Phylogeny-Based Analyses of Evolution with a Paleo-Focus Part 2. Diversification of Lineages (Mar 02, 2012 David W. Bapst

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1 Phylogeny-Based Analyses of Evolution with a Paleo-Focus Part 2. Diversification of Lineages (Mar 02, 2012 David W. Bapst Recommended Reading: Nee, S Birth-Death Models in Macroevolution. Annual Review of Ecology, Evolution, and Systematics 37(1):1-17. Ricklefs, R. E Estimating diversification rates from phylogenetic information. Trends in Ecology & Evolution 22(11): Stadler, T Inferring speciation and extinction processes from extant species data. Proceedings of the National Academy of Sciences 108(39): Models of Diversification (Birth-Death Models) Another parade of models, often compared using AIC. Equal Rates Markov o Not a model of diversification as much a model of branching o Every time speciation occurs, every leaf/tip of the tree has the same probability of splitting Only parameter is the number of tips o Used as a null model in studies of tree asymmetry Pure Birth: The Simplest Model o One parameter: branching rate (lambda, λ) o Lineages branch as a Poisson process, never go extinct o Although only lineage accumulation is immediately apparent from a molecular phylogeny, fitting a pure-birth model is definitely not equivalent to measuring net diversification rate under a birth-death model (Nee, 2001) Birth-Death Model o Two Parameters: branching rate and extinction rate λ and μ (p and q generally in paleo literature) o The events occur as Poisson processes; waiting times between events are exponentially distributed ( competing exponential ) Lineages Vary o Some sort of discrete variation across a tree o Example: Key Innovation that affects both rates: λ 0, μ 0, λ 1, μ 1 o Example: Sudden change in rates after time t: o λ time<t, μ time<t, λ time>t, μ time>t Example: Clade B Radiated on an Island, Extinction Constant: λ a, λ B, μ Rates Vary Continuously Over Time (General Birth-Death Model)

2 o o o Rather than rates varying between discrete intervals, rates continuously vary over time Example: Speciation rate linearly decays over time λ 0, Δλ, μ The change parameter describes how speciation rate changes over time Diversity Dependence o Speciation or Extinction or both vary with richness o Can be difficult to differentiate from a time-varying model on a molecular phylogeny o Example: Five parameters in full model with carrying capacity: λ K, Δλ, μ K, Δμ, K o Example: diversity-dependent speciation: λ (time=t) = λ K - Δλ * (K- (richness at time=t)) Inheritance of Rates (Roy et al., 2009; Rabosky, 2009) o Diversification rate varies among lineages but with interspecific inheritance, like a trait evolving under Brownian Motion (i.e. high phylogenetic signal) o For example: a three-parameter model where speciation is constant but extinction is varies: root-ancestral extinction rate and rate of extinction rate evolution λ, μ 0, Δμ o Pie and Tscha (2009) argued for this model based on a high phylogenetic signal for genus size using the Moreau et al. ant tree (analyzed genus size as a trait using Pagel s lambda) Clade-Level Turnover (Pyron and Burbrink, 2011) Individual sub-clades experience bursts of speciation followed by sudden declines Two phases: λ 1 > μ 1 followed by μ 2 > λ 2 o Transition occurs when half-life of clade is reached; point when agediversity plot peaks <- diagram from Pyron and Burbrink) Moran Process (Hey, 1992; Nee, 2001; 2006) o Not derived from BM; a single parameter: turnover rate o A simulation where the extinction of a lineage is immediately followed by the speciation of another lineage, such that the number of lineages remains constant

3 o o o Similar but not identical to diversity-dependent BD models Moran process is expected to produce clades where most speciation is very recent ( speed-up of diversification) Rabosky (2009) fitted a modified version (see below) Uses other than Quantifying Diversification Branch-Length Priors in Bayesian Phylogenetics (e.g. BEAST) o Branch-length priors based on a diversification model o Some studies use a pure-birth prior (including Pyron, 2011) Estimating number of unobserved branching points o Such as testing punctuated equilibrium (see Trait lecture) Basis for stochastic simulations; testing other methods o What is the world like? Will our methods perform well? o Importance of proper conditioning: Hartmann et al., 2010 Analyses of Diversification using Molecular Phylogenies As paleontologists, it is sometimes easy to treat extant-only diversification analyses as preposterous. I have done this myself, in the past. However, many biologists work on groups with no fossil record. We don t yet fully understand the limits of using molecular phylogenies to test hypotheses of diversification. Hey, 1992 Used waiting times between speciation events Tested Moran process versus pure-birth; found support for the pure-birth model Rabosky (2009) shows this is due to Moran process favoring weird trees with early single divergence and the rest of the speciation being very recent (unrealistic pattern)

