PHYLOGENETIC ANALYSIS OF THE EVOLUTIONARY CORRELATION USING LIKELIHOOD

Many evolutionary processes can lead to a change in the correlation between continuous characters over time or on different branches of a phylogenetic tree. Shifts in genetic or functional constraint, in the selective regime, or in some combination thereof can influence both the evolution of continuous traits and their relation to each other. These changes can often be mapped on a phylogenetic tree to examine their influence on multivariate phenotypic diversification. We propose a new likelihood method to fit multiple evolutionary rate matrices (also called evolutionary variance–covariance matrices) to species data for two or more continuous characters and a phylogeny. The evolutionary rate matrix is a matrix containing the evolutionary rates for individual characters on its diagonal, and the covariances between characters (of which the evolutionary correlations are a function) elsewhere. To illustrate our approach, we apply the method to an empirical dataset consisting of two features of feeding morphology sampled from 28 centrarchid fish species, as well as to data generated via phylogenetic numerical simulations. We find that the method has appropriate type I error, power, and parameter estimation. The approach presented herein is the first to allow for the explicit testing of how and when the evolutionary covariances between characters have changed in the history of a group.     

Limb morphogenesis in the branchiopod crustacean, Thamnocephalus platyurus, and the evolution of proximal limb lobes within Anostraca

Crustacean limbs exhibit highly diverse morphologies. One major route of diversification is in the number and position of branches arising from the proximal part of the limb. Here I describe development of larvae of the branchiopod crustacean, Thamnocephalus platyurus and describe in detail the development of the thoracic limbs. The thoracic limbs bear proximal branches both medially and laterally. The most proximal branches on either side (gnathobase and pre-epipod) show a similar developmental history: they develop via fusion of two rudiments into a single adult branch. However, phylogenetic analysis suggests that the developmental fusions have distinct evolutionary histories. In one case (gnathobase), the developmental rudiments reflect the ancestral adult morphology of two distinct branches. In the other (pre-epipod), the rudiments are an apparent novelty within the Anostraca and develop into two adult structures in only a single derived family.     

Detecting Site-Specific Biochemical Constraints Through Substitution Mapping

The neutral theory of molecular evolution states that most mutations are deleterious or neutral. It results that the evolutionary rate of a given position in an alignment is a function of the level of constraint acting on this position. Inferring evolutionary rates from a set of aligned sequences is hence a powerful method to detect functionally and/or structurally important positions in a protein. Some positions, however, may be constrained while having a high substitution rate, providing these substitutions do not affect the biochemical property under constraint. Here, I introduce a new evolutionary rate measure accounting for the evolution of specific biochemical properties (e.g., volume, polarity, and charge). I then present a new statistical method based on the comparison of two rate measures: a site is said to be constrained for property X if it shows an unexpectedly high conservation of X knowing its total evolutionary rate. Compared to single-rate methods, the two-rate method offers several advantages: it (i) allows assessment of the significance of the constraint, (ii) provides information on the type of constraint acting on each position, and (iii) detects positions that are not proposed by previous methods. I apply this method to a 200-sequence data set of triosephosphate isomerase and report significant cases of positions constrained for polarity, volume, or charge. The three-dimensional localization of these positions shows that they are of potential interest to the molecular evolutionist and to the biochemist.     

Evolution of RNA polymerases and branching patterns of the three major groups of archaebacteria

