CAJSALISAANDERSON DatingDivergenceTimesinPhylogenies 322 DigitalComprehensiveSummariesofUppsalaDissertationsfromtheFacultyofScienceandTechnology

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(1)Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 322. Dating Divergence Times in Phylogenies CAJSA LISA ANDERSON. ACTA UNIVERSITATIS UPSALIENSIS UPPSALA 2007. ISSN 1651-6214 ISBN 978-91-554-6937-5 urn:nbn:se:uu:diva-8155.

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(155) List of papers. This thesis is based on the following papers, which are referred to in the text by their Roman numerals: I Cajsa Lisa Anderson, Kåre Bremer and Else Marie Friis. 2005. Dating phylogenetically basal eudicots using rbcL sequences and multiple fossil constraints. American Journal of Botany 92(10): 1737–1748 II Per G. P. Ericson, Cajsa L. Anderson, Tom Britton, Andrzej Elzanowski, Ulf S. Johansson, Mari Källersjö, Jan I. Ohlson, Thomas J. Parsons, Dario Zuccon and Gerald Mayr. 2006. Diversification of Neoaves through time: integration of molecular sequence data and fossils. Biology Letters 2(4): 543-547 III Per G. P. Ericson, Cajsa Lisa Anderson and Gerald Mayr. 2007. Hangin’ on to our rocks ’n clocks: a reply to Brown et al. Biology Letters 3(3): 260-261 IV Tom Britton, Cajsa Lisa Anderson, David Jaquet, Samuel Lundqvist and Kåre Bremer. 2007. Estimating divergence times in large phylogenetic trees. Systematic Biology (in press, October 2007) V Cajsa Lisa Anderson and Thomas Janssen. Monocots. Chapter in Timetree of life, eds. Hedges and Kumar (accepted) VI Cajsa Lisa Anderson. Dating phylogenies: an evaluation of three methods based on the lycopod family Selaginellaceae. (manuscript). Reprints were made with the permission of the publishers..

(156) Cover: The cover was designed by the author, based on a black-and-white photo of a painting by Jerry Anderson.. Pictures in the thesis: All photos were taken by the author. All figures were designed and created by the author. The ink drawings of plants, fossils and birds included in some figures were created by Jerry Anderson..

(157) Contents. Introduction.....................................................................................................5 Things you need to get a date.....................................................................5 The (outdated) molecular clock concept.........................................................7 Methods that relax the molecular clock ..........................................................9 Nonparametric autocorrelation methods ....................................................9 Parametric methods ..................................................................................10 Maximum likelihood methods ......................................................................10 Bayesian methods .........................................................................................11 What factors affect the outcome – and which do not? ..................................14 Influence of method on age estimates ......................................................14 Branch lengths estimation and choice of gene .........................................15 Topology ..................................................................................................17 Number of taxa.........................................................................................17 Sequence lengths ......................................................................................19 Influence of models and prior assumptions..............................................19 Age constraints from the fossil record .....................................................20 Drawbacks of different methods ...................................................................25 Concluding remarks ......................................................................................28 Summary of paper I ......................................................................................30 Divergence times of basal eudicots ..........................................................30 Summary of paper II and III .........................................................................33 Modern birds ............................................................................................33 Summary of paper IV....................................................................................36 PATHd8 ...................................................................................................36 Summary of paper V.....................................................................................37 Timetree of monocots – author’s cut........................................................37 Background ...................................................................................................37 Data and methods..........................................................................................37 Results...........................................................................................................38 Discussion .....................................................................................................39.

(158) Summary of paper VI....................................................................................50 Selaginella meets three dating methods ...................................................50 Svensk sammanfattning (Swedish summary) ...............................................52 Introduktion : Datummärkning av gamla döda släktingar........................52 Placera de utdöda släktingarna på rätt hylla.............................................54 In med både levande och utdöda släktingar i den svarta lådan (dateringsmetoderna) .........................................................................................54 Klockan som gick fel ....................................................................................55 Klockor som går lite som de vill...................................................................55 Frågor om de svarta lådorna.....................................................................57 Går och går klockorna utan att komma till dörren?..................................60 Svensk sammanfattning av artiklarna i avhandlingen (Swedish summary of included papers) ............................................................................................61 I ................................................................................................................61 Datering av "basala äkta tvåhjärtbladiga" växter. ....................................61 II och III ...................................................................................................63 Datering av moderna fåglars släktträd......................................................63 IV..............................................................................................................66 PATHd8 ...................................................................................................66 V...............................................................................................................66 Enhjärtbladiga växtfamiljer och deras åldrar ...........................................66 VI..............................................................................................................68 Undersökning av tre dateringsmetoder baserat på ett släktträd över Selaginella, mosslumrar...............................................................................68 Acknowledgements.......................................................................................70 Abstract ....................................................................................................70 Introduction ..............................................................................................70 References.....................................................................................................76.

(159) Introduction. Our understanding of the history of life on earth is dependent on a number of scientific fields. Systematic biology provides phylogenies (the relationships between organisms), paleontology provides knowledge about the fossil record, and historical biogeography information on ancient distributions of organisms. To estimate divergence times, the timing of the splitting-up of different evolutionary lineages, information on phylogenies and their corresponding fossil record needs to be combined, and analyzed using mathematical and statistical methods. This thesis addresses different aspects on such dating of phylogenies.. Things you need to get a date Let us start with an (over-)simplified picture of the process of finding dates for the nodes (the hypothetical divergences) in a phylogeny (figure 1). The methods of biological systematics are used to infer phylogenies (relationships between organisms, described in the form of trees) for the organisms in which we are interested. A phylogram describes not only the relationships, but also the number of evolutionary changes along a branch. In a phylogram inferred by molecular methods, the branch lengths represent nucleotide substitutions. What we want to do is to transform the phylogram into a chronogram, where the branch lengths equal units of time. As of today, there are a number of different methods and computer programs for dating, each one with their own drawbacks and problems. Which method is the best, or least bad, is still highly unclear, and parts of this thesis address the properties of different methods. To set absolute, real ages on the nodes of the phylogeny we need external information on times. This information can be provided by the fossil record of the organisms or geological events likely to have influenced the divergence of the group, e.g. split-up of continents, formation of mountain chains or the development of volcanic islands.. 5.

