Expansion dating: calibrating molecular clocks in marine species from expansions onto the Sunda Shelf Following the Last Glacial Maximum

The rate of change in DNA is an important parameter for understanding molecular evolution and hence for inferences drawn from studies of phylogeography and phylogenetics. Most rate calibrations for mitochondrial coding regions in marine species have been made from divergence dating for fossils and vicariant events older than 1-2 My and are typically 0.5-2% per lineage per million years. Recently, calibrations made with ancient DNA (aDNA) from younger dates have yielded faster rates, suggesting that estimates of the molecular rate of change depend on the time of calibration, decaying from the instantaneous mutation rate to the phylogenetic substitution rate. aDNA methods for recent calibrations are not available for most marine taxa so instead we use radiometric dates for sea-level rise onto the Sunda Shelf following the Last Glacial Maximum (starting ～18,000 years ago), which led to massive population expansions for marine species. Instead of divergence dating, we use a two-epoch coalescent model of logistic population growth preceded by a constant population size to infer a time in mutational units for the beginning of these expansion events. This model compares favorably to simpler coalescent models of constant population size, and exponential or logistic growth, and is far more precise than estimates from the mismatch distribution. Mean rates estimated with this method for mitochondrial coding genes in three invertebrate species are elevated in comparison to older calibration points (2.3-6.6% per lineage per million years), lending additional support to the hypothesis of calibration time dependency for molecular rates.     

Bayesian estimation of sequence damage in ancient DNA

DNA extracted from archaeological and paleontological remains is usually damaged by biochemical processes postmortem. Some of these processes lead to changes in the structure of the DNA molecule, which can result in the incorporation of incorrect nucleotides during polymerase chain reaction. These base misincorporations, or miscoding lesions, can lead to the inclusion of spurious additional mutations in ancient DNA (aDNA) data sets. This has the potential to affect the outcome of phylogenetic and population genetic analyses, including estimates of mutation rates and genetic diversity. We present a novel model, termed the delta model, which estimates the amount of damage in DNA data and accounts for its effects in a Bayesian phylogenetic framework. The ability of the delta model to estimate damage is first investigated using a simulation study. The model is then applied to 13 aDNA data sets. The amount of damage in these data sets is shown to be significant but low (about 1 damaged base per 750 nt), suggesting that precautions for limiting the influence of damaged sites, such as cloning and enzymatic treatment, are worthwhile. The results also suggest that relatively high rates of mutation previously estimated from aDNA data are not entirely an artifact of sequence damage and are likely to be due to other factors such as the persistence of transient polymorphisms. The delta model appears to be particularly useful for placing upper credibility limits on the amount of sequence damage in an alignment, and this capacity might be beneficial for future aDNA studies or for the estimation of sequencing errors in modern DNA.     

Identifiability of parameters in MCMC Bayesian inference of phylogeny

Methods for Bayesian inference of phylogeny using DNA sequences based on Markov chain Monte Carlo (MCMC) techniques allow the incorporation of arbitrarily complex models of the DNA substitution process, and other aspects of evolution. This has increased the realism of models, potentially improving the accuracy of the methods, and is largely responsible for their recent popularity. Another consequence of the increased complexity of models in Bayesian phylogenetics is that these models have, in several cases, become overparameterized. In such cases, some parameters of the model are not identifiable; different combinations of nonidentifiable parameters lead to the same likelihood, making it impossible to decide among the potential parameter values based on the data. Overparameterized models can also slow the rate of convergence of MCMC algorithms due to large negative correlations among parameters in the posterior probability distribution. Functions of parameters can sometimes be found, in overparameterized models, that are identifiable, and inferences based on these functions are legitimate. Examples are presented of overparameterized models that have been proposed in the context of several Bayesian methods for inferring the relative ages of nodes in a phylogeny when the substitution rate evolves over time.     

