Component-compatibility in historical biogeography
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-The problems of reconstructing historical relationships for areas of endemism from distributional data for groups of taxa and the cladistic relationships among the members of those groups can be solved by applying the two principles of parsimony and mutual inclusion or exclusion (compatibility) of components. Components can be extracted from a data matrix by means of transcription into partial monothetic sets. The data matrix thus derived represents the distribution over areas for the monophyletic groups in one or more cladograms. It is derived from two different matrices by boolean multiplication. The first matrix gives the binary representation of distributions of taxa over areas of endemism; the second describes the cladogram for the same taxa, in terms of character states converted into binary form by additive binary coding. The derived data matrix can be used in historical biogeography to represent the given phyletic data ( Assumption 0 here newly defined), and can be amended to reflect Assumptions 1 or 2 to accomodate the problems of wide-spread taxa and missing areas. Areacladograms are determined from the derived matrix by searching for the largest sets of mutually compatible components. Area-cladograms are evaluated in terms of support (vicariance) and contradiction (ad hoc interpretations such as dispersal and extinction). Area-cladograms that best fit the data matrix regarding the balance between support and contradiction are selected as the best possible recontructions of relationships among the areas of endemism. The procedure is illustrated by the example of the poeciliid fish genera Heterandria and Xiphophorus, and several other standard examples.Keywords:
Cladogram
Monophyly
Endemism
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Monophyly
Sequence (biology)
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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.
Univariate
Monophyly
Cladogram
Phylogenetic comparative methods
Tree (set theory)
Data Matrix
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Cladogram
Data Matrix
Tree (set theory)
Matrix representation
Representation
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The problems of reconstructing historical relationships for areas of endemism from distributional data for groups of taxa and the cladistic relationships among the members of those groups can be solved by applying the two principles of parsimony and mutual inclusion or exclusion (compatibility) of components. Components can be extracted from a data matrix by means of transcription into partial monothetic sets. The data matrix thus derived represents the distribution over areas for the monophyletic groups in one or more cladograms. It is derived from two different matrices by boolean multiplication. The first matrix gives the binary representation of distributions of taxa over areas of endemism; the second describes the cladogram for the same taxa, in terms of character states converted into binary form by additive binary coding. The derived data matrix can be used in historical biogeography to represent the given phyletic data (Assumption 0 here newly defined), and can be amended to reflect Assumptions 1 or 2 to accomodate the problems of wide-spread taxa and missing areas. Areacladograms are determined from the derived matrix by searching for the largest sets of mutually compatible components. Area-cladograms are evaluated in terms of support (vicariance) and contradiction (ad hoc interpretations such as dispersal and extinction). Area-cladograms that best fit the data matrix regarding the balance between support and contradiction are selected as the best possible recontructions of relationships among the areas of endemism. The procedure is illustrated by the example of the poeciliid fish genera Heterandria and Xiphophorus, and several other standard examples.
Cladogram
Monophyly
Endemism
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Part 1 Cladistic theory: form - homology and analogy special similarity conflicting similarities and parsimony the relations between similarities homoplasty and the interpretation of character conflict monophyletic, paraphyletic and polyphyletic groups sister groups and ancestor-descendant relationships the transformation of cladistics phenetics eclectic of evolutionary taxonomy. Part 2 Character coding: character types binary characteristics multistate characters transformation between character states unordered and ordered characters additive binary coding branched character state trees other user-defined models of transformation character popularity cladograms and roots. Part 3 The determination of character polarity: outgroup comparison - the indirect method ontogeny - the direct method inadequate criteria ingroup commonality a priori models - Robertsonian changes, allelic dominance hierarchy, functional morphology, underlying synapomorphy. Part 4 Tree building techniques: parsimony criteria - Wagner, Fitch, Dollo, Camin-Sokal, polymorphism, generalized delayed and accelerated transformations optimization of values x-coding searching for the most parsimonious trees - exact algorithms, heuristic methods. Part 5 Tree statistics, trees and confidence, concensus trees, alternatives to parsimony, character weighting, character conflict and its resolution: tree statistics - tree length, measures of fit between trees and data trees and confidence - bootstrap and jackknife, randomization, data decisiveness consensus trees - strict consensus, combinable components consensus, Nelson consensus, Adams consensus alternatives to parsimony - cliques, maximum likelihood, three-taxon statements phenetics character weighting character conflict and its resolution - re-evaluation of characters, consensus trees. Part 6 DNA analysis - theory: homology, homology testing - similarity, conjunction, congruence, results of testing for homology, orthology, paralogy, xenology, paraxenology, plerology nucleotide sequence data - the characters - substitutions, gaps, insertions and deletions (indels) tree construction - preliminaries note on rooting trees. Part 7 DNA analysis - methods: matrix methods - definitions, distance measures, metrics, tree reconstruction - phenetic methods, distance methods, problems parsimony methods - weighing, a priori weighting, a posteriori weighting, problems, invariants. Part 8 Fossils and cladistic analysis: fossils and ancestors age and rank stem groups and crown groups influence of fossils on classification of recent organisms - missing data, basal taxa, fossils and stratigraphy. Part 9 Cladistics and biogeography: life and earth together cladistics and biogeography - the progression rule, vacariance biogeography. (part contents)
Cladogram
Character evolution
Polyphyly
Paraphyly
Synapomorphy
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Classification and biogeography should be informed by reliable phylogenetic reconstruction. This may be recovered from the mainly speculative literature by a nine-step protocol of critical methods, the operative transform. Piecemeal total evidence is attained by combining separately published support values for the same branch arrangement with Bayes' Formula. Joint probability correction is advanced for multiple test problems of conclusions of monophyly necessarily regarded as sets. Tables are given for conversion of nonparametric bootstrap values and decay indexes into probabilities, based on four-taxon simulations. Uncontested morphology-based branch arrangements are assigned high priors. Probabilities associated with unaccounted assumptions are addressed by a general correction factor. A probabilistic calculation allows the inference of two or more reliable internodes from a series of less well-supported internodes. A patristic distance of at least two internodes is used to support inference from molecular data alone of an intermediate lineage for recognition of supraspecific segregate taxonomic entities. Recognizing paraphyletic taxa when appropriate preserves attributes of inferred functional evolution providing taxic unity and value. Evolutionary Lazarus taxa contravening Dollo's Rule against re-evolution of complex traits justify interpretations of reticulation. This method of evaluation of the decisiveness of published molecular studies is exemplified with previously published cladograms focused on Malpighiales and the moss family Pottiaceae. Additional consideration of evolutionary process not reflected in phylogenetic analysis leads to reliable hypotheses of evolutionary relationship.
