TIME‐DEPENDENT SPECIATION AND EXTINCTION FROM PHYLOGENIES: A LEAST SQUARES APPROACH

Molecular phylogenies contribute to the study of the patterns and processes of macroevolution even though past events (fossils) are not recorded in these data. In this article, I consider the general time‐dependent birth–death model to fit any model of temporal variation in speciation and extinction to phylogenies. I establish formulae to compute the expected cumulative distribution function of branching times for any model, and, building on previous published works, I derive maximum likelihood estimators. Some limitations of the likelihood approach are described, and a fitting procedure based on least squares is developed that alleviates the shortcomings of maximum likelihood in the present context. Parametric and nonparametric bootstrap procedures are developed to assess uncertainty in the parameter estimates, the latter version giving narrower confidence intervals and being faster to compute. I also present several general algorithms of tree simulation in continuous time. I illustrate the application of this approach with the analysis of simulated datasets, and two published phylogenies of primates (Catarrhinae) and lizards (Agamidae).

[1]  Charles R Marshall,et al.  Diversity dynamics: molecular phylogenies need the fossil record. , 2010, Trends in ecology & evolution.

[2]  Daniel L Rabosky,et al.  EXTINCTION RATES SHOULD NOT BE ESTIMATED FROM MOLECULAR PHYLOGENIES , 2010, Evolution; international journal of organic evolution.

[3]  D. Rabosky.  Heritability of extinction rates links diversification patterns in molecular phylogenies and fossils. , 2009, Systematic biology.

[4]  Richard G FitzJohn,et al.  Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies. , 2009, Systematic biology.

[5]  T. Stadler.  On incomplete sampling under birth-death models and connections to the sampling-based coalescent. , 2009, Journal of theoretical biology.

[6]  M. Pie,et al.  The Macroevolutionary Dynamics of Ant Diversification , 2009, Evolution; international journal of organic evolution.

[7]  D. Rabosky.  Ecological Limits on Clade Diversification in Higher Taxa , 2009, The American Naturalist.

[8]  M. Donoghue,et al.  A Bayesian approach for evaluating the impact of historical events on rates of diversification , 2009, Proceedings of the National Academy of Sciences.

[9]  J. Losos,et al.  Adaptive Radiation: Contrasting Theory with Data , 2009, Science.

[10]  Mark A McPeek,et al.  The Ecological Dynamics of Clade Diversification and Community Assembly , 2008, The American Naturalist.

[11]  I. Lovette,et al.  Explosive Evolutionary Radiations: Decreasing Speciation or Increasing Extinction Through Time? , 2008, Evolution; international journal of organic evolution.

[12]  J. Wakeley.  Coalescent Theory: An Introduction , 2008 .

[13]  R. Ricklefs,et al.  Estimating diversification rates from phylogenetic information. , 2007, Trends in ecology & evolution.

[14]  Peter E Midford,et al.  Estimating a binary character's effect on speciation and extinction. , 2007, Systematic biology.

[15]  Kate E. Jones,et al.  The delayed rise of present-day mammals , 1990, Nature.

[16]  F. Bokma.  Artificial neural networks can learn to estimate extinction rates from molecular phylogenies. , 2006, Journal of theoretical biology.

[17]  Daniel L Rabosky,et al.  LIKELIHOOD METHODS FOR DETECTING TEMPORAL SHIFTS IN DIVERSIFICATION RATES , 2006, Evolution; international journal of organic evolution.

[18]  R. Ree.  DETECTING THE HISTORICAL SIGNATURE OF KEY INNOVATIONS USING STOCHASTIC MODELS OF CHARACTER EVOLUTION AND CLADOGENESIS , 2005, Evolution; international journal of organic evolution.

[19]  E. Paradis.  STATISTICAL ANALYSIS OF DIVERSIFICATION WITH SPECIES TRAITS , 2005, Evolution; international journal of organic evolution.

[20]  E. Paradis.  Can extinction rates be estimated without fossils? , 2004, Journal of theoretical biology.

[21]  Korbinian Strimmer,et al.  APE: Analyses of Phylogenetics and Evolution in R language , 2004, Bioinform..

[22]  E. Paradis.  Analysis of diversification: combining phylogenetic and taxonomic data , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[23]  J. Losos,et al.  Tempo and Mode of Evolutionary Radiation in Iguanian Lizards , 2003, Science.

[24]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[25]  G. Turner.  The Ecology of Adaptive Radiation , 2001, Heredity.

[26]  S. Nee,et al.  INFERRING SPECIATION RATES FROM PHYLOGENIES , 2001, Evolution; international journal of organic evolution.

[27]  Oliver G. Pybus,et al.  Testing macro–evolutionary models using incomplete molecular phylogenies , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  E. Paradis.  Detecting Shifts in Diversification Rates without Fossils , 1998, The American Naturalist.

[29]  A. Cooper,et al.  Evolutionary explosions and the phylogenetic fuse. , 1998, Trends in ecology & evolution.

[30]  E. Paradis.  Assessing temporal variations in diversification rates from phylogenies: estimation and hypothesis testing , 1997, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[31]  Yoh Iwasa,et al.  INFERRING THE RATES OF BRANCHING AND EXTINCTION FROM MOLECULAR PHYLOGENIES , 1995, Evolution; international journal of organic evolution.

[32]  A. Purvis.  A composite estimate of primate phylogeny. , 1995, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[33]  P H Harvey,et al.  Macroevolutionary inferences from primate phylogeny , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[34]  Frederick R. Adler,et al.  Stumped by Trees? A Generalized Null Model for Patterns of Organismal Diversity , 1995, The American Naturalist.

[35]  D. Madigan,et al.  Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window , 1994 .

[36]  R. Tibshirani,et al.  An Introduction to the Bootstrap , 1995 .

[37]  Sean Nee,et al.  PHYLOGENIES WITHOUT FOSSILS , 1994, Evolution; international journal of organic evolution.

[38]  R M May,et al.  The reconstructed evolutionary process. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[39]  R M May,et al.  Extinction rates can be estimated from molecular phylogenies. , 1994, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[40]  P H Harvey,et al.  Tempo and mode of evolution revealed from molecular phylogenies. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[41]  D. Kendall.  On the Generalized "Birth-and-Death" Process , 1948 .

[42]  Nils Lid Hjort,et al.  Model Selection and Model Averaging: Contents , 2008 .

[43]  Nils Lid Hjort,et al.  Model Selection and Model Averaging , 2001 .

[44]  Robert Tibshirani,et al.  An Introduction to the Bootstrap CHAPMAN & HALL/CRC , 1993 .

[45]  J. Kingman.  On the genealogy of large populations , 1982, Journal of Applied Probability.