Primate Divergences through an Integrated Analysis of Palaeontological and Molecular Data

—Estimation of divergence times is usually done using either the fossil record or sequence data from modern species. We provide an integrated analysis of palaeontological and molecular data to give estimates of primate divergence times that utilize both sources of information. The number of preserved primate species discovered in the fossil record, along with their geological age distribution, is combined with the number of extant primate species to provide initial estimates of the primate and anthropoid divergence times. This is done by using a stochastic forwards-modeling approach where speciation and fossil preservation and discovery are simulated forward in time. We use the posterior distribution from the fossil analysis as a prior distribution on node ages in a molecular analysis. Sequence data from two genomic regions (CFTR on human chromosome 7 and the CYP7A1 region on chromosome 8) from 15 primate species are used with the birth–death model implemented in mcmctree in PAML to infer the posterior distribution of the ages of 14 nodes in the primate tree. We find that these age estimates are older than previously reported dates for all but one of these nodes. To perform the inference, a new approximate Bayesian computation (ABC) algorithm is introduced, where the structure of the model can be exploited in an ABC-within-Gibbs algorithm to provide a more efficient analysis. [Approximate Bayesian computation; molecular phylogeny; palaeontological data; primate divergence. ] Fossil evidence is the only direct source of information about long-extinct species and their evolution. Morphological similarities between extant species and fossil remains are used to infer the existence of ancestral species during the geological period to which the fossil is allocated. Conditional on there being no classification or dating error, the fossil’s age provides a minimum bound for the divergence time of the evolutionary lineage it represents. Sequence data from extant species provide an indirect source of information about evolutionary history. The pattern and variability observed in homologous sequences of DNA from different species contain traces of the history of the divergence and evolution of the phylogeny, and mathematical models of evolution can be used to combine our knowledge of genetics with the sequence data to extract information about evolutionary history, particularly divergence times. Many methods and models have been proposed with this aim, but all rely in some way on fossil evidence, as an external source of information must be used to calibrate the substitution rate. Fossil evidence is used to provide initial estimates for node ages in phylogenetic trees, which are then updated in light of molecular evidence. Yang and Rannala (2006) found that, for divergence time estimates based on sequence data, the largest source of uncertainty came from the fossil calibration dates used. Although fossils provide good explicit minimum bounds on the age of a clade, maximum bounds need to be inferred rather than measured and thus are inherently uncertain. Uncertainty about a maximum bound on the node age has been dealt with in various ways in molecular analyses, typically by relying upon a subjective judgement about the node age based on the age of the oldest fossil (i.e., a maximum bound, or the weight of the tail in a more general prior distribution). In this paper, we use a database of recorded fossil species combined with a model of speciation to find a model-based estimate of node ages. These estimates are then used as prior distributions for estimating molecular divergence times. The benefit of introducing an element of process modeling into the analysis of the fossil record is that it moves the subjective judgements further from important quantities and allows us to utilize more of the fossil record, thus letting data play a larger role in the analysis. In determining the expected gap between the age of the oldest fossil and the divergence time, a key influence is exerted by rates of fossil preservation and discovery, which are unknown and believed to vary through time (e.g., Foote et al. 1999; Smith and Peterson 2002; Tavaré et al. 2002; Soligo et al. 2007; Paul 2009). We use the pattern of species diversity through the Cenozoic and the number of extant primate species to estimate the sampling rate and the divergence 16 at U nirsity of S ouhern C alornia on M arch 3, 2011 sysbio.ordjournals. org D ow nladed fom 2011 WILKINSON ET AL.