Cladogram
Monophyly
Paraphyly
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Classification and biogeography should be informed by reliable phylogenetic reconstruction. This may be recovered from the mainly speculative literature by a nine-step protocol of critical methods, the eeoperative transform.ii Piecemeal total evidence is attained by combining separately published support values for the same branch arrangement with Bayesi Formula. Joint probability correction is advanced for multiple test problems of conclusions of monophyly necessarily regarded as sets. Tables are given for conversion of nonparametric bootstrap values and decay indexes into probabilities, based on four-taxon simulations. Uncontested morphology-based branch arrangements are assigned high priors. Probabilities associated with unaccounted assumptions are addressed by a general correction factor. A probabilistic calculation allows the inference of two or more reliable internodes from a series of less well-supported internodes. A patristic distance of at least two internodes is used to support inference from molecular data alone of an intermediate lineage for recognition of supraspecific segregate taxonomic entities. Recognizing paraphyletic taxa when appropriate preserves attributes of inferred functional evolution providing taxic unity and value. Evolutionary Lazarus taxa contravening Dollois Rule against re-evolution of complex traits justify interpretations of reticulation. This method of evaluation of the decisiveness of published molecular studies is exemplified with previously published cladograms focused on Malpighiales and the moss family Pottiaceae. Additional consideration of evolutionary process not reflected in phylogenetic analysis leads to reliable hypotheses of evolutionary relationship.
Cladogram
Monophyly
Paraphyly
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A two-state character is defined as uniquely derived if it has only evolved once in the history of a group, without subsequent reversal. Two independent characters cannot both be uniquely derived if all four possible combinations (or all three excluding that of the two ancestral forms) occur. A number of ways of choosing compatible sets of uniquely derived characters are discussed and used to derive possible unrooted and rooted trees. Results of these are related to those chosen on parsimony criteria, using data for orthopteroid groups, and the assumptions of both methods are compared. Application of compatibility analysis to the moth genera Teldenia and Argodrepana is also discussed. Compatibility and parsimony methods are complementary rather than exclusive of each other.
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Abstract- Algorithms to reconstruct character evolution on polytomous cladograms or phylogenetic trees have to date interpreted each polytomy literally, as if it were an event of multiple speciation, with multiple daughter species descending independently from a mother species, thus requiring any similarities shared by only some of these daughters to be accounted for by convergence. These algorithms are not appropriate when the polytomy is interpreted in the usual way, namely as representing uncertainty in the cladogram's resolution. New algorithms for both ordered and unordered characters are presented to reconstruct character evolution under the uncertain-resolution interpretation of polytomies. These algorithms allow the cladogram to resolve itself so as to be favourable for the character whose evolution is being reconstructed. Because different characters may have different favourable resolutions, it is not possible in general to use these algorithms to determine the total parsimony of a polytomous cladogram (the number of evolutionary steps required over all characters by the cladogram), for which the only adequate approach is to find a most parsimonious dichotomous resolution of the cladogram.
Cladogram
Polytomous Rasch model
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As we have argued previously, for the valid derivation of general area cladograms in vicariance biogeography, two requirements should be met. First, sets of area cladograms derived under assumptions 0, 1 and 2 should be inclusive (requirement I). Second, general area cladograms should be based on area cladograms, for different monophyletic groups, derived under the same assumption (requirement II). We now assess for their actual implementation of assumptions A0, A1, and A2 and for the extent to which they meet requirements I and II, the following methods (and correlated computer programs): Component Compatibility Analysis (CAFCA), Brooks Parsimony Analysis (PAUP), Component Analysis (Component 1.5), Reconciled Tree Analysis (Component 2.0), and Three Area Statement Analysis (TAS). For this purpose we use empirical (Heterandria, Xiphophorus, Cyttaria, Eriococcus/Madarococcus) and theoretical data sets. All programs appear to violate, to a different degree, requirement I (deriving inclusive sets of area cladograms under assumptions) when dealing with sympatric taxa under A1 or A2. Dealing with sympatric taxa a posteriori only prevents this violation. All programs examined appear to meet requirement II (deriving general area cladograms under a single assumption).
Cladogram
Vicariance
Monophyly
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