AN EXPLORATION OF MODELS OF DIVERSIFICATION AND THE TEMPO OF DIVERSIFICATION USING LINEAGES THROUGH TIME PLOTS by Dennis Ho-Jay Wong BSc., Simon Fraser University, 2002 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science In the Graduate Academic Unit of Biology Supervisor: Stephen B. Heard, PhD, Department of Biology, Univeristy of New Brunswick Examining Board: Stephen B. Heard, PhD Department of Biology, Chair Linley Jesson, PhD, Department of Biology External Examiner: R. Steve Turner, PhD, Department of History This thesis is accepted Dean of Graduate Studies THE UNIVERSITY OF NEW BRUNSWICK May, 2007 ©Dennis Ho-Jay Wong, 2007 DEDICATION I dedicate this work to my friends and family, but especially my late grandmother who always encouraged me to never forget family. ii ABSTRACT Explaining species richness is one of the major goals in evolutionary biology. One approach to explain species richness is through models of species level diversification, and recent attention has been placed on testing for instances of non-constant rates of diversification. Translated from phylogenies, lineages through time (LTT) plots are one way to examine rates of diversification. However, the degree which LTT data reflect a model of diversification is unknown. I conducted a simulation study that determines the power of LTT plots to distinguish different models from each other. The results generally show that LTT plots can identify non-constant diversification, although, power is low. There was also low power for LTT plots to distinguish alternative models from each other, and alternative models of extinction from a constant background rate. Including extinct lineages increases power, but power depends on whether models change the shape of an LTT plot. As corroborating lines of evidence, information about the natural history of a clade and tree shape statistics would be insightful. iii ACKNOWLEDGEMENTS This research project could not have been completed without the help of several people. I would like to thank my supervisor, Dr. Stephen Heard for his intellectual support, time, and feedback. His enthusiasm helped spark initial interest in this research. I thank both my supervisory committee members, Dr. Gary Saunders and Dr. James Watmough for their guidance, input in this research, and excellent advice to improve this document. I thank Dr. Arne Mooers at Simon Fraser University for his intellectual support, feedback, and encouragement. For their valuable feedback, I thank members of the Quiring and Heard labs, the UNB evolution graduate group and members of the Alan Wilson Centre at the University of Canterbury, NZ. For a seemingly unlimited amount of intellectual support and general entertainment I thank Hana Kucera, Graham Cox, Colin Curry, Tiffany Thornhill, Brian McDonald, Rodney Withall, William Godsoe, and Jon Freedman. Lastly I extend my thanks to my family (especially Amie, Mike Jeff, and Jasmine Wong) who all provided me with unconditional love, support and encouragement. iv Table of Contents DEDICATION............................................................................................................... ii ABSTRACT.................................................................................................................. iii ACKNOWLEDGEMENTS............................................................................................iv List of Figures ................................................................................................................ix List of Symbols, Nomenclature or Abbreviations...........................................................xv 1 GENERAL INTRODUCTION..................................................................................1 1.1 Why study diversification and how it can be studied ...........................................1 1.2 Studying past evolution via phylogenies .............................................................8 1.3 Models of diversification and the expected shape of lineages through time plots... ........................................................................................................................................14 1.4 Distinguishing models of diversification from each other using LTT plots ........20 1.5 How stochastic models can be used to answer question about diversification ....22 1.6 Non-LTT plot approaches to analyzing the tempo of diversification..................26 1.7 Summary ..........................................................................................................27 1.8 Contribution and Authorship.............................................................................28 1.8.1 Identification and design of research proposal ............................................28 1.8.2 Practical aspects of the research .................................................................28 1.8.3 Data analysis..............................................................................................29 1.8.4 Manuscript preparation...............................................................................29 1.9 LITERATURE CITED .....................................................................................30 2 LINEAGE ACCUMULATION PLOTS, THE CONSTANT RATE AND ALTERNATIVE MODELS OF DIVERSIFICATION: COMPLETELY DIFFERENT OR ALL THE SAME? ..................................................................................................36 ABSTRACT..............................................................................................................36 2.1 Introduction ......................................................................................................37 v 2.2 Models of speciation and extinction ..................................................................42 2.2.1 Equal rates Markov ....................................................................................42 2.2.2 Trait based speciation rates.........................................................................43 2.2.3 Maximum diversity ....................................................................................44 2.3 Computer program and simulations...................................................................46 2.3.1 General approach .......................................................................................46 2.3.2 Parameter values and sample sizes .............................................................48 2.4 Statistical procedures ........................................................................................51 2.5 Results and Discussion......................................................................................56 2.5.1 ERM model and the TBS model of diversification......................................56 2.5.2 ERM model and the MD model of diversification ......................................61 2.5.3 Gamma versus LTT plots ...........................................................................65 2.5.4 A critique of our statistical techniques, and direction for future studies.......66 2.5.5 What lessons can be applied to the study of the diversification of actual clades? ........................................................................................................................68 2.6 Conclusion........................................................................................................73 2.7 LITERATURE CITED .....................................................................................74 3 CAN LINEAGE ACCUMULATION PLOTS DISTINGUISH MODELS OF EXTINCTION OR ALTERNATIVE MODELS OF DIVERSIFICATION FROM EACH OTHER? .......................................................................................................................78 ABSTRACT..............................................................................................................78 3.1 Introduction ......................................................................................................79 3.2 Computer program and models of diversification..............................................81 3.2.1 Computer program .....................................................................................81 3.2.2 Equal rates Markov ....................................................................................82 vi 3.2.3 Alternative models of diversification..........................................................83 3.2.4 Models of extinction ..................................................................................85 3.3 Simulations.......................................................................................................87 3.4 Statistical procedures ........................................................................................88 3.5 Results and discussion ......................................................................................91 3.5.1 Distinguishing alternative models of extinction from the CRE model.........91 3.5.2 Distinguishing alternative models of diversification from each other? ........98 3.6 Conclusion......................................................................................................112 3.7 LITERATURE CITED ...................................................................................113 4 GENERAL DISCUSSION ....................................................................................116 4.1 Branching evolution is not perfectly dichotomous...........................................117 4.2 Phylogenies of real clades are estimates, whereas