—DATING PRIMATE DIVERGENCES 17 time of the primates. The posterior distributions from the fossil analysis are used as the prior distribution in the molecular analysis to estimate a posterior distribution for the divergence time that uses both the fossil and molecular records more fully than previous analyses. The paper is organized as follows. The first section describes the analysis of the fossil record. The following section contains the molecular analysis and the final section contains a discussion. The details of the inference procedure used in the analysis of the fossil data are given in the Appendix, where we introduce a new variant on the Markov chain Monte Carlo (MCMC)– approximate Bayesian computation (ABC) (Marjoram et al. 2003) algorithm in order to improve the efficiency of our analysis. USING THE FOSSIL RECORD Fossil calibrations are essential when dating evolutionary events. Even if the analysis primarily uses molecular data, fossil evidence is used to provide prior distributions for one or more nodes in the phylogeny. This information is then used to calibrate the molecular clock and thus has consequences for estimation of other node ages. Early analyses using the molecular clock to date divergence times typically treated the oldest fossil representative as if it estimated the age of the node without error (Graur and Martin 2004; Hedges and Kumar 2004). This progressed to introducing uncertainty by specifying a range of possible values with hard bounds representing the limits of the uncertainty (Thorne et al. 1998), with zero probability assigned to ages outside of this range. Fossil evidence is well suited to providing a good hard minimum bound on the age of a node based on the oldest fossil representative, with the level of accuracy limited only by the accuracy of taxonomic assignment of the fossil and of the dating procedure used. However, the fossil record does not directly give any information regarding a maximum bound on the age (Benton and Donoghue 2007; Steiper and Young 2008). Thus, hard bounds are often either overconfident, where they are set too low, or too conservative, where unrealistically high maximum bounds are used. Yang and Rannala (2006) moved beyond the use of uniform distributions for calibration dates to allow general prior distributions, which can incorporate more information about the calibration age. These allow for most of the probability to be placed on dates near to the minimum bound, but with long tails to account for the a priori unlikely event that the node age is actually much older than the fossil evidence suggested. They chose prior distributions by fitting a parametric form (a gamma distribution) to estimated maximum and minimum bounds on the node age, allowing for 5% uncertainty outside this range. However, the fossil record contains more information about a node age than that contained solely in the oldest fossil ascribed to a particular lineage. The age of the oldest fossil may be the single most informative piece of data, but other parts of the record can help reduce the uncertainty in any estimate and provide a more nuanced picture. By considering more of the fossil record, we can move from using prior distributions based on the oldest fossil to distributions based on a wider appreciation of the fossil record and its underlying processes. The distribution of fossil ages contains information about the diversity (number of species) of a phylogeny through time. When combined with extant diversity counts, this can be used to infer the sampling rate or completeness of the fossil record (Tavaré et al. 2002; Soligo et al. 2007; Wilkinson and Tavaré 2009). For periods and phylogenies with high sampling rates, we expect the age of the oldest known fossil to be close to the divergence time of the phylogeny, whereas if the sampling rate is low, we expect the range of values possible for the gap between the oldest fossil and the root of the phylogeny it represents to be much more variable. For terrestrial vertebrates, the completeness (the proportion of species that have been preserved and then discovered in the fossil record) is generally believed to be low. For example, Martin (1993) and Tavaré et al. (2002) estimate the completeness of the primate fossil record to be less than 7% compared with an estimate of 29% for dinosaurs (Wang and Dobson 2006). Model for the Fossil Data The model for the fossil data can be thought of in two parts: 1) speciation and 2) fossilization and recovery. The speciation model describes the growth of the number of species (the diversity) from a common ancestor to the observed extant diversity, whereas the fossilization and recovery model describes how the phylogeny is recorded in the known fossil record. To model speciation, we use a continuous-time inhomogeneous binary Markov branching process (Harris 1963). To aid description, we use the language of family trees and refer to the direct descendants of a species as its offspring. Let Z(t) denote the number of species extant at time t, where t = 0 denotes the present. The age of the oldest known fossil representative is used as an absolute minimum bound on the age of the clade. The root of the tree is placed at this age plus τ million years, where τ represents the temporal gap between the oldest primate fossil and the primate divergence time. We assume that two species are present at this time and that each species lives for an exponentially distributed period of tim