Summary The amino acid sequences of the largest subunits of the RNA polymerases I, II, and III from eukaryotes were compared with those of archaebacterial and eubacterial homologs, and their evolutionary relationships were analyzed in detail by a recently developed tree-making method, the likelihood method of protein phylogeny, as well as by the neighbor-joining method and the parsimony method, together with bootstrap analyses. It was shown that the best tree topologies predicted by the first two methods are identical, whereas the last one predicts a distinct tree. The maximum likelihood tree revealed that, after the separation from archaebacteria, the three eukaryotic RNA polymerases diverged from an ancestral precursor in the eukaryotic lineage. This result is contrasted with the published result showing multiple origins for the three eukaryotic polymerases. It was shown that eukaryotic RNA polymerase I evolved much more rapidly than RNA polymerases II and III: The N-terminal half of RNA polymerase I shows an extraordinarily high evolutionary rate, possibly due to relaxed functional constraints. In contrast the evolutionary rate of archaebacterial RNA polymerase is remarkably limited. In addition, including the second largest subunit of the RNA polymerase, a detailed analysis for the branching pattern of the three major groups of archaebacteria was carried out by the maximum likelihood method. It was shown that the three major groups of archaebacteria are likely to form a single cluster; that is, archaebacteria are likely to be monophyletic as originally proposed by Woese and his colleagues.     

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.]     

Adaptive diversification of germination strategies.

Evolution of the germination rate (the proportion of newly produced and dormant seeds that germinates every year) of annual plants is investigated, when the environment is temporally stochastic and spatially heterogeneous. The environment consists of two habitats with synchronous stochastic variation in the annual yield and permanent difference in constant seed survival rates. Density dependence operates within the habitats, which are connected via restricted seed dispersal. We find that instead of a single common evolutionarily stable strategy the coexistence of several germination strategies is possible and that in an initially monomorphic population evolutionary branching may occur. During evolutionary branching the population undergoes disruptive selection and splits into two branches of different lineages that converge to the evolutionarily stable coalition of different germination strategies. It is shown that spatial heterogeneity and restricted dispersal are essential for evolutionary branching. Disruptive selection on the germination rate presents yet another possibility for parapatric speciation.     

PHYLOGENETIC ANALYSES OF THE CORRELATED EVOLUTION OF CONTINUOUS CHARACTERS: A SIMULATION STUDY

We use computer simulation to compare the statistical properties of several methods that have been proposed for estimating the evolutionary correlation between two continuous traits, and define alternative evolutionary correlations that may be of interest. We focus on Felsenstein's (1985) method and some variations of it and on several “minimum evolution” methods (of which the procedure of Huey and Bennett [1987] is a special case), as compared with a nonphylogenetic correlation. The last, a simple correlation of trait values across the tips of a phylogeny, virtually always yields inflated Type I error rates, relatively low power, and relatively poor estimates of evolutionary correlations. We therefore cannot recommend its use. In contrast, Felsenstein's (1985) method yields acceptable significance tests, high power, and good estimates of what we term the input correlation and the standardized realized evolutionary correlation, given complete phylogenetic information and knowledge of the rate and mode of character change (e.g., gradual and proportional to time [“Brownian motion”] or punctuational, with change only at speciation events). Inaccurate branch length information may affect any method adversely, but only rarely does it cause Felsenstein's (1985) method to perform worse than do the others tested. Other proposed methods generally yield inflated Type I error rates and have lower power. However, certain minimum evolution methods (although not the specific procedure used by Huey and Bennett [1987]) often provide more accurate estimates of what we term the unstandardized realized evolutionary correlation, and their use is recommended when estimation of this correlation is desired. We also demonstrate how correct Type I error rates can be obtained for any method by reference to an empirical null distribution derived from computer simulations, and provide practical suggestions on choosing an analytical method, based both on the evolutionary correlation of interest and on the availability of branch lengths and knowledge of the model of evolutionary change appropriate for the characters being analyzed. Computer programs that implement the various methods and that will simulate (correlated) character evolution along a known phylogeny are available from the authors on request. These programs can be used to test the effectiveness of any new methods that might be proposed, and to check the generality of our conclusions with regard to other phylogenies.     