Partition number,rate priors and unreliable divergence times in Bayesian phylogenetic dating

More loci/partitions should improve Bayesian estimation of divergence times on phylogenies but it has recently been shown that this can lead to surprisingly poor estimation due to the way it affects the prior on mean substitution rate. Here we consider the likely impact of partition number on divergence time analyses carried out using the program BEAST. Mitochondrial genome data from toad‐headed lizards (genus Phrynocephalus) from the Qinghai–Tibetan Plateau were used to examine this effect. Under increased partitioning of the sequences, BEAST posterior divergence times became unreasonably narrow and downwardly biased due to misspecification of the mean substitution rate prior. This effect was detectable when relatively few partitions were used (i.e. between four and eight), but became very acute for 27–86 partitions. Fortunately, a correction that adjusts the standard deviation of the mean of locus rates led to results that were equivalent to those obtained using the latest version of the program MCMCtree, which implements a new gamma‐Dirichlet prior to overcome this problem. A review of the literature shows that a substantial number of BEAST dating studies are likely to have been affected by this misspecification of the rate prior.     

Estimating mutation parameters,population history and genealogy simultaneously from temporally spaced sequence data

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.     

Coestimation of recombination,substitution and molecular adaptation rates by approximate Bayesian computation

The estimation of parameters in molecular evolution may be biased when some processes are not considered. For example, the estimation of selection at the molecular level using codon-substitution models can have an upward bias when recombination is ignored. Here we address the joint estimation of recombination, molecular adaptation and substitution rates from coding sequences using approximate Bayesian computation (ABC). We describe the implementation of a regression-based strategy for choosing subsets of summary statistics for coding data, and show that this approach can accurately infer recombination allowing for intracodon recombination breakpoints, molecular adaptation and codon substitution rates. We demonstrate that our ABC approach can outperform other analytical methods under a variety of evolutionary scenarios. We also show that although the choice of the codon-substitution model is important, our inferences are robust to a moderate degree of model misspecification. In addition, we demonstrate that our approach can accurately choose the evolutionary model that best fits the data, providing an alternative for when the use of full-likelihood methods is impracticable. Finally, we applied our ABC method to co-estimate recombination, substitution and molecular adaptation rates from 24 published human immunodeficiency virus 1 coding data sets.     

The relative performance of Bayesian and parsimony approaches when sampling characters evolving under homogeneous and heterogeneous sets of parameters

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.
© The Willi Hennig Society 2006.     

Joint inference of microsatellite mutation models, population history and genealogies using transdimensional Markov Chain Monte Carlo

We provide a framework for Bayesian coalescent inference from microsatellite data that enables inference of population history parameters averaged over microsatellite mutation models. To achieve this we first implemented a rich family of microsatellite mutation models and related components in the software package BEAST. BEAST is a powerful tool that performs Bayesian MCMC analysis on molecular data to make coalescent and evolutionary inferences. Our implementation permits the application of existing nonparametric methods to microsatellite data. The implemented microsatellite models are based on the replication slippage mechanism and focus on three properties of microsatellite mutation: length dependency of mutation rate, mutational bias toward expansion or contraction, and number of repeat units changed in a single mutation event. We develop a new model that facilitates microsatellite model averaging and Bayesian model selection by transdimensional MCMC. With Bayesian model averaging, the posterior distributions of population history parameters are integrated across a set of microsatellite models and thus account for model uncertainty. Simulated data are used to evaluate our method in terms of accuracy and precision of estimation and also identification of the true mutation model. Finally we apply our method to a red colobus monkey data set as an example.     

