A Reconsideration of Three-Item Analysis, the Use of Implied Weights in Cladistics, and a Practical Application in Gentianaceae
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K.U.Leuven Faculteit der Wetenschappen Instituut voor Plantkunde Laboratorium voor Systematiek A reconsideration of three-item analysis, the use of implied weights in cladistics, and a practical application in Gentianaceae Jan De Laet Proefschrift voorgedragen tot het behalen van de graad van Doctor in de Wetenschappen Promotor: Prof. Dr. E. Smets This pdf version has subtle differences in page layout (but not content) compared to the original hardcopy K.U.Leuven Faculteit der Wetenschappen Instituut voor Plantkunde Laboratorium voor Systematiek A reconsideration of three-item analysis, the use of implied weights in cladistics, and a practical application in Gentianaceae Jan De Laet Proefschrift voorgedragen tot het behalen van de graad van Doctor in de Wetenschappen 27 mei 1997 Leden van de jury: Promotor, Prof. Dr. E. Smets K.U.Leuven Prof. Dr. F. Symons K.U.Leuven Prof. Dr. J. Van Assche K.U.Leuven Prof. Dr. E. Robbrecht Nationale Plantentuin van België, U.I.A. Dr. J. S. Farris Naturhistoriska Riksmuseet, Stockholm There is a lesson in all this. We do not know in advance what are the right questions to ask, and we often do not find out until we are close to an answer. (Weinberg 1997: 215) Vooraf ... ... wil ik een woordje van dank richten aan Prof. Dr. E. Smets, promotor van dit proefschrift, voor zijn steun en begeleiding, vooral tijdens de laatste maanden. Met grote snelheid las hij de geschreven stukken door en gaf hij waar nodig zijn advies. aan alle labcollega’s van vroeger en nu voor de toffe werksfeer en samenwerking; in het bijzonder aan Peter voor het maken van figuren 1.1 en 1.5. aan Jos voor de steeds bereidwillige hulp bij het bibliotheekwerk (en het wisselen van vijffrankstukken voor de koffiemachine...). aan alle studenten die de voorbije jaren mijn pad gekruist hebben; ik hoop dat ze zoveel van mij geleerd hebben als ik van hen. aan Sandra, broers en zussen en alle vrienden die me de voorbije maanden een welgemeend duwtje in de rug gegeven hebben; de laatste loodjes wogen inderdaad zwaar. Tenslotte wil ik mijn ouders vermelden. Zonder hen zou dit werk er niet gekomen zijn, en dat is meer dan een triviale biologische vaststelling. Jan vii Contents Introduction ................................................................................................................. xiii 1. Inleiding tot het cladisme .......................................................................................... 1 2. Three-item analysis ................................................................................................ 27 3. Homoplasy-based weighting schemes in parsimony analysis ................................ 69 4. A commentary on the circumscription and evolution of the order Gentianales, with special emphasis on the position of the Rubiaceae ....................................... 101 5. Phylogeny of temperate Gentianaceae: a morphological approach ...................... 111 6. Indecisive data and missing entries ...................................................................... 131 References ............................................................................................................... 141 Appendix A. ViTA, a program for parsimony analysis using implied weights ............. 157 Appendix B. With hyperbolic weighting functions, maximization of fit and minimization of weighted homoplasy are equivalent ................................................. 185 Appendix C. Derivation of S and G for minimal indecisive data sets ......................... 191 Samenvatting ............................................................................................................ 197 viii 1. Inleiding tot het cladisme .......................................................................................... 1 1.1 Inleiding ............................................................................................................... 1 1.2 Basisprincipes ..................................................................................................... 4 1.3 Cladisme in een breder kader: het homologieconcept ....................................... 14 1.4 Polariseren en ordenen van kenmerken ............................................................ 18 1.4.1 Buitengroepvergelijking ............................................................................... 19 1.4.2 Het ontogenetisch criterium ......................................................................... 20 1.4.3 Polariseren versus ordenen ......................................................................... 21 1.5 De cladistische classificatie ............................................................................... 23 1.6 Samenvatting..................................................................................................... 25 2. Three-item analysis ................................................................................................ 27 2.1. Introduction ....................................................................................................... 27 2.2. Three-item analysis .......................................................................................... 28 2.2.1. Theory ........................................................................................................ 28 2.2.2. Example ..................................................................................................... 30 2.3. The problem of irreversibility ............................................................................. 32 2.3.1. Introduction ................................................................................................ 32 2.3.2. Solution ...................................................................................................... 33 2.3.3. Examples ................................................................................................... 35 2.4. Algorithms ........................................................................................................ 37 2.4.1. Introduction ................................................................................................ 37 2.4.2. Calculating the number of accommodated four-item statements ................ 39 2.4.3. Calculating the number of unaccommodated four-item statements ............ 41 2.4.4. An example ................................................................................................ 42 2.5. The problem of dependency ............................................................................. 45 2.5.1. Introduction ................................................................................................ 45 2.5.2. Fractional weighting.................................................................................... 47 2.5.3. Calculating the number of independent accommodated four-item statements ................................................................................................. 52 2.6. The problem of mutual exclusiveness ............................................................... 58 2.6.1. Introduction ................................................................................................ 58 2.6.2. Calculating the number of independent compatible taxon pairs for fixed inner node state assignments ....................................................... 60 2.6.3. Dependency revisited ................................................................................. 64 2.6.4. Removing the relational constraint: back to the standard approach ............ 66 2.7. Summary and conclusion ................................................................................. 67 ix 3. Homoplasy-based weighting schemes .................................................................... 69 3.1 Introduction ........................................................................................................ 69 3.2 Successive weighting ........................................................................................ 72 3.2.1 Weighting function ....................................................................................... 73 3.2.2 Initial set of weights ..................................................................................... 74 3.2.3 Differential weighting of state transformations in multistate characters ....... 75 3.2.3.1 Ordered characters ........................................................................... 75 3.2.3.2 Unordered characters........................................................................ 75 3.2.4 Multiple most parsimonious trees ................................................................ 77 3.3 Implied weights .................................................................................................. 78 3.3.1 Self-consistency .......................................................................................... 78 3.3.2 Character fit as a concave decreasing function of the homoplasy ............... 79 3.3.3 Maximizing total fit ....................................................................................... 80 3.3.4 Choice of a convex decreasing function ...................................................... 81 3.4 Using implied weights as weights during parsimony analysis ............................ 83 3.4.1 Maximizing fit versus minimizing weighted homoplasy ................................ 84 3.4.2 Justifying concave weighting functions ........................................................ 85 3.4.3 A special property of hyperbolic weighting functions...................................