Additive Uncorrelated Relaxed Clock Models for the Dating of Genomic Epidemiology Phylogenies

Phylogenetic dating is one of the most powerful and commonly used methods of drawing epidemiological interpretations from pathogen genomic data. Building such trees requires considering a molecular clock model which represents the rate at which substitutions accumulate on genomes. When the molecular clock rate is constant throughout the tree then the clock is said to be strict, but this is often not an acceptable assumption. Alternatively, relaxed clock models consider variations in the clock rate, often based on a distribution of rates for each branch. However, we show here that the distributions of rates across branches in commonly used relaxed clock models are incompatible with the biological expectation that the sum of the numbers of substitutions on two neighboring branches should be distributed as the substitution number on a single branch of equivalent length. We call this expectation the additivity property. We further show how assumptions of commonly used relaxed clock models can lead to estimates of evolutionary rates and dates with low precision and biased confidence intervals. We therefore propose a new additive relaxed clock model where the additivity property is satisfied. We illustrate the use of our new additive relaxed clock model on a range of simulated and real data sets, and we show that using this new model leads to more accurate estimates of mean evolutionary rates and ancestral dates.     

Reconciling extreme branch length differences: decoupling time and rate through the evolutionary history of filmy ferns

The rate of molecular evolution is not constant across the Tree of Life. Characterizing rate discrepancies and evaluating the relative roles of time and rate along branches through the past are both critical to a full understanding of evolutionary history. In this study, we explore the interactions of time and rate in filmy ferns (Hymenophyllaceae), a lineage with extreme branch length differences between the two major clades. We test for the presence of significant rate discrepancies within and between these clades, and we separate time and rate across the filmy fern phylogeny to simultaneously yield an evolutionary time scale of filmy fern diversification and reconstructions of ancestral rates of molecular evolution. Our results indicate that the branch length disparity observed between the major lineages of filmy ferns is indeed due to a significant difference in molecular evolutionary rate. The estimation of divergence times reveals that the timing of crown group diversification was not concurrent for the two lineages, and the reconstruction of ancestral rates of molecular evolution points to a substantial rate deceleration in one of the clades. Further analysis suggests that this may be due to a genome-wide deceleration in the rate of nucleotide substitution.     

The minimum number of mutations in an evolutionary network

The problem when given an evolutionary network representing the ancestral relationships between either a set of proteins, or a set of RNA molecules, is to determine the numbers of mutations along the single branches of the network in such a way that their sum, i.e. the number of mutations in the complete network, is as small as possible. In case of proteins either amino acid substitutions, or nucleotide substitutions may be considered. It is shown that such problems are equivalent to an integer linear programming problem which generally has multiple solutions. In fact, the numbers of mutations along the single branches of the network may not uniquely be determined by sequence data and network topology. However, their sum is unique and is a measure for the probability to describe evolution properly, assigned to this network by the maximum parsimony hypothesis.     

When does the incongruence length difference test fail?

This paper examines the efficiency of the incongruence length difference test (ILD) proposed by Farris et al. (1994) for assessing the incongruence between sets of characters. DNA sequences were simulated under various evolutionary conditions: (1) following symmetric or asymmetric trees, (2) with various mutation rates, (3) with constant or variable evolutionary rates along the branches, and (4) with different among-site substitution rates. We first compared two sets of sequences generated along the same tree and under the same evolutionary conditions. The probability of a Type-I error (wrongly rejecting the true hypothesis of congruence) was substantially below the standard 5% level of significance given by the ILD test; this finding indicates that the choice of the 5% level is rather conservative in this case. We then compared two data sets, still generated along the same tree, but under different evolutionary conditions (constant vs. variable evolutionary rate, homogeneity vs. heterogeneity rate of substitution). Under these conditions, the probability of rejecting the true hypothesis of congruence was greater than the 5% given by the ILD test and increased with the number of sites and the degree to which the tree was asymmetric. Finally, the comparison of the two data sets, simulated under contrasting tree structures (symmetric vs. asymmetric) but under the same evolutionary conditions, led us to reject the hypothesis of congruence, albeit weakly, particularly when the number of informative sites was low and among-site substitution rate heterogeneous. We conclude that the ILD test has only limited power to detect incongruence caused by differences in the evolutionary conditions or in the tree topology, except when numerous characters are present and the substitution rate is homogeneous from site to site.     