(160) Figure 1. The picture describes the process of dating divergence times in a phylogenetic tree. A phylogenetic tree is inferred from a group of organisms. This phylogeny, with branch lengths representing nucleotide changes, is put into the "black box" of dating methods, together with external information on time, in this case fossil ages. The methods attempt to disentangle the components of branch lengths - evolutionary rate and time. The result is a chronogram, where the branch lengths represent time units between divergences.. 6.

(161) The (outdated) molecular clock concept. A clock is expected to tick at a constant rate. A global molecular clock implies that the evolutionary rate in a phylogeny is constant over the whole phylogeny. If this was the case, branch lengths of a phylogram would be exactly proportional to time (figure 2), and therefore a single calibration point (e.g. a fossil age) could be used to extrapolate times on all nodes in a phylogeny. The idea of a global molecular clock was coined by Zuckerkandl and Pauling in 1962, and later mathematically formalized by Kimura in 1965. The global molecular clock seemed to be very useful for calculating divergence times and set up models of evolution for other purposes. The molecular clock indeed got much attention, and was used for dating of divergence times for many groups of organisms. Unfortunately, the clock turned out to be an oversimplified model, and many studies presented highly unlikely results. Comparisons with the fossil record often showed large discrepancies between molecular and fossil ages. It is now widely appreciated that the dynamics of molecular evolution is far more complex. However, despite the fall of the molecular clock, researchers continued to try to date divergences, using methods relying on the clock assumption; it was just too appealing to get the results and be able to use them, to stop trying to date phylogenies. Examples of such methods are linear regression methods by Nei (1987) and Li and Graur (1991), and different maximum likelihood clock optimizations by Langley and Fitch, 1974, and Felsenstein, 1981. Methods were later developed to get around the problem with the nonexistent global clock. One approach is removal of the data that does not follow an assumed global clock; branches that clearly do not follow a global constant rate are simply pruned off the tree. Examples of this are the methods by Li and Tanimura (1987), Takezaki et al. (1995) and Hedges et al. (1996). In most cases, this approach probably means loss of a lot of data. Another solution is to correct for rate heterogeneity by applying local clocks, by dividing phylogenies into lineages with similar rates, and dating them separately before putting the analyses together. Examples of local clock methods include those developed by Hasegawa et al. (1989), Uyenoyama (1995), Rambaut and Bromham (1998) and Yoder and Yang (2000).. 7.

(162) Figure 2. The picture describes the principle of a global molecular clock. If a data set follows a clock, the evolutionary rate is constant over time, and the branch lengths equal the product of rate and time. From this follows that the branch lengths can be used to infer relative rates and times. If external information of the age of one node in the tree is available, the relative ages can be transformed to absolute ages over the whole tree.. 8.

(163) Methods that relax the molecular clock. Disentangling evolutionary rate and time, when rate is not constant, is not trivial. The branch lengths of a phylogram equal the product of time and rate, and since we have two unknown factors in this equation, the problem seems impossible to resolve. To relax the molecular clock, additional assumptions about rate and time are needed. One commonly used assumption in relaxed clock methods is that evolutionary rate can evolve over time, and that the rate is inherited, so that the rate of a daughter lineage is similar, but maybe not the same, as the rate of the mother lineage. This autocorrelation assumption (Gillespie, 1986) is included in different methods through minimizing / smoothing of the differences in rate between adjacent branches. Methods that allow for evolutionary rate to change over time, using either rate autocorrelation or other approaches, are described in more detail below.. Nonparametric autocorrelation methods Nonparametric methods do not model the autocorrelation, but smooth differences in rate by minimizing them between adjacent branches. Nonparametric rate smoothing (NPRS) (Sanderson, 1997) and PATHd8 (Britton et al., in press) utilize two different smoothing methods.. NPRS The basic assumption in NPRS is that rate is inherited from a mother lineage to the daughter lineages. The method therefore minimizes rate differences between these; the optimization is made by penalizing large rate variations, according to a squared function of rate changes between adjacent branches. The NPRS algorithm calculates different rates over the whole tree at the same time. Multiple fossil age constraints can be used to calibrate the tree.. PATHd8 PATHd8 smoothes between sister groups – the opposite direction compared to NPRS and other autocorrelation methods. PATHd8 has a very sim-. 9.

(164) ple algorithm (easy enough to calculate by hand for small data sets), which smoothes locally, one pair of sister groups at a time, by taking the mean of the paths; the added branch lengths from a terminal taxon to a node. This is done for all paths from terminals to the root of the tree. Because of the simple algorithm, the method is stable and very fast, allowing for thousands of taxa. The calibration can be done with multiple fossil constraints, and one node can have both a minimum and a maximum age specified. PATHd8 is described in detail in Paper V and elaborated upon in the summary of the paper.. Parametric methods Parametric, or model-based, methods include explicit models on evolutionary rate. Rates along a branch can be assumed to have e.g. a Poisson distribution or a lognormal distribution. The autocorrelation of rates between mother and daughter lineages are described by different models in different methods, and represent different interpretations of the concept of autocorrelation, and different ways of penalizing rate changes. Examples of such methods are the exponential model, that has a hard penalty against rate changes and implying that changes occurs at nodes, the lognormal model, where rates change in small steps along the branches and the OrnsteinUhlenbeck process, where rate change is skewed towards rates decreasing over time.. Maximum likelihood methods Branch lengths are, as said before, a product of time and rate, and if our data follow a molecular clock, the branch lengths would be proportional to the divergence times. The likelihood p(X|T,R) is then the probability of observing the data X, given a particular time T and rate R. If the data are not clock-like, assumptions need to be made about either time or rate. The calculation therefore requires a specified substitution model for the rate. Penalized likelihood (PL) Penalized likelihood (PL) (Sanderson 2002) is a semi-parametric method, which combines a model-based likelihood with a roughness penalty regulated by a smoothing parameter. Substitutions along a branch are assumed to have a Poisson distribution. PL uses a saturated model for rate change that allows rates to vary freely over the tree. This model actually means that there are more parameters than observations, and therefore a penalty for sudden rate changes, is needed. The smoothing parameter is objectively chosen by a cross validation process, which sequentially removes data to find the smoothing that best fits the data. If the smoothing parameter is large, the 10.

