Artifactual phylogenies caused by correlated distribution of substitution rates among sites and lineages: the good, the bad, and the ugly

Despite the advances in understanding molecular evolution, current phylogenetic methods barely take account of a fraction of the complexity of evolution. We are chiefly constrained by our incomplete knowledge of molecular evolutionary processes and the limits of computational power. These limitations lead to the establishment of either biologically simplistic models that rarely account for a fraction of the complexity involved or overfitting models that add little resolution to the problem. Such oversimplified models may lead us to assign high confidence to an incorrect tree (inconsistency). Rate-across-site (RAS) models are commonly used evolutionary models in phylogenetic studies. These account for heterogeneity in the evolutionary rates among sites but do not account for changing within-site rates across lineages (heterotachy). If heterotachy is common, using RAS models may lead to systematic errors in tree inference. In this work we show possible misleading effects in tree inference when the assumption of constant within-site rates across lineages is violated using maximum likelihood. Using a simulation study, we explore the ways in which gamma stationary models can lead to wrong topology or to deceptive bootstrap support values when the within-site rates change across lineages. More precisely, we show that different degrees of heterotachy mislead phylogenetic inference when the model assumed is stationary. Finally, we propose a geometry-based approach to visualize and to test for the possible existence of bias due to heterotachy.     

The likelihood node density effect and consequences for evolutionary studies of molecular rates

Many molecular phylogenies show longer root-to-tip path lengths in species-rich groups, encouraging hypotheses linking cladogenesis with accelerated molecular evolution. However, the pattern can also be caused by an artifact called the node density effect (NDE): this effect occurs when the method used to reconstruct a tree underestimates multiple hits that would have been revealed by extra nodes, leading to longer root-to-tip path lengths in clades with more terminal taxa. Here we use a twofold approach to demonstrate that maximum likelihood and Bayesian methods also suffer from the NDE known to affect parsimony. First, simulations deliberately mismatching the simulation and reconstruction models show that the greater the model disparity, the greater the gap between actual and reconstructed tree lengths, and the greater the NDE. Second, taxon sampling manipulation with empirical data shows that NDE can still be present when using optimized models: across 12 datasets, 70 out of 109 sister path comparisons showed significant evidence of NDE. Unless the model fairly accurately reconstructs the real tree length-and given the complexity of real sequence evolution this may be uncommon -- it will consistently produce a node density artifact. At commonly encountered divergence levels, a 10% underestimation of tree length results in > or = 80% of simulated phylogenies showing a positive NDE. Bayesian trees have a slight but consistently stronger effect. This pervasive methodological artifact increases apparent rate heterogeneity, and can compromise investigations of factors influencing molecular evolutionary rate that use path lengths in topologically asymmetric trees.     

Heterogeneity in the rate of molecular sequence evolution substantially impacts the accuracy of detecting shifts in diversification rates

As species richness varies along the tree of life, there is a great interest in identifying factors that affect the rates by which lineages speciate or go extinct. To this end, theoretical biologists have developed a suite of phylogenetic comparative methods that aim to identify where shifts in diversification rates had occurred along a phylogeny and whether they are associated with some traits. Using these methods, numerous studies have predicted that speciation and extinction rates vary across the tree of life. In this study, we show that asymmetric rates of sequence evolution lead to systematic biases in the inferred phylogeny, which in turn lead to erroneous inferences regarding lineage diversification patterns. The results demonstrate that as the asymmetry in sequence evolution rates increases, so does the tendency to select more complicated models that include the possibility of diversification rate shifts. These results thus suggest that any inference regarding shifts in diversification pattern should be treated with great caution, at least until any biases regarding the molecular substitution rate have been ruled out.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