An examination of the monophyly of morning glory taxa using Bayesian phylogenetic inference

The objective of this study was to obtain a quantitative assessment of the monophyly of morning glory taxa, specifically the genus Ipomoea and the tribe Argyreieae. Previous systematic studies of morning glories intimated the paraphyly of Ipomoea by suggesting that the genera within the tribe Argyreieae are derived from within Ipomoea; however, no quantitative estimates of statistical support were developed to address these questions. We applied a Bayesian analysis to provide quantitative estimates of monophyly in an investigation of morning glory relationships using DNA sequence data. We also explored various approaches for examining convergence of the Markov chain Monte Carlo (MCMC) simulation of the Bayesian analysis by running 18 separate analyses varying in length. We found convergence of the important components of the phylogenetic model (the tree with the maximum posterior probability, branch lengths, the parameter values from the DNA substitution model, and the posterior probabilities for clade support) for these data after one million generations of the MCMC simulations. In the process, we identified a run where the parameter values obtained were often outside the range of values obtained from the other runs, suggesting an aberrant result. In addition, we compared the Bayesian method of phylogenetic analysis to maximum likelihood and maximum parsimony. The results from the Bayesian analysis and the maximum likelihood analysis were similar for topology, branch lengths, and parameters of the DNA substitution model. Topologies also were similar in the comparison between the Bayesian analysis and maximum parsimony, although the posterior probabilities and the bootstrap proportions exhibited some striking differences. In a Bayesian analysis of three data sets (ITS sequences, waxy sequences, and ITS + waxy sequences) no supoort for the monophyly of the genus Ipomoea, or for the tribe Argyreieae, was observed, with the estimate of the probability of the monophyly of these taxa being less than 3.4 x 10(-7).     

Recombination estimation under complex evolutionary models with the coalescent composite-likelihood method

The composite-likelihood estimator (CLE) of the population recombination rate considers only sites with exactly two alleles under a finite-sites mutation model (McVean, G. A. T., P. Awadalla, and P. Fearnhead. 2002. A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 160:1231-1241). While in such a model the identity of alleles is not considered, the CLE has been shown to be robust to minor misspecification of the underlying mutational model. However, there are many situations where the putative mutation and demographic history can be quite complex. One good example is rapidly evolving pathogens, like HIV-1. First we evaluated the performance of the CLE and the likelihood permutation test (LPT) under more complex, realistic models, including a general time reversible (GTR) substitution model, rate heterogeneity among sites (Gamma), positive selection, population growth, population structure, and noncontemporaneous sampling. Second, we relaxed some of the assumptions of the CLE allowing for a four-allele, GTR + Gamma model in an attempt to use the data more efficiently. Through simulations and the analysis of real data, we concluded that the CLE is robust to severe misspecifications of the substitution model, but underestimates the recombination rate in the presence of exponential growth, population mixture, selection, or noncontemporaneous sampling. In such cases, the use of more complex models slightly increases performance in some occasions, especially in the case of the LPT. Thus, our results provide for a more robust application of the estimation of recombination rates.     

太湖新银鱼线粒体D-loop和Cytb片段序列结构与进化速率比较

共获得49个太湖新银鱼(Neosalanx taihuensis)个体的线粒体细胞色素b(Cyt b)全序列和控制区(D-loop)部分序列。所测线粒体D-loop部分序列长度变化范围为648～680bp,识别到位于前端的一个串联重复序列、一个终止相关序列(ETAS),3个中央保守区保守序列(CSB-F、CSB-E、CSB-D)及一个保守序列区保守序列(CSB-1),结构与其他鱼类的研究结果类似。太湖新银鱼线粒体Cyt b和D-loop片段的相对进化速率的比较研究结果表明,太湖新银鱼D-loop总的序列多态性位点的比例为0.83%,低于线粒体Cyt b部分总的序列多态性位点的比例(1.31%)。假设太湖新银鱼Cyt b基因平均进化速率相对值为1,贝叶斯(Bayes)MCMC模拟给出Cyt b基因的相对速率区间估计为1.000±0.131,而D-loop基因的相对速率为0.859±0.261,表明太湖新银鱼D-loop基因的进化速率低于Cyt b基因,同时,后验概率分布的变异方差也比较大。说明Cyt b基因比D-loop基因具有相对较高的进化速率,也相对更接近分子钟假设。因此,可以认为Cyt b基因比D-loop基因更适于太湖新银鱼种内及近缘种间相关分子生态及系统地理格局的研究。     