(165) function is dominated by the roughness penalty, and this leads to a clock-like model. If it is low, the smoothing will be effectively unconstrained, and the method will then behave similarly to NPRS. Heuristic rate smoothing (AHRS) Yang (2004a) developed heuristic rate smoothing, which performs dating analyses in two steps. The first is a smoothing step ("ad hoc rate smoothing", AHRS) using a penalized likelihood approach. The AHRS algorithm differs somewhat from PL above; it uses a lognormal model for the rate changes along a branch, and a Brownian motion model for rate change, adopted from Thorne et al. (1998) and Kishino et al. (2001) to penalize sudden rate changes. AHRS results in one rate estimate for each branch. The branches are divided into small groups of rate classes; branches with similar rates are assigned to the same class. In the second step these rate groups are used for a ML local clock analysis. Overdispersed clock Most relaxed clock methods assume that different lineages can have different evolutionary rates. The overdispersed clock method by Cutler (2000) instead relies on the assumption that all lineages have approximately the same basic evolutionary rate. The reason for branch heterogeneity is that the process of molecular evolution can be highly variable and the variations are not lineage specific and hence some lineages can undergo very rapid substitutions. Instead of smoothing between lineages this method therefore penalizes departures from the mean rate over the tree. This has the effect that adjacent branches do not have a larger tendency to have similar rates to each other than they have to any other branches in the tree. The method explicitly models overdispersion, i.e. that adjacent branches can have very different numbers of substitutions, by use of a stochastic Poisson process, without the assumptions that variance in substitutions have to equal the mean, as in the constant-rate Poisson process.. Bayesian methods In the Bayesian framework, the posterior probability of time (T) and rate (R), given the data (X), equals the probability of the data given time and rate multiplied with the probability of time and rate, divided by the probability of the data. p(T,R|X) = p(X|T,R) p(T,R) /p(X) Since the branch length is a product of time and rate, when assuming that the prior for the rate is independent of the divergence time, the probability for time and rate is p(T,R). p(X|T,R) is the likelihood of observing the data 11.

(166) given the time and rate. The prior distributions of divergence times are decided by a model for rate distribution, e.g. lognormal, exponential, Ornstein– Uhlenbeck and others. A Markov chain Monte Carlo (MCMC) (Gilks et al., 1996) procedure is utilized to approximate the posterior distribution of rates and ages. Below, some of the Bayesian methods are described under the name of the computer software where they are implemented. Multidivtime This method that has been developed progressively in three publications (Thorne et al., 1998, Kishino et al., 2001, Thorne and Kishino, 2002) is implemented in three steps, where the software multidivtime is the last one. The first step is performed in the baseml program, which is part of the PAML package (Yang, 2004b), see below. In baseml the model parameters are estimated from the sequence data using the F84+gamma model (Kishino and Hasegawa, 1989, Felsenstein, 1993). In the second step these parameters are used to estimate the maximum likelihood of the branch lengths and a variance-covariance table, using the estbranches program from the multidistribute package (Thorne et al., 1998). These data are used as input for the multidivtime program (Kishino et al., 2001; Thorne and Kishino, 2002), together with the chosen topology and a number of priors. Priors of autocorrelation, rate at root node and whether the internal nodes should repel or attract each other are specified by the user. The rate is described by a geometric Brownian motion constant, and the autocorrelation model assumes that the Brownian motion is homogeneous, which means that the prior for the rate at the root is the mean rate over the whole tree. PhyBayes Aris-Brosou and Yang (2002, 2003) developed a Bayesian method where models describing speciation and extinction processes are used. Six different models for autocorrelated rate distributions can be chosen; lognormal, ”stationarized”-lognormal, truncated normal, Ornstein-Uhlenbeck process, gamma, and exponential. The method only allows one age constraint, but that one constraint can have soft bounds. PAML Yang and Rannala (2006) developed a method that can accommodate for uncertainties in multiple fossil constraints, using soft bounds. The method however assumes a strict molecular clock. In 2007 Rannala and Yang published the extended version, which relaxes the clock and can use data from multiple genes. Two models for the rate variation can be specified prior to analysis. The first one is assuming autocorrelation, and is similar to the model used in multidivtime. If no autocorrelation is assumed, rate models are suggested to be able to handle rapid shifts in evolutionary rate. The sec12.

(167) ond one is not assuming autocorrelation. A birth-death process is used to allow soft bounds. This model was also implemented in PhyBayes, but only for one fossil calibration point. The probability that a divergence time lies outside the bound is small, but not zero, as opposed to other methods. When using a birth-death process the parameters of e.g. speciation and extinction rates can be adjusted, so that chronograms with different shapes can be obtained. PAML calculates the exact likelihood (as opposed to the approximation in e.g. multidivtime), which is computationally demanding, and the algorithm is probably not useful for more than 100 taxa. BEAST Drummond et al. (2006) proposed a method where a relaxed clock model is used to estimate both phylogeny and divergence times at the same time. Uncorrelated rate change is assumed, but autocorrelation can be tested for. Different models for nucleotide substitutions, distributions of substitutions along a branch and rate variation can be chosen. A problem when providing external information on ages is that a fossil cannot be securely placed in a phylogeny, when the phylogeny is unknown. Drummond et al. attempt to get around this by specifying the age for the most recent common ancestor of a set of taxa. To incorporate calibration uncertainties, probabilistic calibration points with normal, lognormal, exponential or gamma distribution are used. MrBayes (Compound Poisson process) Huelsenbeck et al. (2000) suggested a compound Poisson process; one Poisson process describes the distribution of nucleotide substitutions along branches, and a second independent Poisson process generates events of substitution rate change. Rate variations can occur anywhere in the tree, and are determined by the number of rate-change events, the point in the tree where they occur, and the magnitude of change at each event. Errors in the first version of this method have been found (F. Ronquist, pers. com.), but an improved method might be implemented in the next version of MrBayes (Huelsenbeck and Ronquist, 2001), the currently most used program for Bayesian phylogeny inference.. 13.