A new phylogenetic method for identifying exceptional phenotypic diversification

Currently available phylogenetic methods for studying the rate of evolution in a continuously valued character assume that the rate is constant throughout the tree or that it changes along specific branches according to an a priori hypothesis of rate variation provided by the user. Herein, we describe a new method for studying evolutionary rate variation in continuously valued characters given an estimate of the phylogenetic history of the species in our study. According to this method, we propose no specific prior hypothesis for how the variation in evolutionary rate is structured throughout the history of the species in our study. Instead, we use a Bayesian Markov Chain Monte Carlo approach to estimate evolutionary rates and the shift point between rates on the tree. We do this by simultaneously sampling rates and shift points in proportion to their posterior probability, and then collapsing the posterior sample into an estimate of the parameters of interest. We use simulation to show that the method is quite successful at identifying the phylogenetic position of a shift in the rate of evolution, and that estimated rates are asymptotically unbiased. We also provide an empirical example of the method using data for Anolis lizards. [This article was published online on September 20, 2011. An error in a co‐author's name was subsequently identified. This notice is included in the online and print versions to indicate that both have been corrected September 21, 2011.]     

A model-based approach to study nearest-neighbor influences reveals complex substitution patterns in non-coding sequences

In this article, we present a likelihood-based framework for modeling site dependencies. Our approach builds upon standard evolutionary models but incorporates site dependencies across the entire tree by letting the evolutionary parameters in these models depend upon the ancestral states at the neighboring sites. It thus avoids the need for introducing new and high-dimensional evolutionary models for site-dependent evolution. We propose a Markov chain Monte Carlo approach with data augmentation to infer the evolutionary parameters under our model. Although our approach allows for wide-ranging site dependencies, we illustrate its use, in two non-coding datasets, in the case of nearest-neighbor dependencies (i.e., evolution directly depending only upon the immediate flanking sites). The results reveal that the general time-reversible model with nearest-neighbor dependencies substantially improves the fit to the data as compared to the corresponding model with site independence. Using the parameter estimates from our model, we elaborate on the importance of the 5-methylcytosine deamination process (i.e., the CpG effect) and show that this process also depends upon the 5' neighboring base identity. We hint at the possibility of a so-called TpA effect and show that the observed substitution behavior is very complex in the light of dinucleotide estimates. We also discuss the presence of CpG effects in a nuclear small subunit dataset and find significant evidence that evolutionary models incorporating context-dependent effects perform substantially better than independent-site models and in some cases even outperform models that incorporate varying rates across sites.     

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon--known as heterotachy--can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.     

Parsimony-based test for identifying changes in evolutionary trends for quantitative characters: implications for the origin of the amniotic egg

The origin of the amniotic egg was a major event in vertebrate evolution and is thought to have contributed to the spectacular evolutionary radiation of amniotes. We test one of the most popular scenarios proposed by Carroll in 1970 to explain the origin of the amniotic egg using a novel method based on an asymmetric version of linear parsimony (aka Wagner parsimony) for identifying the most parsimonious split of a tree into two parts between which the evolution of the character is allowed to differ. The new method evaluates the cost of splitting a phylogenetic tree at a given node as the integral, over all pairs of asymmetry parameters, of the most parsimonious costs that can be achieved by using the first parameter on the subtree pending from this node and the second parameter elsewhere. By testing all the nodes, we then obtain the most parsimonious split of a tree with regard to the character values at its tips. Among the nine trees and two characters tested, our method yields a total of 517 parsimonious trend changes in Permo-Carboniferous stegocephalians, a single one of which occurs in a part of the tree (among stem-amniotes) where Carroll's scenario predicts that there should have been distinct changes in body size evolutionary trends. This refutes the scenario because the amniote stem does not appear to have elevated rates of evolutionary trend shifts. Our nodal body size estimates offer less discriminating power, but they likewise fail to find strong support for Carroll's scenario.     

