade size when noise was added, but were less so when character states were replaced with noise. When a signal matrix is complemented with a noise matrix of equal size, parsimony will trace the original signal about half the time when there is only one synapomorphy per node, and about 90% of the time when there are three synapomorphies per node. Similar results obtain when 20% of a matrix is replaced by noise. Successive weighting does not improve performance. Adding noise to only some taxa is more damaging, but replacing characters in only some taxa is less so. The bootstrap and g1 (tree skewness) statistics are shown to be uninterpretable measures of noise or departures from randomness. Empirical data sets illustrate that commonly recommended schemes of differential weighting (e.g. downweighting third positions) are not well supported from the point of view of reducing the influence of noise nor are more noisy data sets likely to degrade signal found in less noisy data sets.     

FREQUENCY DISTRIBUTIONS OF LENGTHS OF POSSIBLE NETWORKS FROM A DATA MATRIX

Abstract— It is common practice to attempt to find the minimum length tree (also known as the Wagner tree) for a given data matrix on a group of OTUs (taxa). However, little study has been made of the pattern of frequency distributions when the lengths of all possible networks (unrooted trees) are taken into consideration. A published real data matrix with eight OTUs was compared with randomly generated data, when the former showed a much larger variance and very marked skewness. A number of published data matrices with a larger number of OTUs were studied by random selection of 10240 out of the possible trees: these were compared with 32 randomly generated data sets with 13 OTUs, using the same program. An algorithm has been found for calculation of the expected mean, variance and skewness for random binary data with up to 13 OTUs, based on the number of characters representing each type of partition of the OTUs. The calculation requires listing of the possible topologies and their relative weighting, which are tabulated.     

Mosaics of convergences and noise in morphological phylogenies: what's in a viverrid-like carnivoran?

Adaptive convergence in morphological characters has not been thoroughly investigated, and the processes by which phylogenetic relationships may be misled by morphological convergence remains unclear. We undertook a case study on the morphological evolution of viverrid-like feliformians (Nandinia, Cryptoprocta, Fossa, Eupleres, Prionodon) and built the largest morphological matrix concerning the suborder Feliformia to date. A total of 349 characters grouped into four anatomical partitions were used for all species of Viverridae and viverrid-like taxa plus representatives of the Felidae, Hyaenidae, Herpestidae, and one Malagasy mongoose. Recent molecular phylogenetic analyses suggest that viverrid-like morphotypes appeared independently at least three times during feliformian evolution. We thus used a synthetic molecular tree to assess morphological evolutionary patterns characterizing the viverrid-like taxa. We examined phylogenetic signal, convergence and noise in morphological characters using (a) tree-length distribution (g1), (b) partitioned Bremer support, (c) RI values and their distribution, (d) respective contributions of diagnostic synapomorphies at the nodes for each partition, (e) patterns of shared convergences among viverrid-like taxa and other feliformian lineages, (f) tree-length differences among alternative hypotheses, and (g) the successive removal of convergent character states from the original matrix. In addition, the lability of complex morphological structures was assessed by mapping them onto the synthetic molecular tree. The unconstrained morphological analysis yielded phylogenetic groupings that closely reflected traditional classification. The use of a synthetic molecular tree (constraint) combined with our thorough morphological investigations revealed the mosaics of convergences likely to have contributed to part of the historical uncertainty over viverrid classification. It also showed that complex morphological structures could be subjected to reversible evolutionary trends. The morphological matrix proved useful in characterizing several feliformian clades with diagnostic synapomorphies. These results support the removal from the traditionally held Viverridae of several viverrid-like taxa into three distinct families: Nandiniidae (Nandinia), Prionodontidae (Prionodon), and the newly defined Eupleridae (including Cryptoprocta, Fossa, Eupleres plus all "mongoose-like" Malagasy taxa). No clearly "phylogenetically misleading" data subsets could be identified, and the great majority of morphological convergences appeared to be nonadaptive. The multiple approaches used in this study revealed that the most disruptive element with regards to morphological phylogenetic reconstruction was noise, which blured the expression of phylogenetic signal. This study demonstrates the crucial need to consider independent (molecular) phylogenies in order to produce reliable evolutionary hypotheses and should promote a new approach to the definition of morphological characters in mammals. [Constrained analysis; convergence; evolutionary scenario; Feliformia; morphology; noise; phylogenetic signal; phylogeny; Viverridae.].     