(168) What factors affect the outcome – and which do not?. Influence of method on age estimates Systematists have talked about rates of evolution for many years, long before the use of non-clock dating methods became commonplace. Rates slowing down in some clades (e.g. palms, Arecaceae) and increasing in others (e.g. grasses, Poaceae) have been postulated by looking at heterogeneity of phylograms (Wilson et al., 2000), and intuitively most researchers agree. What this means in terms of divergence times, how it would be reflected in a chronogram, is problematic, and prone to bias if different methods give different results - a researcher might end up choosing the dating method that results in chronograms that are in least conflict with his or her own personal view on evolution. Currently used phylogenetic methods often produce, if not the same, at least similar results. This is not the case with the different dating approaches. Some studies have suggested that e.g. penalized likelihood and the Bayesian method implemented in the multidivtime software package converge to approximately the same results, but this clearly has to do with what data set you are exploring. For a relatively homogeneous phylogram, combined with a large number of evenly spread fossil constraints, all methods, including even global clock methods, would yield approximately the same results. This is not the case for other data sets. From my research, I conclude that there can actually be large differences in age estimates between methods (see paper VI, and picture 3 and 4). Point estimates from the Selaginellaceae study (paper VI) can differ in the magnitude of 100 my between PATHd8 and Bayesian (multidivtime) results. The large confidence and credibility intervals do overlap, but from the look of the chronograms resulting from the different approaches, it should be clear that there are real differences. Several Bayesian methods tend to smooth the chronograms to the degree that divergences occur at evenly spread time intervals, no matter how heterogeneous the underlying phylogram looks. In a well-sampled data set, this could of course be the case. For example, palms generally have longer gen14.

(169) eration times than grasses, and might therefore have shorter branches in a phylogram. Within the metazoans, internal parasites from different phyla tend to have extremely long branches compared to their sister groups within the same phylum. In these cases an extensive smoothing seems reasonable. On the other hand, when looking at the fossil record (or speciation in extant taxa), it seems likely that some groups have had not only an acceleration in molecular evolution, but have also diverged in a short time interval, and in those cases some Bayesian methods seem to over-smooth rates and hence the timing between divergences. On the other hand, PATHd8 is likely to underestimate the crown node ages in a large clade with short branches, as in the case of the palms, when its sister group has much longer and heterogeneous branches (paper V).. Branch lengths estimation and choice of gene Since the branch lengths are the only information we have on the evolutionary rates in a phylogeny (except for absolute ages from fossil record and geological events), incorrect branch lengths can be expected to have an impact on the final age estimates. Phylograms can be inferred using parsimony, or a model-based method. These methods have different properties when it comes to the calculation of branch lengths. It has been shown that branch lengths are often underestimated in parsimony analyses. (Felsenstein, 1978) On the other hand, maximum likelihood and Bayesian methods might produce incorrect branch lengths if an incorrect substitution model is applied (Yang and Rannala, 2005). Different genes evolve at different rates, which will have a big effect on the branch lengths. More slowly evolving genes tend to lay closer to a molecular clock, while fast-evolving genes tend to be more heterogeneous in branch lengths. In figure 3, an empirical example, using Selaginellaceae, is used to illustrate the difference in age estimates obtained from the slower evolving ribosomal gene 26s, compared to the faster evolving chloroplast gene rbcL. The PATHd8 method seems in this example to be affected more than the other two methods by the different genes. Whether this is a general pattern has not been further examined. Magallon and Sanderson (2005) concluded that ages vary both with genes and the codon positions. When analyzing four genes different results were obtained. The mean of these estimates were almost the same as the result when using a phylogram from a concatenated data set of all genes. In all phylogenetic methods, an extensive sampling of taxa is beneficial for calculating branch lengths in a phylogeny, and has also been shown to increase the stability of age estimates (Linder et al., 2005), see below.. 15.

(170) rbcL. 26s. penalized likelihood. Bayesian autocorrelation (multidivtime). PATHd8. 300. 100. mya. 300. 100. mya. Figure 3.The figure demonstrates how chronograms of Selaginella (data set from Korall and Kenrick, 2002, 2004) obtained from three different methods change with choice of gene. RbcL is generally regarded as a faster evolving gene than 26s, and the Selaginella rbcL phylogram shows more heterogeneous branch lengths than the 26s phylogram, and hence the chronograms obtained from 26s has more smooth look than the ones obtained from rbcL. The effect is most notable in PATHd8 in this example, but whether this is a pattern that could be expected for other data sets has not been examined.. 16.

(171) Topology Intuitively one might think that a wrong topology of a phylogeny would have a huge influence on divergence times. Yoder and Yang (2000) however suggested that plausible topologies would yield similar age estimates, and Bremer et al. (2004) showed that alternative topologies have surprisingly little effect on the age estimates. In the cases when alternative topologies are due to insecurity because of short branches, it follows that age differences will be small. Very different topologies, clearly erroneous, would most likely result in different ages, and the error in estimates would depend on how wrong the topology is (Soltis et al, 2002).. Number of taxa Assuming that autocorrelation is a valid assumption: extended taxon sampling could add important information and thereby improve age estimates. Larger sampling results in better branch lengths estimates and all methods get more stable results with better sampling (Linder et al. 2005). The age estimates from the different methods do however not converge to similar results with an increased taxon sampling, and increased taxon sampling affects the results in different ways. Methods adopting the mother - daughter smoothing approach are sensitive to the number of taxa, therefore obtaining older ages for more "basal" nodes. Increased sampling systematically results in over-estimates in methods smoothing between mother-daughter lineages (Janssen and Bremer, 2004, Sanderson and Doyle, 2001). Since the PATHd8 method smoothes between sister lineages, the age estimations are dependent on heterogeneity and branch lengths of sister groups, but not on the actual number of taxa per se, as in the other methods. Experimenting with reduced data sets from the eudicot and Selaginella IV) (from paper I and IV), suggests very little influence on the number of taxa for the internal node ages, when estimated by PATHd8, and a large influence when estimated with PL or BAC. Simulations of different sizes of data sets, and possibly re-analysis of the data sets from Linder et al. (2005) would be valuable to further explore this observation for PATHd8.. 17.

(172) 22 ingroup taxa. 62 ingroup taxa. penalized likelihood. Bayesian autocorrelation (multidivtime). PATHd8. 300. 100. mya. 300. 100. Figure 4. The number of taxa greatly affects divergence time estimates. The smaller Selaginella data set (modified from Korall and Kenrick, 2002, 2004) will suffer from over-smoothing when analyzed with PL and Bayesian autocorrelation (multidivtime), while PATHd8 is fairly stable.. 18. mya.