Phylogenetic eigenvectors and nonstationarity in the evolution of theropod dinosaur skulls

Despite the long‐standing interest in nonstationarity of both phenotypic evolution and diversification rates, only recently have methods been developed to study this property. Here, we propose a methodological expansion of the phylogenetic signal‐representation (PSR) curve based on phylogenetic eigenvectors to test for nonstationarity. The PSR curve is built by plotting the coefficients of determination R² from phylogenetic eigenvector regression (PVR) models increasing the number of phylogenetic eigenvectors against the accumulated eigenvalues. The PSR curve is linear under a stationary model of trait evolution (i.e. the Brownian motion model). Here we describe the distribution of shifts in the models R² and used a randomization procedure to compare observed and simulated shifts along the PSR curve, which allowed detecting nonstationarity in trait evolution. As an applied example, we show that the main evolutionary pattern of variation in the theropod dinosaur skull was nonstationary, with a significant shift in evolutionary rates in derived oviraptorosaurs, an aberrant group of mostly toothless, crested, birdlike theropods. This result is also supported by a recently proposed Bayesian‐based method (AUTEUR). A significant deviation between Ceratosaurus and Limusaurus terminal branches was also detected. We purport that our new approach is a valuable tool for evolutionary biologists, owing to its simplicity, flexibility and comprehensiveness.     

Tempo and mode of climatic niche evolution in Primates

Climatic niches have increasingly become a nexus in our understanding of a variety of ecological and evolutionary phenomena, from species distributions to latitudinal diversity gradients. Despite the increasing availability of comprehensive datasets on species ranges, phylogenetic histories, and georeferenced environmental conditions, studies on the evolution of climate niches have only begun to understand how niches evolve over evolutionary timescales. Here, using primates as a model system, we integrate recently developed phylogenetic comparative methods, species distribution patterns, and climatic data to explore primate climatic niche evolution, both among clades and over time. In general, we found that simple, constant‐rate models provide a poor representation of how climatic niches evolve. For instance, there have been shifts in the rate of climatic niche evolution in several independent clades, particularly in response to the increasingly cooler climates of the past 10 My. Interestingly, rate accelerations greatly outnumbered rate decelerations. These results highlight the importance of considering more realistic evolutionary models that allow for the detection of heterogeneity in the tempo and mode of climatic niche evolution, as well as to infer possible constraining factors for species distributions in geographical space.     

Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

Diversity Dynamics in Nymphalidae Butterflies: Effect of Phylogenetic Uncertainty on Diversification Rate Shift Estimates

The species rich butterfly family Nymphalidae has been used to study evolutionary interactions between plants and insects. Theories of insect-hostplant dynamics predict accelerated diversification due to key innovations. In evolutionary biology, analysis of maximum credibility trees in the software MEDUSA (modelling evolutionary diversity using stepwise AIC) is a popular method for estimation of shifts in diversification rates. We investigated whether phylogenetic uncertainty can produce different results by extending the method across a random sample of trees from the posterior distribution of a Bayesian run. Using the MultiMEDUSA approach, we found that phylogenetic uncertainty greatly affects diversification rate estimates. Different trees produced diversification rates ranging from high values to almost zero for the same clade, and both significant rate increase and decrease in some clades. Only four out of 18 significant shifts found on the maximum clade credibility tree were consistent across most of the sampled trees. Among these, we found accelerated diversification for Ithomiini butterflies. We used the binary speciation and extinction model (BiSSE) and found that a hostplant shift to Solanaceae is correlated with increased net diversification rates in Ithomiini, congruent with the diffuse cospeciation hypothesis. Our results show that taking phylogenetic uncertainty into account when estimating net diversification rate shifts is of great importance, as very different results can be obtained when using the maximum clade credibility tree and other trees from the posterior distribution.     