Accounting for variation of substitution rates through time in Bayesian phylogeny reconstruction of Sapotoideae (Sapotaceae)

We used Bayesian phylogenetic analysis of 5 kb of chloroplast DNA data from 68 Sapotaceae species to clarify phylogenetic relationships within Sapotoideae, one of the two major clades within Sapotaceae. Variation in substitution rates through time was shown to be a very important aspect of molecular evolution for this data set. Relative rates tests indicated that changes in overall rate have taken place in several lineages during the history of the group and Bayes factors strongly supported a covarion model, which allows the rate of a site to vary over time, over commonly used models that only allow rates to vary across sites. Rate variation over time was actually found to be a more important model component than rate variation across sites. The covarion model was originally developed for coding gene sequences and has so far only been tested for this type of data. The fact that it performed so well with the present data set, consisting mainly of data from noncoding spacer regions, suggests that it deserves a wider consideration in model based phylogenetic inference. Repeatability of phylogenetic results was very difficult to obtain with the more parameter rich models, and analyses with identical settings often supported different topologies. Overparameterization may be the reason why the MCMC did not sample from the posterior distribution in these cases. The problem could, however, be overcome by using less parameter rich evolutionary models, and adjusting the MCMC settings. The phylogenetic results showed that two taxa, previously thought to belong in Sapotoideae, are not part of this group. Eberhardtia aurata is the sister of the two major Sapotaceae clades, Chrysophylloideae and Sapotoideae, and Neohemsleya usambarensis belongs in Chrysophylloideae. Within Sapotoideae two clades, Sideroxyleae and Sapoteae, were strongly supported. Bayesian analysis of the character history of some floral morphological traits showed that the ancestral type of flower in Sapotoideae may have been characterized by floral parts (sepals, petals, stamens, and staminodes) in single whorls of five, entire corolla lobes, and seeds with an adaxial hilum.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.     

Inferring complex DNA substitution processes on phylogenies using uniformization and data augmentation

A new method is developed for calculating sequence substitution probabilities using Markov chain Monte Carlo (MCMC) methods. The basic strategy is to use uniformization to transform the original continuous time Markov process into a Poisson substitution process and a discrete Markov chain of state transitions. An efficient MCMC algorithm for evaluating substitution probabilities by this approach using a continuous gamma distribution to model site-specific rates is outlined. The method is applied to the problem of inferring branch lengths and site-specific rates from nucleotide sequences under a general time-reversible (GTR) model and a computer program BYPASSR is developed. Simulations are used to examine the performance of the new program relative to an existing program BASEML that uses a discrete approximation for the gamma distributed prior on site-specific rates. It is found that BASEML and BYPASSR are in close agreement when inferring branch lengths, regardless of the number of rate categories used, but that BASEML tends to underestimate high site-specific substitution rates, and to overestimate intermediate rates, when fewer than 50 rate categories are used. Rate estimates obtained using BASEML agree more closely with those of BYPASSR as the number of rate categories increases. Analyses of the posterior distributions of site-specific rates from BYPASSR suggest that a large number of taxa are needed to obtain precise estimates of site-specific rates, especially when rates are very high or very low. The method is applied to analyze 45 sequences of the alpha 2B adrenergic receptor gene (A2AB) from a sample of eutherian taxa. In general, the pattern expected for regions under negative selection is observed with third codon positions having the highest inferred rates, followed by first codon positions and with second codon positions having the lowest inferred rates. Several sites show exceptionally high substitution rates at second codon positions that may represent the effects of positive selection.     