THE EFFECT OF BIASED INCLUSION OF TAXA ON THE CORRELATION BETWEEN DISCRETE CHARACTERS IN PHYLOGENETIC TREES

In a published paper, a method for testing the correlation between two discrete characters was presented and applied to test whether in butterfly larvae origins of gregariousness are concentrated to lineages with aposematic coloration. The relationship was found to be nonsignificant. However, the butterfly data on which the test was applied had been compiled in another study to investigate evolutionary sequences and was biased, because there was an overrepresentation of aposematic, as compared to cryptic, branches in the sample. In the paper presented here, aposematic and cryptic clades of the original phylogeny were resolved to the same degree, and the resulting set of branches may be regarded as unbiased with respect to the hypothesis being tested. A method for testing the contingency of states in two characters was then applied to the new data set, resulting in a highly significant relationship between origins of gregariousness and aposematic coloration. I argue that when using statistical methods on phylogenetic data, it is crucial to resolve various parts of the phylogeny to the same comparable systematic unit in order not to get a distorted sample of taxa/branches.     

Comparison of likelihood and Bayesian methods for estimating divergence times using multiple gene Loci and calibration points, with application to a radiation of cute-looking mouse lemur species

Divergence time and substitution rate are seriously confounded in phylogenetic analysis, making it difficult to estimate divergence times when the molecular clock (rate constancy among lineages) is violated. This problem can be alleviated to some extent by analyzing multiple gene loci simultaneously and by using multiple calibration points. While different genes may have different patterns of evolutionary rate change, they share the same divergence times. Indeed, the fact that each gene may violate the molecular clock differently leads to the advantage of simultaneous analysis of multiple loci. Multiple calibration points provide the means for characterizing the local evolutionary rates on the phylogeny. In this paper, we extend previous likelihood models of local molecular clock for estimating species divergence times to accommodate multiple calibration points and multiple genes. Heterogeneity among different genes in evolutionary rate and in substitution process is accounted for by the models. We apply the likelihood models to analyze two mitochondrial protein-coding genes, cytochrome oxidase II and cytochrome b, to estimate divergence times of Malagasy mouse lemurs and related outgroups. The likelihood method is compared with the Bayes method of Thorne et al. (1998, Mol. Biol. Evol. 15:1647-1657), which uses a probabilistic model to describe the change in evolutionary rate over time and uses the Markov chain Monte Carlo procedure to derive the posterior distribution of rates and times. Our likelihood implementation has the drawbacks of failing to accommodate uncertainties in fossil calibrations and of requiring the researcher to classify branches on the tree into different rate groups. Both problems are avoided in the Bayes method. Despite the differences in the two methods, however, data partitions and model assumptions had the greatest impact on date estimation. The three codon positions have very different substitution rates and evolutionary dynamics, and assumptions in the substitution model affect date estimation in both likelihood and Bayes analyses. The results demonstrate that the separate analysis is unreliable, with dates variable among codon positions and between methods, and that the combined analysis is much more reliable. When the three codon positions were analyzed simultaneously under the most realistic models using all available calibration information, the two methods produced similar results. The divergence of the mouse lemurs is dated to be around 7-10 million years ago, indicating a surprisingly early species radiation for such a morphologically uniform group of primates.     