(173) Sequence lengths In phylogenetic reconstruction, longer sequences usually add more information to the data set, since they add more informative characters. Besides more taxa, this is a way to find more synapomorphies supporting the topology, and thereby hopefully a tree approximating the true one, or at least obtain better resolution and support for the phylogeny. It is a common misconception that adding more genes and/or longer sequences introduces more information also in dating studies. Adding longer sequences or more genes to a data set might increase the precision of the branch lengths estimations, but not add more information for the actual dating process. Britton (2005) concluded that in the absence of a global molecular clock, no methods can estimate divergence times consistently by collecting longer sequences. Theoretically, consistent estimates could be obtained if absolute fossil constraints could be assigned to every node in the tree. However, even if fossils could be assigned to every branch where rate change occurs, there will always be uncertainties present (e.g. regarding stratigraphic dates and systematic placement, see paragraph “Age constraints” below), and a fossil can never be assumed to actually constitute a node in the tree; the nodes will remain hypothetical ancestors. Rannala and Yang (2007) concluded from simulations that shorter sequences seemed to be nearly as informative as very long sequences. Rannala and Yang also formulated the “infinite-sites theory”, which is based on essentially the same conclusions as Britton (2005). The theory states that, even if an infinitely long sequence is used, and branch lengths thereby correctly estimated, the ages cannot be estimated consistently. However they theorize that the uncertainties, which cannot be reduced by additional sequence data, can be quantified. This is done by plotting the width of the posterior probability intervals against the mean of the estimates. The relationship between the intervals and the means will be increasingly linear with the addition of sequence data, and furthermore the slope of the regression line will be reduced. The infinite-sites theory predicts that, with an infinite number of genes and an infinite number of nucleotides in each gene, the slope will eventually converge to the slope that would be obtained by a global molecular clock.. Influence of models and prior assumptions The influence of nucleotide substitution models and models for rate change along branches, within the Bayesian framework, has been increasingly discussed the last couple of years. Still it remains a controversial issue, and more work is needed.. 19.

(174) The more informative data we have, the less influence will the prior assumptions have on the results of a Bayesian analysis. As has been concluded above, for molecular datings the sequence data contain little information on rates and dates we want to infer, even if multiple fossil constraints are accommodated. It would therefore not be surprising, if priors had a relatively large effect on age estimates, and even converge to the prior beliefs (Welch et al., 2005). In phylogenetic inference, choice of model can be tested, and chosen according to relative rates tests (Posada and Crandall, 2001), Bayesian information criteria (Schwartz, 1978) or the Akaike information criteria (Akaike, 1973). A model is chosen when it has a significantly better fit to the data, than a less parameter rich model. Because of lack of information, the models cannot be tested, and hence not be objectively chosen, and the choice of model can be expected to be a result of the authors’ expectations. Aris-Brosou and Yang (2003) concluded that the Ornstein-Uhlenbeck model of rate change performed best in estimating ages of deep nodes within the metazoans, when compared to the fossil record. The Cambrian explosion of animal phyla has been concluded from the fossil record, and Aris-Brosou and Yang’s use of a model favoring a deceleration in rates from root to leaves in a phylogeny, could be a reflection on their expectations. Welch et al. (2005) criticized the study partly on this basis, and concluded that prior assumptions on rate change and distributions have a large influence in dating analyses, not only in Aris-Brosou and Yang’s study. In paper VI I conclude that priors on autocorrelation and distribution of internal nodes in the Bayesian method implemented in multidivtime (see methods section above), affect the outcome of analyses. However, when using “flat” priors (priors with large standard deviations), as recommended, the credibility intervals will be very large (pers. obs.) This influence of multidivtime priors of autocorrelation and rate at root node has previously been suggested by e.g. Wahlberg (2006) and Bell et al. (2005), but also in their studies the credibility intervals are wide. In paper VI I discuss if we should trust the patterns we see, or the credibility intervals obtained.. Age constraints from the fossil record The importance of fossil age calibrations, and the complexity of using them, has been discussed by numerous authors (e.g. Sanderson and Doyle, 2001, Magallon 2004, Bremer et al., 2004, Perez-Losada et al., 2004, Anderson et al., 2005). If good fossil constraints could be placed on every branch where a rate change had occurred, we would not only see a convergence between age estimates from different methods, but also get very close to the actual divergence times. On the other hand, one might think that the fossil record would be enough, and why then bother trying to use molecules 20.

(175) for dating? In reality, the fossil record however gives the complete temporal perspective only in a few exceptional cases. In most cases, the fossil record can only give us a glimpse, and for many organism groups there simply is no fossil record. When using fossil constraints, the placement of the fossil taxa on the correct node in the phylogeny is crucial. It is important to remember that it is never possible to estimate crown group ages using fossils with any certainty; fossils can only provide the earliest possible age for a stem group (figure 5).. Figure 5. The first fossil with a character of a group can statistically never be the first individual having that character. The origin of the character, and the divergence separating sister groups are also separated in time.. Fossils to be used as minimum ages are implicitly placed on a stem lineage, and hence the age is placed on the node where the stem lineage splits from its sister group (figure 6). To be able to connect fossils to the correct branch with some certainty, reliable synapomorphies for the group needs to be recognized (figure 7). In some cases, the approach of placing a fossil as a minimum age means that the resulting crown group age can be much younger than the stem group age. This is true for all methods. Since PATHd8 smoothes between sister groups, as opposed to the other methods that smooth mother-daughter lineages, this can lead to very different age estimates compared to the other available methods. An example of this can be seen in the comparison of nonparametric rate smoothing (NPRS) and PATHd8 on the 800+ monocot data set (paper IV, Britton et al., accepted). The palm clade, family Arecaceae, have much shorter branches in the phylogram, compared to the rest of 21.

(176) the monocots, indicating a slow down in evolutionary rate at some point (Janssen and Bremer, 2004, Wilson et al. 1990), and the absolute age estimates for the crown group resulting from PATHd8 and NPRS are differing by almost 100 myr. If the stem lineage minimum age of Arecaceae (determined by the fossil Sphinizonocolpites) was placed as the maximum age for the crown group we would obtain an older age of the crown group using PATHd8. In paper V, a fossil pollen belonging to the crown group (Mauritiidites) has been used as a minimum age constraint, and we then obtain a much older crown group age by PATHd8 (65 myr), however not as old as the age calculated by NPRS (110 myr) and PL (97 myr).. Figure 6. Some of the fossils used in the dating of basal eudicots (paper I, Anderson et al., 2005). The fossils were assigned to a stem lineage, and hence gave a minimum age to the divergence between the lineage and its sister group. The fossils are, from top down, male flowers of Platanocarpus, fruit of a buxalean plant, and flower of Spanomera marylandensis. For references, see paper I.. 22.