Testing the Effect of Metabolic Rate on DNA Variability at the Intra-Specific Level

We tested the metabolic rate hypothesis (whereby rates of mtDNA evolution are postulated to be mediated primarily by mutagenic by-products of respiration) by examining whether mass-specific metabolic rate was correlated with root-to-tip distance on a set of mtDNA trees for the springtail Cryptopygus antarcticus travei from sub-Antarctic Marion Island.Using Bayesian analyses and a novel application of the comparative phylogenetic method, we did not find significant evidence that contemporary metabolic rates directly correlate with mutation rate (i.e., root-to-tip distance) once the underlying phylogeny is taken into account. However, we did find significant evidence that metabolic rate is dependent on the underlying mtDNA tree, or in other words, lineages with related mtDNA also have similar metabolic rates.We anticipate that future analyses which apply this methodology to datasets with longer sequences, more taxa, or greater variability will have more power to detect a significant direct correlation between metabolic rate and mutation rate. We conclude with suggestions for future analyses that would extend the preliminary approach applied here, in particular highlighting ways to tease apart oxidative stress effects from the effects of population size and/or selection coefficients operating on the molecular evolutionary rate.     

Exploring the tempo of species diversification in legumes

Whatever criteria are used to measure evolutionary success – species numbers, geographic range, ecological abundance, ecological and life history diversity, background diversification rates, or the presence of rapidly evolving clades – the legume family is one of the most successful lineages of flowering plants. Despite this, we still know rather little about the dynamics of lineage and species diversification across the family through the Cenozoic, or about the underlying drivers of diversification. There have been few attempts to estimate net species diversification rates or underlying speciation and extinction rates for legume clades, to test whether among-lineage variation in diversification rates deviates from null expectations, or to locate species diversification rate shifts on specific branches of the legume phylogenetic tree. In this study, time-calibrated phylogenetic trees for a set of species-rich legume clades – Calliandra, Indigofereae, Lupinus, Mimosa and Robinieae – and for the legume family as a whole, are used to explore how we might approach these questions. These clades are analysed using recently developed maximum likelihood and Bayesian methods to detect species diversification rate shifts and test for among-lineage variation in speciation, extinction and net diversification rates. Possible explanations for rate shifts in terms of extrinsic factors and/or intrinsic trait evolution are discussed. In addition, several methodological issues and limitations associated with these analyses are highlighted emphasizing the potential to improve our understanding of the evolutionary dynamics of legume diversification by using much more densely sampled phylogenetic trees that integrate information across broad taxonomic, geographical and temporal levels.     

Relaxed phylogenetics and dating with confidence

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of “relaxed phylogenetics.” Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.     

Sperm size evolution in African greenbuls (Passeriformes: Pycnonotidae)

Sperm morphology is highly diversified across the animal kingdom and recent comparative evidence from passerine birds suggests that postcopulatory sexual selection is a significant driver of sperm evolution. In the present study, we describe sperm size variation among 20 species of African greenbuls and one bulbul (Passeriformes: Pycnonotidae) and analyze the evolutionary differentiation of sperm size within a phylogenetic framework. We found significant interspecific variation in sperm size; with some genera exhibiting relatively long sperm (e.g. Eurillas) and others exhibiting short sperm head lengths (e.g. Phyllastrephus). However, our results suggest that contemporary levels of sperm competition are unlikely to explain sperm diversification within this clade: the coefficients of inter‐male variation (CV_bm) in sperm length were generally high, suggesting relatively low and homogeneous rates of extra‐pair paternity. Finally, in a comparison of six evolutionary or tree transformation models, we found support for both the Kappa (evolutionary change primarily at nodes) and Lambda (lineage‐specific evolutionary rates along branches) models in the evolutionary trajectories of sperm size among species. We therefore conclude that African greenbuls have more variable rates of sperm size evolution than expected from a neutral model of genetic drift. Understanding the evolutionary dynamics of sperm diversification remains a future challenge.     