Purifying Selection Determines the Short-Term Time Dependency of Evolutionary Rates in SARS-CoV-2 and pH1N1 Influenza

High-throughput sequencing enables rapid genome sequencing during infectious disease outbreaks and provides an opportunity to quantify the evolutionary dynamics of pathogens in near real-time. One difficulty of undertaking evolutionary analyses over short timescales is the dependency of the inferred evolutionary parameters on the timespan of observation. Crucially, there are an increasing number of molecular clock analyses using external evolutionary rate priors to infer evolutionary parameters. However, it is not clear which rate prior is appropriate for a given time window of observation due to the time-dependent nature of evolutionary rate estimates. Here, we characterize the molecular evolutionary dynamics of SARS-CoV-2 and 2009 pandemic H1N1 (pH1N1) influenza during the first 12 months of their respective pandemics. We use Bayesian phylogenetic methods to estimate the dates of emergence, evolutionary rates, and growth rates of SARS-CoV-2 and pH1N1 over time and investigate how varying sampling window and data set sizes affect the accuracy of parameter estimation. We further use a generalized McDonald–Kreitman test to estimate the number of segregating nonneutral sites over time. We find that the inferred evolutionary parameters for both pandemics are time dependent, and that the inferred rates of SARS-CoV-2 and pH1N1 decline by ∼50% and ∼100%, respectively, over the course of 1 year. After at least 4 months since the start of sequence sampling, inferred growth rates and emergence dates remain relatively stable and can be inferred reliably using a logistic growth coalescent model. We show that the time dependency of the mean substitution rate is due to elevated substitution rates at terminal branches which are 2–4 times higher than those of internal branches for both viruses. The elevated rate at terminal branches is strongly correlated with an increasing number of segregating nonneutral sites, demonstrating the role of purifying selection in generating the time dependency of evolutionary parameters during pandemics.     

Evaluation of methods for determination of a reconstructed history of gene sequence evolution

With whole-genome sequences being completed at an increasing rate, it is important to develop and assess tools to analyze them. Following annotation of the protein content of a genome, one can compare sequences with previously characterized homologous genes to detect novel functions within specific proteins in the evolution of the newly sequenced genome. One common statistical method to detect such changes is to compare the ratios of nonsynonymous (K(a)) to synonymous (K(s)) nucleotide substitution rates. Here, the effects of several parameters that can influence this calculation (sequence reconstruction method, phylogenetic tree branch length weighting, GC content, and codon bias) are examined. Also, two new alternative measures of adaptive evolution, the point accepted mutations (PAM)/neutral evolutionary distance (NED) ratio and the sequence space assessment (SSA) statistic are presented. All of these methods are compared using two sequence families: the recent divergence of leptin orthologs in primates, and the more ancient divergence of the deoxyribonucleoside kinase family. The examination of these and other measures to detect changes of gene function along branches of a phylogenetic tree will become increasingly important in the postgenomic era.     

A random effects branch-site model for detecting episodic diversifying selection

Adaptive evolution frequently occurs in episodic bursts, localized to a few sites in a gene, and to a small number of lineages in a phylogenetic tree. A popular class of "branch-site" evolutionary models provides a statistical framework to search for evidence of such episodic selection. For computational tractability, current branch-site models unrealistically assume that all branches in the tree can be partitioned a priori into two rigid classes--"foreground" branches that are allowed to undergo diversifying selective bursts and "background" branches that are negatively selected or neutral. We demonstrate that this assumption leads to unacceptably high rates of false positives or false negatives when the evolutionary process along background branches strongly deviates from modeling assumptions. To address this problem, we extend Felsenstein's pruning algorithm to allow efficient likelihood computations for models in which variation over branches (and not just sites) is described in the random effects likelihood framework. This enables us to model the process at every branch-site combination as a mixture of three Markov substitution models--our model treats the selective class of every branch at a particular site as an unobserved state that is chosen independently of that at any other branch. When benchmarked on a previously published set of simulated sequences, our method consistently matched or outperformed existing branch-site tests in terms of power and error rates. Using three empirical data sets, previously analyzed for episodic selection, we discuss how modeling assumptions can influence inference in practical situations.     