(177) Figure 7. Assignments of fossils to branches in a phylogeny must be based on synapomorphies. Lepidodendron has rhizomes, a character found in Isoetaceae but not Selaginellaceae, and is hence placed along the stem lineage of Isoetaceae. Leclerqia possessed a ligule, but did not have microand megaspores as Isoetaceae and Selaginellaceae, which place it somewhere along the branch leading to both these families, and between the evolution of the characters ligules and heterospory. Minimum, maximum and fixed ages will always bias the results of a dating study. Provided that a minimum age fossil is correctly dated and correctly placed within the tree, it will always be an underestimate of a node. Therefore soft bounds on fossil age constraints are desirable, but then the question of how to specify reasonable intervals arises. There are always ghost ranges in the fossil record; the oldest discovered fossil from a taxon found is not the first possible fossil of that taxon. The explanation for this is linked to taphonomy (how an organism gets preserved as a fossil), and how likely an organism or a part of it is to be preserved. Some structures are abundant and easily preserved. Others are not. It is much more likely to find wind-dispersed fossil pollen and spores, than a fossilized three-dimensionally preserved coot in a hot-spring deposit. Angiosperm pollen appears quite suddenly in the fossil record about 135 mya, and from then on they are common in fossil strata. It can therefore be presumed that the ghost range of angiosperm fossils is not very large. The finding of a fos23.

(178) silized coot however, is probably a singular event (Channing et al., 2005). From one single specimen, we cannot say anything about the ghost range of coots. Recent studies on statistical methods for estimating ghost ranges (Cavin and Forey, 2007) are promising, and might give us tools to choose reasonable limits for soft bounds in an objective way. It does however mean that the fossil collections need to be scrutinized and quantified, which is a massive work.. 24.

(179) Drawbacks of different methods. There are serious drawbacks with all dating methods; they should all be used with caution, and results critically interpreted in the light of their respective drawbacks. To be able to draw any valid conclusions from dating analyses, we need to have knowledge about the methods, and when to expect a method to fail. Most model-based methods are probably not stable enough to handle huge datasets (>1000) taxa), and the ones that presumably are, would be computationally very demanding. The fossil-based cross validation implemented in r8s (Sanderson, 2003, Near and Sanderson, 2004) increases the possibility to find a solution for large data sets in PL, but it cannot be used when the number of fossils are less than three, and for large heterogeneous data sets the program still has problems finding a solution. Nonparametric rate smoothing will probably be able to find a solution, but the algorithm is time consuming. PATHd8 was developed to cope with large data sets, and if time consumption is of interest, the ability to date more than 5000 taxa in less than a second (Anderson and Wallberg, in prep.) is certainly an attractive property. For a smaller, but well sampled data set with many good fossil age constraints, the choice of method is more a matter of philosophy and personal judgment. Autocorrelation is a convenient assumption, because it can be modeled, not because it is valid as a biological assumption. It seems reasonable to assume that rates among closely related lineages are likely to be similar in a well sampled and relatively homogeneous phylogram. Very heterogeneous data sets are however more problematic, since branch lengths can be interpreted in different ways. A long branch could mean a long time span, where many stem groups have gone extinct, as well as a fast evolutionary rate. The autocorrelation methods that smooth between mother and daughter lineages have a tendency to produce older ages when more taxa are added. This phenomenon is thought to level out with a large number of taxa (Linder et al., 2005), but it might be that the age estimates stabilize on overestimates.. 25.

(180) Sanderson (2002) suggests that PL should be chosen over NPRS when possible. His comparisons show that NPRS has a tendency to produce rapid fluctuations in groups with short internal branches. In multidivtime, short branches, resulting from a rapid or recent divergence will be over-estimated, due to the autocorrelation prior that favors an even distribution of internal node ages. PATHd8 would treat the same data set in the opposite way, partly due to the other direction of smoothing. Short branches due to a slow-down in rate in one clade will result in too young ages when the sister group has much longer or heterogeneous branch lengths. Since PATHd8 underestimates large crown groups with short internal branches, it is important to add minimum ages, if available, for those crown groups, or be aware of this property. This short-coming of the method is easy to detect for empirical data sets – if one critical fossil is removed, the ages of the crown group will get younger and will not fit the fossil record. In the case where PL, NPRS and Bayesian methods overestimate the same groups, there is however no way to prove they do, when studying an empirical data set. They might produce unreasonably large ghost ranges (divergence dates far older than the first fossil occurrence), but it could always be argued that the earliest fossils remain to be found. To look into this issue, simulations of large and highly heterogeneous data sets with many constraints are needed. As said above, it is unclear whether the existing relaxed Bayesian clock implementations are stable enough to make these simulations possible. In phylogenetic reconstruction, the assumption of a time component in evolution has previously had two extremes to choose from; the molecular clock, or the unrooted tree. The latter implies that rates in different parts of the tree are independent, and hence no estimations of time and rate can be done. Drummond et al. (2006) have developed a method that relaxes the clock assumption in phylogenetic reconstruction, and infers rates and divergence times together with the topology. It is an exciting prospect, but the method has certain problems, such as the impossibility to add external information about age on a node when the phylogeny is unknown. The authors also conclude that the method should be used when phylogenetic reconstruction is of primary interest, and rates and dates are of less importance. The problem of possible over-smoothing by several methods needs more attention. If we believe that heterogeneity in branch lengths, as seen in a phylogram, contain any information on evolutionary rate, some of the heterogeneity should be preserved in the final chronogram. I do not believe that a chronogram with evenly spread internal node ages provide a good explanation of the evolutionary history of an old group of organisms. Possible oversmoothing by PL and multidivtime is discussed in paper VI.. 26.

(181) If your data set happens to follow a molecular clock after all, all the nonclock methods will perform pretty well.. 27.