Phylogenetic signal in bone histology of amniotes revisited

Legendre, L, Le Roy, N, Martinez‐Maza, C, Montes, L, Laurin, M & Cubo, J. (2012). Phylogenetic signal in bone histology of amniotes revisited. —Zoologica Scripta, 42, 44–53. There is currently a debate about the presence of a phylogenetic signal in bone histological data, but very few rigorous tests have fuelled the discussions on this topic. Here, we performed new analyses using a larger set of seven histological traits and including 25 taxa (nine extinct and 16 extant taxa), using three methods: the phylogenetic eigenvector regression, the tree length distribution and the regressions on distance matrices. Our results clearly show that the phylogenetic signal in our sample of bone histological characters is strong, even after correcting for multiple testing. Most characters exhibit a significant phylogenetic signal according to at least one of our three tests, with the phylogeny often explaining 20–60% of the variation in the histological characters. Thus, we conclude that the phylogenetic comparative method should be systematically used in interspecific analyses of bone histodiversity to avoid problems of non‐independence among observations.     

The phylogenetic trunk: maximal inclusion of taxa with missing data in an analysis of the lepospondyli (Vertebrata,Tetrapoda)

The importance of fossils to phylogenetic reconstruction is well established. However, analyses of fossil data sets are confounded by problems related to the less complete nature of the specimens. Taxa that are incompletely known are problematic because of the uncertainty of their placement within a tree, leading to a proliferation of most-parsimonious solutions and "wild card" behavior. Problematic taxa are commonly deleted based on a priori criteria of completeness. Paradoxically, a taxon's problematic behavior is tree dependent, and levels of completeness are not directly associated with problematic behavior. Exclusion of taxa on the basis of completeness eliminates real character conflict and, by not allowing incomplete taxa to determine tree topology, diminishes the phylogenetic hypothesis. Here, the phylogenetic trunk approach is proposed to allow optimization of taxonomic inclusion and tree stability. The use of this method in an analysis of the Paleozoic Lepospondyli finds a single most-parsimonious tree, or trunk, after the removal of one taxon identified as being problematic. Moreover, the 38 trees found at one additional step from this primary trunk were reduced to 2 by removal of one additional taxon. These trunks are compared with the trees that were found by excluding taxa with various degrees of completeness, and the effects of incomplete taxa are explored with regard to use of the trunk. Correlated characters associated with limblessness are discussed regarding the assumption of character independence; however, inclusion of intermediate taxa is found to be the single best method for breaking down long branches.     

The systematic utility of floral and vegetative fragrance in two genera of nyctaginaceae

We examined relationships between fragrance and phylogeny using a number of approaches to coding fragrance data and comparing the hierarchical information in fragrance data with the phylogenetic signal in a DNA sequence data set. We first used distance analyses to determine which coding method(s) best distinguishes species while grouping conspecifics. Results suggest that interspecific differences in fragrance composition were maximized by coding as presence/absence of fragrance compounds and biosynthetic pathways rather than when quantitative information was also included. Useful systematic information came from both compounds and pathways and from fragrance emitted by both floral and vegetative tissues. The coding methods that emerged from the distance analyses as best distinguishing species were then adapted for use in phylogenetic analysis. Although hierarchical signal among fragrance data sets was congruent, this signal was highly incongruent with the phylogenetic signal in the DNA sequence data. Notably, topologies inferred from fragrance data sets were congruent with the DNA topology only in the most distal portions (e.g., sister group pairs or closely related species that had similar fragrance profiles were often recovered by analyses of fragrance). Examination of consistency and retention indices for individual fragrance compounds and pathways as optimized onto one of the most-parsimonious trees inferred from DNA data revealed that although most compounds were homoplastic, some compounds were perfectly congruent with the DNA phylogeny. In particular, compounds and pathways found in a few taxa were less homoplastic than those found in many taxa. Pathways that synthesize few volatiles also seem to have lower homoplasy than those that produce many. Although fragrance data as a whole may not be useful in phylogeny reconstruction, these data can provide additional support for clades reconstructed with other types of characters. Factors other than phylogeny, including pollinator interactions, also likely influence fragrance composition.     