4 Nee et al. (1992; 1994a; 1994b; 2006; Harvey et al. 1994) Probabilistic / likelihood framework for estimating diversification rates based on age of surviving lineages o Estimated diversification rates using maximum likelihood and also evaluated the fit of some models, including a diversity dependent model (Nee et al., 1992) o Appendix to Nee (2001) showed that internode intervals (as used in Hey, 1992) contain the same information as node times o Nee et al. (1994) give likelihood equations for both constant rate and time-varying birth-death rates o Rabosky (2006) extended this work for comparing models via AIC o Paradis (2010) extended models to allow rates to vary with any definable function over time Kubo and Iwasa (1995) o Showed that you could estimated rates from fitting regression models to the slope of the LTT curve, but poor ability to obtain the extinction rate Paradis (1997; 1998) o Developed a ML survival analysis framework o Used AIC to test models of diversification shifts Magallon and Sanderson (2001) (see Rabosky, 2007 for example) o Using birth-death equations from Raup, developed methods to estimate diversification rates when just species richness and stem and/or crown ages are known for clades o Including hypothesis testing of rate differences and conf.ints Detecting General Rate Variation in a Dataset o Tree Balance/symmetry/shape Mooers and Heard, 1997; Chan and Moore, 2003 Evidence for considerable variation in rates across a large dataset of phylogenies o Sims and McConway 2003 and McConway and Sims 2004 develop likelihood based methods for testing for rate variability within a phylogeny based on asymmetry in number of extant species in sister clades

5 o Harcourt-Brown et al. (2001) found that combining taxa from multiple time-intervals added to the asymmetry of trees considered (pers.obs.: simulated paleo-trees very unbalanced) Estimating Rates on Incomplete Phylogenies o Paradis, 2003; Bokma, 2009; Rabosky et al. (2006) obtained likelihood solution o MEDUSA (Alfaro et al., 2009) A stepwise-aic method which fits the best model of diversification rate shifts across the (incomplete) tree Inferring aspects of speciation drivers from branch lengths o Venditti et al. (2010) fit distributions to internal branch lengths ( waiting times to speciation ) Testing for Effects of Traits on Diversification Several methods (Paradis, 2005; Ree, 2005; Moore and Donoghue, 2009) Probably susceptible to tangled asymmetries (Maddison, 2006) Testing for Slowdowns in Diversification Rate First test of this in Nee et al., 1992 Gamma statistic: Pybus and Harvey (2000) o Gamma: estimate of much diversification occurs closer or further from the root than expected, which is normally distributed around 0 under a pure-birth process o applicable to partially incomplete phylogenies Liow et al. (2010) found that gamma was only useful if measured soon after the equilibrium level in diversity-dependent diversification was hit; the signal deteriorated after being at the equilibrium for too long (what does this sound like?) o McInnes et al. (2011) calculate the expected waiting times of this deterioration under different rates Expect to see some support for slow-downs even in large clades under constant rates because clades will only get large under constant rates by having high levels of branching early on; however, a large nearly complete dataset of bird phylogenies shows even greater support for slow-downs than expected by simulations (Phillimore and Price, 2007)

6 Are slowdowns due to decreasing speciation or increasing extinction? Rabosky and Lovette (2008) simulated these scenarios. The resulting LTT plots suggest decreasing speciation (A,B) because in empirical data there is no upturn near the recent suggestive of high extinction rates (C,D) Rabosky and Lovette (2008) developed ML models based on Nee et al which are pure-birth models with rates dependent on the inferred diversity of surviving lineages (as did Nee et al. 1992). They fit this model to the Dendroica phylogeny (LTT to the left) Bokma critized this analysis (2009) Kubo and Iwasa (1995) showed that the number of inferred lineages is expected to correlate to the number of actual lineages Age-Richness relationships (McPeek and Brown, 2007) o Appears to be no clear relationship o Evidence for diversity-dependence? (Rabosky, 2009) What have we found in general? 1. Little support for extinction: no Push of the Present 2. Slow-downs in net diversification 3. No Age-Richness Relationship A Typical-looking LTT plot of ant diversification from Moreau et al., 2006 From Pie and Tscha (2009) Interpretations of the Slow-downs Bias from how trees are dated (e.g. Revell et al., 2005)