Model misspecification and probabilistic tests of topology: evidence from empirical data sets

Probabilistic tests of topology offer a powerful means of evaluating competing phylogenetic hypotheses. The performance of the nonparametric Shimodaira-Hasegawa (SH) test, the parametric Swofford-Olsen-Waddell-Hillis (SOWH) test, and Bayesian posterior probabilities were explored for five data sets for which all the phylogenetic relationships are known with a very high degree of certainty. These results are consistent with previous simulation studies that have indicated a tendency for the SOWH test to be prone to generating Type 1 errors because of model misspecification coupled with branch length heterogeneity. These results also suggest that the SOWH test may accord overconfidence in the true topology when the null hypothesis is in fact correct. In contrast, the SH test was observed to be much more conservative, even under high substitution rates and branch length heterogeneity. For some of those data sets where the SOWH test proved misleading, the Bayesian posterior probabilities were also misleading. The results of all tests were strongly influenced by the exact substitution model assumptions. Simple models, especially those that assume rate homogeneity among sites, had a higher Type 1 error rate and were more likely to generate misleading posterior probabilities. For some of these data sets, the commonly used substitution models appear to be inadequate for estimating appropriate levels of uncertainty with the SOWH test and Bayesian methods. Reasons for the differences in statistical power between the two maximum likelihood tests are discussed and are contrasted with the Bayesian approach.     

Estimation of population parameters and recombination rates from single nucleotide polymorphisms

Some general likelihood and Bayesian methods for analyzing single nucleotide polymorphisms (SNPs) are presented. First, an efficient method for estimating demographic parameters from SNPs in linkage equilibrium is derived. The method is applied in the estimation of growth rates of a human population based on 37 SNP loci. It is demonstrated how ascertainment biases, due to biased sampling of loci, can be avoided, at least in some cases, by appropriate conditioning when calculating the likelihood function. Second, a Markov chain Monte Carlo (MCMC) method for analyzing linked SNPs is developed. This method can be used for Bayesian and likelihood inference on linked SNPs. The utility of the method is illustrated by estimating recombination rates in a human data set containing 17 SNPs and 60 individuals. Both methods are based on assumptions of low mutation rates.     

Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.     

Estimating recombination rates from population genetic data.

We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationally intensive statistical procedure (importance sampling) to calculate the likelihood under a coalescent-based model. Detailed comparisons of the new algorithm with two existing methods (the importance sampling method of Griffiths and Marjoram and the MCMC method of Kuhner and colleagues) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum-likelihood estimator of the recombination rate and its robustness to misspecification of the demographic model.     

A dirichlet process prior for estimating lineage-specific substitution rates

We introduce a new model for relaxing the assumption of a strict molecular clock for use as a prior in Bayesian methods for divergence time estimation. Lineage-specific rates of substitution are modeled using a Dirichlet process prior (DPP), a type of stochastic process that assumes lineages of a phylogenetic tree are distributed into distinct rate classes. Under the Dirichlet process, the number of rate classes, assignment of branches to rate classes, and the rate value associated with each class are treated as random variables. The performance of this model was evaluated by conducting analyses on data sets simulated under a range of different models. We compared the Dirichlet process model with two alternative models for rate variation: the strict molecular clock and the independent rates model. Our results show that divergence time estimation under the DPP provides robust estimates of node ages and branch rates without significantly reducing power. Further analyses were conducted on a biological data set, and we provide examples of ways to summarize Markov chain Monte Carlo samples under this model.     

Bayesian inference of errors in ancient DNA caused by postmortem degradation

Methods for extracting and amplifying sequences using ancient DNA (aDNA) can be prone to errors caused by postmortem modifications of the DNA strand. A new statistical method is developed for predicting errors in aDNA sequences caused by such processes. In addition to the canonical DNA substitution model parameters, a discrete Markov chain is used to describe nucleotide substitutions occurring via postmortem degradation of the aDNA sequences. A computer program, BYPASSR-degr, was developed implementing the method and was used in subsequent analyses of simulated data sets under the new model. Simulation studies show that the new method can be powerful and accurate in identifying damaged sites. The method is applied to analyze aDNA sequences of Etruscans, Adélie penguins, and horses. No significant signals of degradation were observed at any sites of the aDNA sequences we analyzed.