Universal Artifacts Affect the Branching of Phylogenetic Trees,Not Universal Scaling Laws

Background

The superficial resemblance of phylogenetic trees to other branching structures allows searching for macroevolutionary patterns. However, such trees are just statistical inferences of particular historical events. Recent meta-analyses report finding regularities in the branching pattern of phylogenetic trees. But is this supported by evidence, or are such regularities just methodological artifacts? If so, is there any signal in a phylogeny?

Methodology

In order to evaluate the impact of polytomies and imbalance on tree shape, the distribution of all binary and polytomic trees of up to 7 taxa was assessed in tree-shape space. The relationship between the proportion of outgroups and the amount of imbalance introduced with them was assessed applying four different tree-building methods to 100 combinations from a set of 10 ingroup and 9 outgroup species, and performing covariance analyses. The relevance of this analysis was explored taking 61 published phylogenies, based on nucleic acid sequences and involving various taxa, taxonomic levels, and tree-building methods.

Principal Findings

All methods of phylogenetic inference are quite sensitive to the artifacts introduced by outgroups. However, published phylogenies appear to be subject to a rather effective, albeit rather intuitive control against such artifacts. The data and methods used to build phylogenetic trees are varied, so any meta-analysis is subject to pitfalls due to their uneven intrinsic merits, which translate into artifacts in tree shape. The binary branching pattern is an imposition of methods, and seldom reflects true relationships in intraspecific analyses, yielding artifactual polytomies in short trees. Above the species level, the departure of real trees from simplistic random models is caused at least by two natural factors –uneven speciation and extinction rates; and artifacts such as choice of taxa included in the analysis, and imbalance introduced by outgroups and basal paraphyletic taxa. This artifactual imbalance accounts for tree shape convergence of large trees.

Significance

There is no evidence for any universal scaling in the tree of life. Instead, there is a need for improved methods of tree analysis that can be used to discriminate the noise due to outgroups from the phylogenetic signal within the taxon of interest, and to evaluate realistic models of evolution, correcting the retrospective perspective and explicitly recognizing extinction as a driving force. Artifacts are pervasive, and can only be overcome through understanding the structure and biological meaning of phylogenetic trees.Catalan Abstract in Translation S1.     

Sensitivity of phylogeny estimation to taxonomic sampling

Recent studies have shown that addition or deletion of taxa from a data matrix can change the estimate of phylogeny. I used 29 data sets from the literature to examine the effect of taxon sampling on phylogeny estimation within data sets. I then used multiple regression to assess the effect of number of taxa, number of characters, homoplasy, strength of support, and tree symmetry on the sensitivity of data sets to taxonomic sampling. Sensitivity to sampling was measured by mapping characters from a matrix of culled taxa onto optimal trees for that reduced matrix and onto the pruned optimal tree for the entire matrix, then comparing the length of the reduced tree to the length of the pruned complete tree. Within-data-set patterns can be described by a second-order equation relating fraction of taxa sampled to sensitivity to sampling. Multiple regression analyses found number of taxa to be a significant predictor of sensitivity to sampling; retention index, number of informative characters, total support index, and tree symmetry were nonsignificant predictors. I derived a predictive regression equation relating fraction of taxa sampled and number of taxa potentially sampled to sensitivity to taxonomic sampling and calculated values for this equation within the bounds of the variables examined. The length difference between the complete tree and a subsampled tree was generally small (average difference of 0-2.9 steps), indicating that subsampling taxa is probably not an important problem for most phylogenetic analyses using up to 20 taxa.     