7 Taxon sampling issues: under-sampled trees look like slowdowns o But under-sampling should also look like high extinction! o Random and non-random sampling has considerable effect Cusimano and Renner, 2010; Hohna et al., 2011 Solutions: Brock et al., 2011; Cusimano et al.; in press o Yet, slowdowns still present in fully sampled phylogenies (e.g. Phillmore and Price, 2007) Diversity-Dependence is widespread and common (Rabosky, 2009) o Counter-opinions: Benton and Emerson, 2007; Wiens, 2011 Prolonged Speciation (Etienne and Rosindell, 2012) o Speciation is not instantaneous, removing push of the present o Similar to a semi-neutral metacommunity theory suggested by McPeek, (2007; 2009) where species are either very similar or very divergent Interpretations of the Lack of Extinction Doesn t agree with the fossil record (Quental and Marshall, 2011) A model of extinction variability removes the ability of Nee et al methods to estimate extinction rate (Rabosky, 2010) The Quest for the Golden Model of Diversification Find the model of diversification which can reconcile the molecular phylogenies with the fossil record, allowing for (better) estimation of extinction rates when no fossils are available Rabosky (2009) developed the HEPT model, which is a 5 parameter variant of the Moran process with temporal variability in turnover rate and inheritance of rates o Fit to warbler data: very high turn-over rates necessary Pyron and Burbrink (2011) Implemented a clade-turnover model which they found to fit better than Rabosky s diversity-dependent models Stadler, 2011 o Presents maximum likelihood methods for a birth-death discrete time shift model (based on Nee et al. framework) In reference to Rabosky s (2006) model: parameters are estimated assuming that the tree before the rate shift is independent of the tree after the rate shift time this assumption is not valid because (of) extinction in the later interval Applied to mammal supertree (Bininda-Emonds et al., 2007); did not find Eocene shift but rather 33 Mya shift o Meredith et al. supermatrix tree of mammal relations shows a mid-cretaceous burst of diversification using both Rabosky s pure-birth and Stadler s methods, with no Cenozoic shifts

8 Etienne et al o Suggest diversity-dependence explains apparent zero extinction o Obtained a complicated Hidden Markov Model algorithm to fit diversity-dependent birth-death models of phylogenies (3 par) Difficulty estimating the number of extinct species Allows inferences of probable reconstructed diversification history o Fit model to a number of datasets, including planktic forams and cetaceans, so to compare reconstructed diversity curve to diversity curve sampled from the fossil record o Similar fit as Rabosky s 5 parameter HEPT model o To fit cetacean dataset, need to fix mu at fossil estimate Morlon et al Develop exact analytic likelihood equation for birth-death process that also includes sampling and (continuous or discrete) rate variation over time, including modification to consider among clade variation in rates The rate variation allows them to consider clades currently in decline (lambda-mu can be negative at t=0) They can also reconstruct probable past diversity curve Fit it to cetaceans and get pure-birth Reject this based on fossil record and instead fit models separately to the four largest families and calculated joint likelihood; constant birth and exp-increasing extinction the best supported model Simpson et al The inferred diversity curve looks a lot like fossil record Essentially, estimated net diversification rate within intervals from both the fossil record (using per-capita rates) and a molecular phylogeny; can compare these time-series Also subtract estimated speciation/extinction rates from molecular net diversification rate: pulsed temporal pattern of diversification Overall, despite phylogenetic uncertainty, obtain similar patterns o But how will this approach fit in with model fitting analyses?

9 Now for Something Completely Different: Paleo-tree Modeling Lieberman, 2001: fit models of pure-birth, birth-death and Bienayme- Galton-Watson process to richness counts at different time intervals based on a time-scaled cladogram of Cambrian trilobite species Cavin and Forey (2007): use average lineage duration of ghost branches to per interval to identify periods of radiation o Pers. Obs.: ghost branch length dependent on speciation type (i.e. bifurcation versus budding) Harcourt-Brown (2002) took time-slices through a foram tree and looked at imbalance at those time-slices; peaks in imbalance seemed to relate to intervals of high turnover although not significant o Ruta et al. (2007) looked at tree symmetry at time-slices using Chan and Moore s 2002 analyses o Tarver and Donoghue (2011) found that these topology-based analyses of paleo-tree time-slices were prone to error and could not reliably identify rate shifts in time

