Phylogeny-Based Analyses of Evolution with a Paleo-Focus Part 2. Diversification of Lineages (Mar 02, 2012 David W. Bapst Recommended Reading: Nee, S. 2006. Birth-Death Models in Macroevolution. Annual Review of Ecology, Evolution, and Systematics 37(1):1-17. Ricklefs, R. E. 2007. Estimating diversification rates from phylogenetic information. Trends in Ecology & Evolution 22(11):601-610. Stadler, T. 2011. Inferring speciation and extinction processes from extant species data. Proceedings of the National Academy of Sciences 108(39):16145-16146. 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)
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
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)
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
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)
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. 1994 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)
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. 1994 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
Etienne et al. 2012 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. 2011 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. 2011 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?
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
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