Canonical phylogenetic ordination

A phylogenetic comparative method is proposed for estimating historical effects on comparative data using the partitions that compose a cladogram, i.e., its monophyletic groups. Two basic matrices, Y and X, are defined in the context of an ordinary linear model. Y contains the comparative data measured over t taxa. X consists of an initial tree matrix that contains all the xj monophyletic groups (each coded separately as a binary indicator variable) of the phylogenetic tree available for those taxa. The method seeks to define the subset of groups, i.e., a reduced tree matrix, that best explains the patterns in Y. This definition is accomplished via regression or canonical ordination (depending on the dimensionality of Y) coupled with Monte Carlo permutations. It is argued here that unrestricted permutations (i.e., under an equiprobable model) are valid for testing this specific kind of groupwise hypothesis. Phylogeny is either partialled out or, more properly, incorporated into the analysis in the form of component variation. Direct extensions allow for testing ecomorphological data controlled by phylogeny in a variation partitioning approach. Currently available statistical techniques make this method applicable under most univariate/multivariate models and metrics; two-way phylogenetic effects can be estimated as well. The simplest case (univariate Y), tested with simulations, yielded acceptable type I error rates. Applications presented include examples from evolutionary ethology, ecology, and ecomorphology. Results showed that the new technique detected previously overlooked variation clearly associated with phylogeny and that many phylogenetic effects on comparative data may occur at particular groups rather than across the entire tree.     

Evaluating the efficacy of continuous quantitative characters for reconstructing the phylogeny of a morphologically homogeneous spider taxon (Araneae, Mygalomorphae, Antrodiaetidae, Antrodiaetus)

The use of continuous quantitative characters for phylogenetic analyses has long been contentious in the systematics literature. Recent studies argue for and against their use, but there have been relatively few attempts to evaluate whether these characters provide an accurate estimate of phylogeny, despite the fact that a number of methods have been developed to analyze these types of data for phylogenetic inference. A tree topology will be produced for a given methodology and set of characters, but little can be concluded with regards to the accuracy of phylogenetic signal without an independent evaluation of those characters. We assess the performance of continuous quantitative characters for the mygalomorph spider genus Antrodiaetus, a group that is morphologically homogeneous and one for which few discrete (morphological) characters have been observed. Phylogenetic signal contained in continuous quantitative characters is compared to an independently derived phylogeny inferred on the basis of multiple nuclear and mitochondrial gene loci. Tree topology randomizations, regression techniques, and topological tests all demonstrate that continuous quantitative characters in Antrodiaetus conflict with the phylogenetic signal contained in the gene trees. Our results show that the use of continuous quantitative characters for phylogenetic reconstruction may be inappropriate for reconstructing Antrodiaetus phylogeny and indicate that due caution should be exercised before employing this character type in the absence of other independently derived sources of characters.     

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.     

Arhynchobdellida (Annelida: Oligochaeta: Hirudinida): phylogenetic relationships and evolution

A remarkable diversity of life history strategies, geographic distributions, and morphological characters provide a rich substrate for investigating the evolutionary relationships of arhynchobdellid leeches. The phylogenetic relationships, using parsimony analysis, of the order Arhynchobdellida were investigated using nuclear 18S and 28S rDNA, mitochondrial 12S rDNA, and cytochrome c oxidase subunit I sequence data, as well as 24 morphological characters. Thirty-nine arhynchobdellid species were selected to represent the seven currently recognized families. Sixteen rhynchobdellid leeches from the families Glossiphoniidae and Piscicolidae were included as outgroup taxa. Analysis of all available data resolved a single most-parsimonious tree. The cladogram conflicted with most of the traditional classification schemes of the Arhynchobdellida. Monophyly of the Erpobdelliformes and Hirudiniformes was supported, whereas the families Haemadipsidae, Haemopidae, and Hirudinidae, as well as the genera Hirudo or Aliolimnatis, were found not to be monophyletic. The results provide insight on the phylogenetic positions for the taxonomically problematic families Americobdellidae and Cylicobdellidae, the genera Semiscolex, Patagoniobdella, and Mesobdella, as well as genera traditionally classified under Hirudinidae. The evolution of dietary and habitat preferences is examined.     

Phylogeny of Trichoptera (caddisflies): characterization of signal and noise within multiple datasets