10 Ruta et al. (2011) tried nine different rate metrics on a timescaled paleo-tree, including a modification of per-capita rates Ezard et al. (2011) consider a wide array of factors affect diversification on a stratophenetic tree of forams using hazard analysis (similar to the survival analysis used by Paradis) and evaluated these models; found that a number of factors influence foram diversification. Paradis, 2004 presented estimators of rates from Keiding, 1975 ignores sampling Bt is number of births, Dt is number of deaths, the denominator is the total branch length (evolutionary history) in interval Pyron and Burbrink, 2011 Stadler, 2010 presented a likelihood equation for a tree with extinct taxa (did not account for sampling) and randomly added 10 fossil snakes to a tree of 40 living species greatly affected rate estimates Model included sampling! Excerpt: This doesn t account for sampling. See the paper for an explanation of the parameters used above References Alfaro, M. E., F. Santini, C. Brock, H. Alamillo, A. Dornburg, D. L. Rabosky, G. Carnevale, and L. J. Harmon Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates. Proceedings of the National Academy of Sciences 106(32): Benton, M. J., and B. C. Emerson How did life become so diverse? The dynamics of diversification according to the fossil record and molecular phylogenetics. Palaeontology 50: Bininda-Emonds, O. R. P., M. Cardillo, K. E. Jones, R. D. E. MacPhee, R. M. D. Beck, R. Grenyer, S. A. Price, R. A. Vos, J. L. Gittleman, and A. Purvis The delayed rise of present-day mammals. Nature 446(7135):

11 Bokma, F Bayesian Estimation of Speciation and Extinction Probabilities from (In) Complete Phylogenies. Evolution 62(9): Bokma, F Problems detecting density-dependent diversification on phylogenies. Proceedings of the Royal Society B: Biological Sciences 276(1659): Brock, C. D., L. J. Harmon, and M. E. Alfaro Testing for Temporal Variation in Diversification Rates When Sampling is Incomplete and Nonrandom. Systematic Biology 60(4): Cavin, L., and P. L. Forey Using ghost lineages to identify diversification events in the fossil record. Biology Letters 3(2): Chan, K. M. A., and B. R. Moore Whole-Tree Methods for Detecting Differential Diversification Rates. Systematic Biology 51(6): Cusimano, N., and S. S. Renner Slowdowns in Diversification Rates from Real Phylogenies May Not be Real. Systematic Biology 59(4): Cusimano, N., T. Stadler, and S. S. Renner A new method for handling missing species in diversification analysis applicable to randomly or non-randomly sampled phylogenies. Systematic Biology. Etienne, R. S., B. Haegeman, T. Stadler, T. Aze, P. N. Pearson, A. Purvis, and A. B. Phillimore Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record. Proceedings of the Royal Society B: Biological Sciences 279(1732): Etienne, R. S., and J. Rosindell Prolonging the Past Counteracts the Pull of the Present: Protracted Speciation Can Explain Observed Slowdowns in Diversification. Systematic Biology 61(2): Ezard, T. H. G., T. Aze, P. N. Pearson, and A. Purvis Interplay Between Changing Climate and Species Ecology Drives Macroevolutionary Dynamics. Science 332(6027): Ezard, T. H. G., and A. Purvis paleophylo: free software to draw paleobiological phylogenies. Paleobiology 35(3): Harcourt-Brown, K. G Tree Balance, Time Slices, and Evolutionary Turnover in Cretaceous Planktonic Foraminifera. Systematic Biology 51(6): Harcourt-Brown, K. G., P. N. Pearson, and M. Wilkinson The imbalance of paleontological trees. Paleobiology 27(2): Hartmann, K., D. Wong, and T. Stadler Sampling Trees from Evolutionary Models. Systematic Biology 59(4): Harvey, P. H., R. M. May, and S. Nee Phylogenies Without Fossils. Evolution 48(3): Hey, J Using Phylogenetic Trees to Study Speciation and Extinction. Evolution 46(3): Höhna, S., T. Stadler, F. Ronquist, and T. Britton Inferring Speciation and Extinction Rates under Different Sampling Schemes. Molecular Biology and Evolution 28(9): Kubo, T., and Y. Iwasa Inferring the Rates of Branching and Extinction from Molecular Phylogenies. Evolution 49(4): Lieberman, B. S A Test of Whether Rates of Speciation Were Unusually High during the Cambrian Radiation. Proceedings: Biological Sciences 268(1477): Liow, L. H., T. B. Quental, and C. R. Marshall When Can Decreasing Diversification Rates Be Detected with Molecular Phylogenies and the Fossil Record? Systematic Biology 59(6): Magallon, S., and M. J. Sanderson Absolute Diversification Rates in Angiosperm Clades. Evolution 55(9):

