A mixed relaxed clock model

Over recent years, several alternative relaxed clock models have been proposed in the context of Bayesian dating. These models fall in two distinct categories: uncorrelated and autocorrelated across branches. The choice between these two classes of relaxed clocks is still an open question. More fundamentally, the true process of rate variation may have both long-term trends and short-term fluctuations, suggesting that more sophisticated clock models unfolding over multiple time scales should ultimately be developed. Here, a mixed relaxed clock model is introduced, which can be mechanistically interpreted as a rate variation process undergoing short-term fluctuations on the top of Brownian long-term trends. Statistically, this mixed clock represents an alternative solution to the problem of choosing between autocorrelated and uncorrelated relaxed clocks, by proposing instead to combine their respective merits. Fitting this model on a dataset of 105 placental mammals, using both node-dating and tip-dating approaches, suggests that the two pure clocks, Brownian and white noise, are rejected in favour of a mixed model with approximately equal contributions for its uncorrelated and autocorrelated components. The tip-dating analysis is particularly sensitive to the choice of the relaxed clock model. In this context, the classical pure Brownian relaxed clock appears to be overly rigid, leading to biases in divergence time estimation. By contrast, the use of a mixed clock leads to more recent and more reasonable estimates for the crown ages of placental orders and superorders. Altogether, the mixed clock introduced here represents a first step towards empirically more adequate models of the patterns of rate variation across phylogenetic trees.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.     

Ancient DNA enables timing of the pleistocene origin and holocene expansion of two adélie penguin lineages in antarctica

The timing of divergent events in history is one of the central goals of contemporary evolutionary biology. Such studies are however dependent on accurate evolutionary rates. Recent developments in ancient DNA analysis enable the estimation of more accurate evolutionary rates and therefore more accurate timing of divergence events. Consequently, this leads to a better understanding of changes in populations through time. We use an evolutionary rate calculated from ancient DNA of Adélie penguins (Pygoscelis adeliae) to time divergent events in their history. We report the presence of two distinct and highly variable mitochondrial DNA lineages and track changes in these lineages through space and time. When the ancient DNA and the phylogenetic rates are used to estimate the time of origin of the lineages, two very different estimates resulted. In addition, these same rates provide very different estimates of the time of expansion of these lineages. We suggest that the rate calculated from ancient DNA is more consistent with the glacial history of Antarctica and requires fewer assumptions than does a narrative based on the phylogenetic rate. Finally, we suggest that our study indicates an important new role for ancient DNA studies in the timing of divergent events in history.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Giants and dwarfs: molecular phylogenies reveal multiple origins of annual spurges within Euphorbia subg. Esula

Euphorbia (Euphorbiaceae) comprises over 2150 species and is thus the second-largest genus of flowering plants. In Europe, it is represented by more than 100 species with highest diversity in the Mediterranean area; the majority of taxa belong to subgenus Esula Pers., including about 500 taxa. The few available phylogenetic studies yielded contrasting results regarding the monophyly of subg. Esula, and the phylogenetic relationships among its constituents remain poorly understood. We have sampled DNA sequences from the nuclear ribosomal internal transcribed spacer (ITS) and the plastid trnT-trnF region from about 100, predominantly European taxa of subg. Esula in order to infer its phylogenetic history. The plastid data support monophyly of subg. Esula whereas the ITS phylogeny, which is generally less resolved, is indecisive in this respect. Although some major clades have partly incongruent positions in the ITS and plastid phylogenies, the taxonomic content of the major terminal clades is congruent in both trees. As traditional sectional delimitations are largely not corroborated, an improved classification is proposed. Character state reconstruction illustrates that the annual life form developed independently several times in different clades of subgenus Esula from perennial ancestors, and that several morphological traits used in previous classifications of Euphorbia developed in parallel in different lineages.     

Incorrect handling of calibration information in divergence time inference: an example from volcanic islands

Divergence time studies rely on calibration information from several sources. The age of volcanic islands is one of the standard references to obtain chronological data to estimate the absolute times of lineage diversifications. This strategy assumes that cladogenesis is necessarily associated with island formation, and punctual calibrations are commonly used to date the splits of endemic island species. Here, we re-examined three studies that inferred divergence times for different Hawaiian lineages assuming fixed calibration points. We show that, by permitting probabilistic calibrations, some divergences are estimated to be significantly younger or older than the age of the island formation, thus yielding distinct ecological scenarios for the speciation process. The results highlight the importance of using calibration information correctly, as well as the possibility of incorporating volcanic island studies into a formal, biogeographical hypothesis-testing framework.     

Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds

We implement a Bayesian Markov chain Monte Carlo algorithm for estimating species divergence times that uses heterogeneous data from multiple gene loci and accommodates multiple fossil calibration nodes. A birth-death process with species sampling is used to specify a prior for divergence times, which allows easy assessment of the effects of that prior on posterior time estimates. We propose a new approach for specifying calibration points on the phylogeny, which allows the use of arbitrary and flexible statistical distributions to describe uncertainties in fossil dates. In particular, we use soft bounds, so that the probability that the true divergence time is outside the bounds is small but nonzero. A strict molecular clock is assumed in the current implementation, although this assumption may be relaxed. We apply our new algorithm to two data sets concerning divergences of several primate species, to examine the effects of the substitution model and of the prior for divergence times on Bayesian time estimation. We also conduct computer simulation to examine the differences between soft and hard bounds. We demonstrate that divergence time estimation is intrinsically hampered by uncertainties in fossil calibrations, and the error in Bayesian time estimates will not go to zero with increased amounts of sequence data. Our analyses of both real and simulated data demonstrate potentially large differences between divergence time estimates obtained using soft versus hard bounds and a general superiority of soft bounds. Our main findings are as follows. (1) When the fossils are consistent with each other and with the molecular data, and the posterior time estimates are well within the prior bounds, soft and hard bounds produce similar results. (2) When the fossils are in conflict with each other or with the molecules, soft and hard bounds behave very differently; soft bounds allow sequence data to correct poor calibrations, while poor hard bounds are impossible to overcome by any amount of data. (3) Soft bounds eliminate the need for "safe" but unrealistically high upper bounds, which may bias posterior time estimates. (4) Soft bounds allow more reliable assessment of estimation errors, while hard bounds generate misleadingly high precisions when fossils and molecules are in conflict.     

Biogeographic calibrations for the molecular clock

Molecular estimates of evolutionary timescales have an important role in a range of biological studies. Such estimates can be made using methods based on molecular clocks, including models that are able to account for rate variation across lineages. All clock models share a dependence on calibrations, which enable estimates to be given in absolute time units. There are many available methods for incorporating fossil calibrations, but geological and climatic data can also provide useful calibrations for molecular clocks. However, a number of strong assumptions need to be made when using these biogeographic calibrations, leading to wide variation in their reliability and precision. In this review, we describe the nature of biogeographic calibrations and the assumptions that they involve. We present an overview of the different geological and climatic events that can provide informative calibrations, and explain how such temporal information can be incorporated into dating analyses.     

Bayesian Network Reconstruction Using Systems Genetics Data: Comparison of MCMC Methods

Reconstructing biological networks using high-throughput technologies has the potential to produce condition-specific interactomes. But are these reconstructed networks a reliable source of biological interactions? Do some network inference methods offer dramatically improved performance on certain types of networks? To facilitate the use of network inference methods in systems biology, we report a large-scale simulation study comparing the ability of Markov chain Monte Carlo (MCMC) samplers to reverse engineer Bayesian networks. The MCMC samplers we investigated included foundational and state-of-the-art Metropolis–Hastings and Gibbs sampling approaches, as well as novel samplers we have designed. To enable a comprehensive comparison, we simulated gene expression and genetics data from known network structures under a range of biologically plausible scenarios. We examine the overall quality of network inference via different methods, as well as how their performance is affected by network characteristics. Our simulations reveal that network size, edge density, and strength of gene-to-gene signaling are major parameters that differentiate the performance of various samplers. Specifically, more recent samplers including our novel methods outperform traditional samplers for highly interconnected large networks with strong gene-to-gene signaling. Our newly developed samplers show comparable or superior performance to the top existing methods. Moreover, this performance gain is strongest in networks with biologically oriented topology, which indicates that our novel samplers are suitable for inferring biological networks. The performance of MCMC samplers in this simulation framework can guide the choice of methods for network reconstruction using systems genetics data.