Trichoptera are holometabolous insects with aquatic larvae that, together with the Lepidoptera, make up the Amphiesmenoptera. Despite extensive previous morphological work, little phylogenetic agreement has been reached about the relationship among the three suborders--Annulipalpia, Spicipalpia, and Integripalpia--or about the monophyly of Spicipalpia. In an effort to resolve this conflict, we sequenced fragments of the large and small subunit nuclear ribosomal RNAs (1078 nt; D1, D3, V4-5), the nuclear elongation factor 1 alpha gene (EF-1 alpha; 1098 nt), and a fragment of mitochondrial cytochrome oxidase I (COI; 411 nt). Seventy adult and larval morphological characters were reanalyzed and added to molecular data in a combined analysis. We evaluated signal and homoplasy in each of the molecular datasets and attempted to rank the particular datasets according to how appropriate they were for inferring relationships among suborders. This evaluation included testing for conflict among datasets, comparing tree lengths among alternative hypotheses, measuring the left-skew of tree-length distributions from maximally divergent sets of taxa, evaluating the recovery of expected clades, visualizing whether or not substitutions were accumulating with time, and estimating nucleotide compositional bias. Although all these measures cast doubt on the reliability of the deep-level signal coming from the nucleotides of the COI and EF-1 alpha genes, these data could still be included in combined analyses without overturning the results from the most conservative marker, the rRNA. The different datasets were found to be evolving under extremely different rates. A site-specific likelihood method for dealing with combined data with nonoverlapping parameters was proposed, and a similar weighting scheme under parsimony was evaluated. Among our phylogenetic conclusions, we found Annulipalpia to be the most basal of the three suborders, with Spicipalpia and Integripalpia forming a clade. Monophyly of Annulipalpia and Integripalpia was confirmed, but the relationships among spicipalpians remain equivocal.     

Escaping from the Felsenstein Zone by Detecting Long Branches in Phylogenetic Data

Long branches in a true phylogeny tend to disrupt hierarchical character covariation (phylogenetic signal) in the distribution of traits among organisms. The distortion of hierarchical structure in character-state matrices can lead to errors in the estimation of phylogenetic relationships and inconsistency of methods of phylogenetic inference. Examination of trees distorted by long-branch attraction will not reveal the identities of problematic taxa, in part because the distortion can mask long branches by reducing inferred branch lengths and through errors in branching order. Here we present a simple method for the detection of taxa whose placement in evolutionary trees is made difficult by the effects of long-branch attraction. The method is an extension of a tree-independent conceptual framework of phylogenetic data exploration (RASA). Taxa that are likely to attract are revealed because long branches leave distinct footprints in the distribution of character states among taxa, and these traces can be directly observed in the error structure of the RASA regression. Problematic taxa are identified using a new diagnostic plot called the taxon variance plot, in which the apparent cladistic and phenetic variances contributed by individual taxa are compared. The procedure for identifying long edges employs algorithms solved in polynomial time and can be applied to morphological, molecular, and mixed characters. The efficacy of the method is demonstrated using simulated evolution and empirical evidence of long branches in a set of recently published sequences. We show that the accuracy of evolutionary trees can be improved by detecting and combating the potentially misleading influences of long-branch taxa.     

Phylogenetic comparative methods complement discriminant function analysis in ecomorphology

In ecomorphology, Discriminant Function Analysis (DFA) has been used as evidence for the presence of functional links between morphometric variables and ecological categories. Here we conduct simulations of characters containing phylogenetic signal to explore the performance of DFA under a variety of conditions. Characters were simulated using a phylogeny of extant antelope species from known habitats. Characters were modeled with no biomechanical relationship to the habitat category; the only sources of variation were body mass, phylogenetic signal, or random “noise.” DFA on the discriminability of habitat categories was performed using subsets of the simulated characters, and Phylogenetic Generalized Least Squares (PGLS) was performed for each character. Analyses were repeated with randomized habitat assignments. When simulated characters lacked phylogenetic signal and/or habitat assignments were random, <5.6% of DFAs and <8.26% of PGLS analyses were significant. When characters contained phylogenetic signal and actual habitats were used, 33.27 to 45.07% of DFAs and <13.09% of PGLS analyses were significant. False Discovery Rate (FDR) corrections for multiple PGLS analyses reduced the rate of significance to <4.64%. In all cases using actual habitats and characters with phylogenetic signal, correct classification rates of DFAs exceeded random chance. In simulations involving phylogenetic signal in both predictor variables and predicted categories, PGLS with FDR was rarely significant, while DFA often was. In short, DFA offered no indication that differences between categories might be explained by phylogenetic signal, while PGLS did. As such, PGLS provides a valuable tool for testing the functional hypotheses at the heart of ecomorphology. Am J Phys Anthropol 153:663–674, 2014. © 2013 Wiley Periodicals, Inc.     