(182) Concluding remarks. My guess is that we are still only in the beginning of the field of phylogenetic dating. We have however come so far that we can see where the problems are. New methods for phylogenetic dating are always exciting, but developing new methods might not be the highest priority right now. More information content, in the data we use, is the key to obtaining better age estimates. The question is how we can introduce more information. Longer sequences or new models for nucleotide substitutions and rate change over branches do not provide the information we need. In some data sets, additional age constraints can be used, but for many groups, there is no fossil record. The use of rates and dates from other studies cannot be recommended. Soft bounds on constraints will make the use of geological events less doubtful. Vicariance events and formation of volcanic islands takes time, but can be dated, and with the possibility of giving a range of possible ages, geology can prove useful. Still, in many phylogenies, age constraints will be hard to find. In some cases we have some information that might tell us something about possible relative rates; extreme environments can induce high evolutionary pressure on organisms, and this is a probable reason for long branch lengths in e.g. clades of internal parasites, compared to their non-parasitic sister groups. Generation time is another such source of information, as in the example of palms and grasses. The short generation time in annual grasses, as opposed to palms with longer generation time, the generation time can be suspected to be an important cause of the difference in branch lengths. This kind of information could probably be incorporated in dating methods, if it was seen as an attractive feature for a method. Comparative studies could perhaps give us a better idea of how well our methods work on real data. Different organism groups with the same biogeographical patterns do not necessarily share the same history, but in regions where geological and fossil constraints are abundant, they could be separately dated and compared, and that might give an indication about the performance of different methods. Within historical biogeography, one of the most important questions at present, is how to combine biogeographical methods with phylogenetic dating, and new methods are in progress (Isabel Sanmartin and Elena Conti, pers. com.).. 28.

(183) Huge molecular data sets are produced today; more taxa can be included in phylogenetic analyses, and whole genomes are increasingly common. Dating methods that can handle such large data sets are needed. Methods stable and fast enough to make large analyses feasible might not be developed in a near future within the Bayesian framework, and non-parametric or semi-parametric methods will then be the choice. It should be possible to set up an algorithm that can combine the two smoothing directions of PATHd8 and NPRS, perhaps by calculating them separately, and thereafter finding the most optimal solution in between. What such a method would implicate, I do not know. I suggest that for all dating analyses using current methods, special caution should be taken when the data set contains sister groups with many versus few representatives, and sister groups with highly different branch lengths. Furthermore, for data sets with highly heterogeneous branch lengths and few age constraints, no currently available method can be trusted to yield age estimates close to true divergence times. Dating of phylogenetic trees will however remain an exiting field. Molecular data, that will improve reconstruction of phylogenies, is being produced at an exponentially increasing rate. Paleontology will provide new fossils, which can be used as age constraints. Technological advances will make increasingly complex computational tasks possible. As we solve the remaining methodological issues, dating will provide a credible temporal framework for the evolution of life on earth.. 29.

(184) Summary of paper I. Cajsa Lisa Anderson, Kåre Bremer and Else Marie Friis. Dating phylogenetically basal eudicots using rbcL sequences and multiple fossil constraints American Journal of Botany 92(10): 1737–1748 (2005). Divergence times of basal eudicots The aim of this study was to present divergence times of the phylogenetically basal eudicots (Ranunculales, Proteales, Sabiales, Buxales and Trochodendrales sensu APGII, 2003) (figure 8). To yield age estimates approaching the real ones, we used as many taxa as possible (all rbcL sequences of the taxa in focus available in GenBank at the time of the study), and as many fossil calibration points from the Cretaceous period as possible (9 assigned to the basal eudicot lineages, and 5 assigned to the core eudicots). The placement of Sabiales was a problem, since the phylogenetic placement of this group was not completely resolved. Different studies have suggested it could be branching off before or after Proteales, or even belong to that clade. In preliminary analyses I tried different placements but it had very little impact, because of the short branches. Eventually, I placed the Sabiales branching off before Proteales, because that placement had received slightly better support in most studies. The most recent phylogeny focusing on basal eudicots (Worberg et al., 2007) concluded that this was the best supported placement. The authors however found high support for Buxales being the sister group to the core eudicots, instead of Trochodendrales, as was assumed in our study. Dating was performed using PL, and compared to NPRS. The results of this study suggest a ”Cretaceous firework”, i.e. a rapid diversification during the late Early Cretaceous (see figure 8), with all the lineages of basal eudicots emerging during the latest part of the Early Cretaceous. This pattern of rapid divergence of major lineages continued within the core eudicots, with the divergence of core eudicots already in the Aptian.. 30.

(185) Magallón and Sanderson (2005) analyzed 63 taxa, half of them angiosperms. They used a maximum age of 121 myr for the crown eudicots, as opposed to our fixed 124 myr stem group age. The effect of these different constraints is the same, and Magallón and Sanderson’s result also show that the eudicots underwent a rapid radiation during the early Cretaceous. In a study by Schneider et al. (2004), the divergence times of angiosperms and ferns were compared. Two different ways of constraining the angiosperm root were used; 1. Fixing the angiosperms at 132 myr, using the earliest pollen record (in the same way as we did with the eudicots in our study), and 2. setting the angiosperm fossil age as a minimum age. These two constraints gave highly different results. A divergence of angiosperms in Late Permian, around 250 mya, and eudicots in Late Triassic, around 210 mya, seems highly unlikely considering their earliest fossil records occurring approximately 120 and 85 myr later respectively. The main conclusion by Schneider et al. is that ferns diverged ”in the shadow of angiosperms” – and that conclusion holds for both approaches of calibrating the angiosperms. Compared to other stem and crown group ages in this study the ages of the ranunculalean clades seem young. Because the ranunculalean clade constitutes about one third of the taxa of the study, but has only one fossil attached within the clade it is possible that the ages within Ranunculales are underestimated. Experimenting with removing other fossils in other clades gives younger ages. However, the estimated ages do not exclude the possibility that some Albian and Aptian leaf imprints, suggestive of Ranunculales, might actually be members of the order. If new fossil data is found from this group (that has mostly herbaceous representatives, and therefore is not easily fossilized.), the divergence times within the Ranunculales will probably be revised.. 31.

(186) Figure 8. Chronogram of the basal eudicots, inferred by penalized likelihood. The eudicots went through a rapid divergence in the early Cretaceous. Crown groups of families within the Ranunculales appear younger than other families. This might be an artifact from the lack of fossil constraints. The large core eudicot group is in this picture represented by a black bar. For the complete chronogram, see paper I.. 32.