Ancestral inference and the study of codon bias evolution: implications for molecular evolutionary analyses of the Drosophila melanogaster subgroup

Reliable inference of ancestral sequences can be critical to identifying both patterns and causes of molecular evolution. Robustness of ancestral inference is often assumed among closely related species, but tests of this assumption have been limited. Here, we examine the performance of inference methods for data simulated under scenarios of codon bias evolution within the Drosophila melanogaster subgroup. Genome sequence data for multiple, closely related species within this subgroup make it an important system for studying molecular evolutionary genetics. The effects of asymmetric and lineage-specific substitution rates (i.e., varying levels of codon usage bias and departures from equilibrium) on the reliability of ancestral codon usage was investigated. Maximum parsimony inference, which has been widely employed in analyses of Drosophila codon bias evolution, was compared to an approach that attempts to account for uncertainty in ancestral inference by weighting ancestral reconstructions by their posterior probabilities. The latter approach employs maximum likelihood estimation of rate and base composition parameters. For equilibrium and most non-equilibrium scenarios that were investigated, the probabilistic method appears to generate reliable ancestral codon bias inferences for molecular evolutionary studies within the D. melanogaster subgroup. These reconstructions are more reliable than parsimony inference, especially when codon usage is strongly skewed. However, inference biases are considerable for both methods under particular departures from stationarity (i.e., when adaptive evolution is prevalent). Reliability of inference can be sensitive to branch lengths, asymmetry in substitution rates, and the locations and nature of lineage-specific processes within a gene tree. Inference reliability, even among closely related species, can be strongly affected by (potentially unknown) patterns of molecular evolution in lineages ancestral to those of interest.     

Recombination Detection Under Evolutionary Scenarios Relevant to Functional Divergence

Recombination can negatively impact methods designed to detect divergent gene function that rely on explicit knowledge of a gene tree. However, we know little about how recombination detection methods perform under evolutionary scenarios encountered in studies of functional molecular divergence. We use simulation to evaluate false positive rates for six recombination detection methods (GENECONV, MaxChi, Chimera, RDP, GARD-SBP, GARD-MBP) under evolutionary scenarios that might increase false positives. Broadly, these scenarios address: (i) asymmetric tree topology and sequence divergence, (ii) non-stationary codon bias and selection pressure, and (iii) positive selection. We also evaluate power to detect recombination under truly recombinant history. As with previous studies, we find that power increases with sequence divergence. However, we also find that accuracy to correctly infer the number of breakpoints is extremely low. When recombination is absent, increased sequence divergence leads to increased false positives. Furthermore, one method (GARD-SBP) is sensitive to tree shape, with higher false positive rates under an asymmetric tree topology. Somewhat surprisingly, all methods are robust to the simulated heterogeneity in codon bias, shifts in selection pressure and presence of positive selection. Based on these findings, we recommend that studies of functional divergence in systems where recombination is plausible can, and should, include a pre-test for recombination. Application of all methods to the core genome of Prochlorococcus reveals a substantial lack of concordance among results. Based on analysis of both real and simulated datasets we present some guidelines for the investigation of recombination in genes that may have experienced functional divergence.     

Fitting models of continuous trait evolution to incompletely sampled comparative data using approximate Bayesian computation

In recent years, a suite of methods has been developed to fit multiple rate models to phylogenetic comparative data. However, most methods have limited utility at broad phylogenetic scales because they typically require complete sampling of both the tree and the associated phenotypic data. Here, we develop and implement a new, tree-based method called MECCA (Modeling Evolution of Continuous Characters using ABC) that uses a hybrid likelihood/approximate Bayesian computation (ABC)-Markov-Chain Monte Carlo approach to simultaneously infer rates of diversification and trait evolution from incompletely sampled phylogenies and trait data. We demonstrate via simulation that MECCA has considerable power to choose among single versus multiple evolutionary rate models, and thus can be used to test hypotheses about changes in the rate of trait evolution across an incomplete tree of life. We finally apply MECCA to an empirical example of body size evolution in carnivores, and show that there is no evidence for an elevated rate of body size evolution in the pinnipeds relative to terrestrial carnivores. ABC approaches can provide a useful alternative set of tools for future macroevolutionary studies where likelihood-dependent approaches are lacking.