Step matrices and the interpretation of homoplasy

Assumptions about the costs of character change, coded in the form of a step matrix, determine most-parsimonious inferences of character evolution on phylogenies. We present a graphical approach to exploring the relationship between cost assumptions and evolutionary inferences from character data. The number of gains and losses of a binary trait on a phylogeny can be plotted over a range of cost assumptions, to reveal the inflection point at which there is a switch from more gains to more losses and the point at which all changes are inferred to be in one direction or the other. Phylogenetic structure in the data, the tree shape, and the relative frequency of states among the taxa influence the shape of such graphs and complicate the interpretation of possible permutation-based tests for directionality of change. The costs at which the most-parsimonious state of each internal node switches from one state to another can also be quantified by iterative ancestral-state reconstruction over a range of costs. This procedure helps identify the most robust inferences of change in each direction, which should be of use in designing comparative studies.     

Toward a Better Understanding of the Phylogeny of the Asplanchnidae (Rotifera)

We investigated the phylogenetic relationships of Family Asplanchnidae using both morphological and molecular data. The morphological database, comprising 23 characters from 19 taxa (15 Asplanchnidae and 4 outgroups), was compiled from a survey of the literature and our own observations; the molecular data (ITS and V4 region nuclear regions and mitochondrial cox1) was sequenced from specimens that we collected. Our analysis of the morphological data set (maximum parsimony) yielded 12 most-parsimonious trees with a tree length of 27 steps. From this analysis we conclude (1) Asplanchnidae is a monophyletic group as are the three genera comprising it, (2) there is no compelling support for the argument that Asplanchna should be separated into two discrete genera, and (3) there is some support for the proposal that Asplanchnidae and Synchaetidae are sister groups. Our analysis of the molecular data set supports the first two of these conclusions while the sister group of the family varied depending on the gene region analyzed and families and genera included. Current understanding of the phylogeny of Asplanchnidae is hampered by the need for additional informative morphological characters and a lack of molecular data for the genus Harringia and several other members of the Asplanchnidae.     

Automated Masking of AFLP Markers Improves Reliability of Phylogenetic Analyses

The amplified fragment length polymorphisms (AFLP) method has become an attractive tool in phylogenetics due to the ease with which large numbers of characters can be generated. In contrast to sequence-based phylogenetic approaches, AFLP data consist of anonymous multilocus markers. However, potential artificial amplifications or amplification failures of fragments contained in the AFLP data set will reduce AFLP reliability especially in phylogenetic inferences. In the present study, we introduce a new automated scoring approach, called “AMARE” (AFLP MAtrix REduction). The approach is based on replicates and makes marker selection dependent on marker reproducibility to control for scoring errors. To demonstrate the effectiveness of our approach we record error rate estimations, resolution scores, PCoA and stemminess calculations. As in general the true tree (i.e. the species phylogeny) is not known, we tested AMARE with empirical, already published AFLP data sets, and compared tree topologies of different AMARE generated character matrices to existing phylogenetic trees and/or other independent sources such as morphological and geographical data. It turns out that the selection of masked character matrices with highest resolution scores gave similar or even better phylogenetic results than the original AFLP data sets.     

NULL MODELS FOR THE NUMBER OF EVOLUTIONARY STEPS IN A CHARACTER ON A PHYLOGENETIC TREE

Random trees and random characters can be used in null models for testing phylogenetic hypothesis. We consider three interpretations of random trees: first, that trees are selected from the set of all possible trees with equal probability; second, that trees are formed by random speciation or coalescence (equivalent); and third, that trees are formed by a series of random partitions of the taxa. We consider two interpretations of random characters: first, that the number of taxa with each state is held constant, but the states are randomly reshuffled among the taxa; and second, that the probability each taxon is assigned a particular state is constant from one taxon to the next. Under null models representing various combinations of randomizations of trees and characters, exact recursion equations are given to calculate the probability distribution of the number of character state changes required by a phylogenetic tree. Possible applications of these probability distributions are discussed. They can be used, for example, to test for a panmictic population structure within a species or to test phylogenetic inertia in a character's evolution. Whether and how a null model incorporates tree randomness makes little difference to the probability distribution in many but not all circumstances. The null model's sense of character randomness appears more critical. The difficult issue of choosing a null model is discussed.