(187) Summary of paper II and III. Per G. P. Ericson, Cajsa L. Anderson, Tom Britton, Andrzej Elzanowski, Ulf S. Johansson, Mari Källersjö, Jan I. Ohlson, Thomas J. Parsons, Dario Zuccon and Gerald Mayr. 2006. Diversification of Neoaves through time: integration of molecular sequence data and fossils. Biology Letters 2(4): 543-547 Per G. P. Ericson, Cajsa Lisa Anderson and Gerald Mayr. 2007. Hangin’ on to our rocks ’n clocks: a reply to Brown et al. Biology Letters 3(3): 260-261. Modern birds I have to confess that one of the reasons I thought it would be a good idea to engage in the Neoaves project was that I had absolutely no knowledge on bird phylogeny, and it would therefore be interesting to analyze a data set that I had no opinion on beforehand. Another reason was the broad sampling of taxa and many fossil constraints. Neoaves, the “modern birds”, includes all extant birds except ratites (ostriches, emus and kiwis) and Galloanserae (Galliformes includes chickens, turkeys and quails, and Anseriformes includes ducks and swans) (picture 9). In this paper we present a phylogeny inferred by a broad sampling of neoavean families, comprising representatives of 75 of the traditionally recognized 145. To date this phylogeny we included 23 age constraints from the neoavean fossil record, and compared results obtained by PATHd8 with penalized likelihood results. The two methods gave similar results, PL giving slightly older ages in most nodes, and hence also larger “ghost intervals” compared to the fossil record. Earlier molecular clock analyses have suggested a diversification of Neoaves before the Cretaceous, even though the neoavian fossil record starts in the Late Cretaceous. Our results indicate that the evolutionary lineages that lead to the crown groups of modern bird families diverged around, or right after the Cretaceous – Tertiary boundary, about 65 million year ago (figure 9). We concluded that the conflict between molecules and fossils in earlier molecular datings is a matter of incorrect calibration and use of dating method.. 33.

(188) Figure 9. Chronogram of Neoaves inferred by PATHd8. Crown groups of modern birds diverged around the Cretaceous/Tertiary boundary. The stem group of. 34.

(189) Neoaves diverged from its sister group Galloanserae (e.g. chicken and duck) in early Late Cretaceous. The sister group of all other extant birds, the ratites (e.g. ostrich, kiwi and emus), are pruned off the tree.. The birds are an engaging group to many people, both researchers and laymen, and many opinions on phylogeny and timing of bird evolution have been put forward. Critique on the Neoaves article was therefore expected. The results suggesting that birds of pray are paraphyletic, and that Neoaves diverged around the K/T boundary were likely to provoke many scientists as well as ornithologists. The first paper criticizing our paper was published about half a year after our study was electronically published on Biology Letters’ homepage. The main critique from Brown et al. (2007) regarded the fossils used, the dating methods, and the results obtained by them. Unfortunately an erroneous early version of our electronic supplement was published on the web, and we had failed to notice that it had not been replaced, even as late as six months after the publication. Fortunately though we were offered the opportunity to respond to the paper by Brown et al., so that the errors could be sorted out during the preparation of the Brown et al. paper, and our reply. Brown et al. re-analyzed our data set, although using slightly different fossil constraints (and inferring the branch lengths in the phylogeny using a different alignment). They also used a Bayesian autocorrelation method, as implemented in the PAML/multidivtime softwares. Their analyses resulted in a chronogram with a smoother look, i.e. more evenly spread divergence times. This chronogram suggests a much earlier divergence of Neoaves than our analyses. As a result, the ghost ranges of the fossil record are much larger. Bird fossils are quite rare in fossil strata, due to preservational (taphonomic) issues. Large ghost ranges are therefore plausible. There are however early fossil birds that are interpreted as stem group Neoaves, but no crown group fossils of the same age. At the K/T boundary not only dinosaurs died out (excluding Aves, the group being nested within the paraphyletic dinosaurs), but extinctions were massive in all animal groups. Even if there were stem group Neoaves present earlier in the Cretaceous, a massive extinction of avian groups, followed by a rapid divergence is a likely scenario, simply because ecological niches earlier inhabited by dinosaurs were free for exploitation by birds and mammals. Our conclusion is that it is not surprising that different data and methods give different results, and that we still think our dating, that is closer to the fossil record is closer to the true divergence times.. 35.

(190) Summary of paper IV. Tom Britton, Cajsa Lisa Anderson, David Jaquet, Samuel Lundqvist and Kåre Bremer. Estimating divergence times in large phylogenetic trees. Systematic Biology (in press, October 2007). PATHd8 We present a new method and program, PATHd8, for phylogenetic dating of large trees without a molecular clock, allowing thousands of taxa and multiple age constraints. The method is a generalization of the mean path length method by Britton et al. (2001). The algorithm calculates node ages by taking the mean of the branch lengths from terminals to node, one pair of sister groups at a time. Because of this local smoothing, as opposed to the methods that estimates ages for all nodes at the same time, PATHd8 is very stable and fast. We compared PATHd8 to other methods (Langley-Fitch clock, NPRS, PL and Bayesian autocorrelation (multidivtime), by simulations and previously published empirical data sets. For well constrained data sets PATHd8 obtains similar ages compared to other methods, but differences in crown group ages are quite common. PATHd8 also collapses zero- or near-zero branch lengths. Properties and drawbacks of the PATHd8 method have been extensively discussed in the first part of this thesis.. 36.

(191) Summary of paper V. Cajsa Lisa Anderson and Thomas Janssen. Monocots. Chapter in Timetree of life, eds. Hedges and Kumar (accepted). Timetree of monocots – author’s cut. Background The Timetree of Life is intended to be an encyclopedia of evolutionary history, presenting chronograms and divergence times down to family level for all living organisms. In total it is planned to contain 83 chapters, and will be both published freely online and sold as a book. All chapters follow a strict format: A brief presentation of the taxa including a review of phylogenetic hypotheses, one chronogram for the extant taxa and one table containing divergence times for the nodes. Because of the restricted format, information that could be interesting for some researchers was left out. In this part of my doctorate thesis I therefore supplement the information in the monocot chapter by Anderson and Janssen.. Data and methods The data set from Janssen and Bremer (2004) is the largest monocot data set analyzed so far (878 taxa). At the time of their dating study, analysis of large datasets was feasible using nonparametric rate smoothing (NPRS), but not penalized likelihood (PL) or any Bayesian autocorrelation method. Developments following Janssen and Bremer’s study include new phylogenetic dating methods and implementations. Two examples are the PATHd8 method (Britton et al., in press), which can handle huge amounts of taxa, and the implementation of a fossil constrained cross validation procedure (Near and Sanderson, 2004) in the r8s program, which makes it possible to use PL for analyzing this large data set. Furthermore, new fossil discoveries have 37.

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