Analysis on the reconstruction accuracy of the Fitch method for inferring ancestral states

Background  

As one of the most widely used parsimony methods for ancestral reconstruction, the Fitch method minimizes the total number of hypothetical substitutions along all branches of a tree to explain the evolution of a character. Due to the extensive usage of this method, it has become a scientific endeavor in recent years to study the reconstruction accuracies of the Fitch method. However, most studies are restricted to 2-state evolutionary models and a study for higher-state models is needed since DNA sequences take the format of 4-state series and protein sequences even have 20 states.     

THE ORIGIN OF WEST EUROPEAN SUBSPECIES OF HONEYBEES (APIS MELLIFERA): NEW INSIGHTS FROM MICROSATELLITE AND MITOCHONDRIAL DATA

Apis mellifera is composed of three evolutionary branches including mainly African (branch A), western and northern European (branch M), and southeastern European (branch C) populations. The existence of morphological clines extending from the equator to the Polar Circle through Morocco and Spain raised the hypothesis that the branch M originated in Africa. Mitochondrial DNA analysis revealed that branches A and M were characterized by highly diverged lineages implying very remote links between both branches. It also revealed that mtDNA haplotypes from lineages A coexisted with haplotypes M in the Iberian Peninsula and formed a south-north frequency cline, suggesting that this area could be a secondary contact zone between the two branches. By analyzing 11 populations sampled along a France-Spain/Portugal-Morocco-Guinea transect at 8 microsatellite loci and the DraI RFLP of the COI-COII mtDNA marker, we show that Iberian populations do not present any trace of “africanization” and are very similar to French populations when considering microsatellite markers. Therefore, the Iberian Peninsula is not a transition area. The higher haplotype A variability observed in Spanish and Portuguese samples compared to that found in Africa is explained by a higher mutation rate and multiple and recent introductions. Selection appears to be the best explanation to the morphological and allozymic clines and to the diffusion and maintenance of African haplotypes in Spain and Portugal.     

A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony

The method of evolutionary parsimony--or operator invariants--is a technique of nucleic acid sequence analysis related to parsimony analysis and explicitly designed for determining evolutionary relationships among four distantly related taxa. The method is independent of substitution rates because it is derived from consideration of the group properties of substitution operators rather than from an analysis of the probabilities of substitution in branches of a tree. In both parsimony and evolutionary parsimony, three patterns of nucleotide substitution are associated one-to-one with the three topologically linked trees for four taxa. In evolutionary parsimony, the three quantities are operator invariants. These invariants are the remnants of substitutions that have occurred in the interior branch of the tree and are analogous to the substitutions assigned to the central branch by parsimony. The two invariants associated with the incorrect trees must equal zero (statistically), whereas only the correct tree can have a nonzero invariant. The chi 2-test is used to ascertain the nonzero invariant and the statistically favored tree. Examples, obtained using data calculated with evolutionary rates and branchings designed to camouflage the true tree, show that the method accurately predicts the tree, even when substitution rates differ greatly in neighboring peripheral branches (conditions under which parsimony will consistently fail). As the number of substitutions in peripheral branches becomes fewer, the parsimony and the evolutionary-parsimony solutions converge. The method is robust and easy to use.      

Revisiting the concept of lineage in prokaryotes: a phylogenetic perspective

Mutation and lateral transfer are two categories of processes generating genetic diversity in prokaryotic genomes. Their relative importance varies between lineages, yet both are complementary rather than independent, separable evolutionary forces. The replication process inevitably merges together their effects on the genome. We develop the concept of “open lineages” to characterize evolutionary lineages that over time accumulate more changes in their genomes by lateral transfer than by mutation. They contrast with “closed lineages,” in which most of the changes are caused by mutation. Open and closed lineages are interspersed along the branches of any tree of prokaryotes. This patchy distribution conflicts with the basic assumptions of traditional phylogenetic approaches. As a result, a tree representation including both open and closed lineages is a misrepresentation. The evolution of all prokaryotic lineages cannot be studied under a single model unless new phylogenetic approaches that are more pluralistic about lineage evolution are designed.