12 McConway, K. J., and H. J. Sims A LIKELIHOOD-BASED METHOD FOR TESTING FOR NONSTOCHASTIC VARIATION OF DIVERSIFICATION RATES IN PHYLOGENIES. Evolution 58(1): McInnes, L., C. D. L. Orme, and A. Purvis Detecting shifts in diversity limits from molecular phylogenies: what can we know? Proceedings of the Royal Society B: Biological Sciences 278(1722): McPeek, M. A The macroevolutionary consequences of ecological differences among species. Palaeontology 50(1): McPeek, Mark A The Ecological Dynamics of Clade Diversification and Community Assembly. The American Naturalist 172(6):E270-E284. McPeek, Mark A., and Jonathan M. Brown Clade Age and Not Diversification Rate Explains Species Richness among Animal Taxa. The American Naturalist 169(4):E97-E106. Meredith, R. W., J. E. Janečka, J. Gatesy, O. A. Ryder, C. A. Fisher, E. C. Teeling, A. Goodbla, E. Eizirik, T. L. L. Simão, T. Stadler, D. L. Rabosky, R. L. Honeycutt, J. J. Flynn, C. M. Ingram, C. Steiner, T. L. Williams, T. J. Robinson, A. Burk-Herrick, M. Westerman, N. A. Ayoub, M. S. Springer, and W. J. Murphy Impacts of the Cretaceous Terrestrial Revolution and KPg Extinction on Mammal Diversification. Science 334(6055): Mooers, A. Ø., and S. B. Heard Inferring evolutionary processes from phylogenetic tree shape. Quarterly Review of Biology 72(1): Moore, B. R., and M. J. Donoghue A Bayesian approach for evaluating the impact of historical events on rates of diversification. Proceedings of the National Academy of Sciences 106(11): Moreau, C. S., C. D. Bell, R. Vila, S. B. Archibald, and N. E. Pierce Phylogeny of the Ants: Diversification in the Age of Angiosperms. Science 312(5770): Morlon, H., T. L. Parsons, and J. B. Plotkin Reconciling molecular phylogenies with the fossil record. Proceedings of the National Academy of Sciences 108(39): Nee, S Inferring Speciation Rates From Phylogenies. Evolution 55(4): Nee, S Birth-Death Models in Macroevolution. Annual Review of Ecology, Evolution, and Systematics 37(1):1-17. Nee, S., E. C. Holmes, R. M. May, and P. H. Harvey Extinction Rates can be Estimated from Molecular Phylogenies. Philosophical Transactions: Biological Sciences 344(1307): Nee, S., R. M. May, and P. H. Harvey The Reconstructed Evolutionary Process. Philosophical Transactions: Biological Sciences 344(1309): Nee, S., A. O. Mooers, and P. H. Harvey Tempo and mode of evolution revealed from molecular phylogenies. Proceedings of the National Academy of Sciences of the United States of America 89(17): Paradis, E Assessing Temporal Variations in Diversification Rates from Phylogenies: Estimation and Hypothesis Testing. Proceedings: Biological Sciences 264(1385): Paradis, E Detecting Shifts in Diversification Rates without Fossils. The American Naturalist 152(2): Paradis, E Analysis of diversification: combining phylogenetic and taxonomic data. Proceedings of the Royal Society of London. Series B: Biological Sciences 270(1532): Paradis, E Can extinction rates be estimated without fossils? Journal of Theoretical Biology 229(1): Paradis, E Statistical Analysis of Diversification with Species Traits. Evolution 59(1):1-12.

13 Paradis, E Time-dependent speciation and extinction from phylogenies: a least squares approach. Evolution:no-no. Phillimore, A. B., and T. D. Price Density-Dependent Cladogenesis in Birds. PLoS Biol 6(3):e71. Pie, M. R., and M. K. Tschá The Macroevolutionary Dynamics Of Ant Diversification. Evolution 63(11): Pybus, O. G., and P. H. Harvey Testing macro-evolutionary models using incomplete molecular phylogenies. Proceedings of the Royal Society of London. Series B: Biological Sciences 267(1459): Pyron, R. A Divergence Time Estimation Using Fossils as Terminal Taxa and the Origins of Lissamphibia. Systematic Biology 60(4): Pyron, R. A., and F. T. Burbrink Extinction, Ecological Opportunity, And The Origins Of Global Snake Diversity. Evolution 66(1): Pyron, R. A., and F. T. Burbrink Trait-dependent diversification and the impact of palaeontological data on evolutionary hypothesis testing in New World ratsnakes (tribe Lampropeltini). Journal of Evolutionary Biology:no-no. Quental, T. B., and C. R. Marshall EXTINCTION DURING EVOLUTIONARY RADIATIONS: RECONCILING THE FOSSIL RECORD WITH MOLECULAR PHYLOGENIES. Evolution 63(12): Quental, T. B., and C. R. Marshall Diversity dynamics: molecular phylogenies need the fossil record. Trends in Ecology & Evolution 25(8): Quental, T. B., and C. R. Marshall The Molecular Phylogenetic Signature of Clades in Decline. PLoS ONE 6(10):e Rabosky, D. L Likelihood methods for detecting temporal shifts in diversification rates. Evolution 60(6): Rabosky, D. L Ecological limits and diversification rate: alternative paradigms to explain the variation in species richness among clades and regions. Ecology Letters 12(8): Rabosky, D. L Heritability of Extinction Rates Links Diversification Patterns in Molecular Phylogenies and Fossils. Systematic Biology 58(6): Rabosky, D. L Extinction Rates Should Not Be Estimated From Molecular Phylogenies. Evolution 64: Rabosky, D. L., S. C. Donnellan, A. L. Talaba, and I. J. Lovette Exceptional among-lineage variation in diversification rates during the radiation of Australia's most diverse vertebrate clade. Proceedings of the Royal Society B: Biological Sciences 274(1628): Rabosky, D. L., and I. J. Lovette Density-dependent diversification in North American wood warblers. Proceedings of the Royal Society B: Biological Sciences 275(1649): Rabosky, D. L., I. J. Lovette, and A. Mooers Explosive Evolutionary Radiations: Decreasing Speciation or Increasing Extinction Through Time? Evolution 62(8): Ree, R. H Detecting the historical signature of key innovations using stochastic models of character evolution and cladogenesis. Evolution 59(2): Revell, L. J., L. J. Harmon, and R. E. Glor Under-parameterized Model of Sequence Evolution Leads to Bias in the Estimation of Diversification Rates from Molecular Phylogenies. Systematic Biology 54(6): Roy, K., G. Hunt, and D. Jablonski Phylogenetic Conservatism of Extinctions in Marine Bivalves. Science 325(5941): Ruta, M., J. C. Cisneros, T. Liebrecht, L. A. Tsuji, and J. MÜLler Amniotes through major biological crises: faunal turnover among

14 Parareptiles and the end-permian mass extinction. Palaeontology 54(5): Ruta, M., D. Pisani, G. T. Lloyd, and M. J. Benton A supertree of Temnospondyli: cladogenetic patterns in the most species-rich group of early tetrapods. Proceedings of the Royal Society B: Biological Sciences 274(1629): Simpson, C., W. Kiessling, H. Mewis, R. C. Baron-Szabo, and J. Müller Evolutionary diversification of reef corals: a comparison of the molecular and fossil records. Evolution 65(11): Sims, H. J., and K. J. McConway Nonstochastic Variation of Species- Level Diversification Rates within Angiosperms. Evolution 57(3): Stadler, T Sampling-through-time in birth-death trees. Journal of Theoretical Biology 267(3): Stadler, T Mammalian phylogeny reveals recent diversification rate shifts. Proceedings of the National Academy of Sciences 108(15): Tarver, J. E., and P. C. J. Donoghue The Trouble with Topology: Phylogenies without Fossils Provide a Revisionist Perspective of Evolutionary History in Topological Analyses of Diversity. Systematic Biology 60(5): Venditti, C., A. Meade, and M. Pagel Phylogenies reveal new interpretation of speciation and the Red Queen. Nature 463(7279): Wiens, John J The Causes Of Species Richness Patterns Across Space, Time, And Clades And The Role Of Ecological Limits. The Quarterly Review of Biology 86(2):75-96.