Estimating the rate of molecular evolution: incorporating non-contemporaneous sequences into maximum likelihood phylogenies

MOTIVATION: TipDate is a program that will use sequences that have been isolated at different dates to estimate their rate of molecular evolution. The program provides a maximum likelihood estimate of the rate and also the associated date of the most recent common ancestor of the sequences, under a model which assumes a constant rate of substitution (molecular clock) but which accommodates the dates of isolation. Confidence intervals for these parameters are also estimated. Results: The approach was applied to a sample of 17 dengue virus serotype 4 sequences, isolated at dates ranging from 1956 to 1994. The rate of substitution for this serotype was estimated to be 7.91 x 10(-4) substitutions per site per year (95% confidence intervals of 6.07 x 10(-4), 9.86 x 10(-4)). This is compatible with a date of 1922 (95% confidence intervals of 1900-1936) for the most recent common ancestor of these sequences. AVAILABILITY: TipDate can be obtained by WWW from http://evolve.zoo. ox.ac.uk/software. The package includes the source code, manual and example files. Both UNIX and Apple Macintosh versions are available from the same site.     

On the rate of molecular evolution

Summary There are at least two outstanding features that characterize the rate of evolution at the molecular level as compared with that at the phenotypic level. They are; (1) remarkable uniformity for each molecule, and (2) very high overall rate when extrapolated to the whole DNA content.The population dynamics for the rate of mutant substitution was developed, and it was shown that if mutant substitutions in the population are carried out mainly by natural selection, the rate of substitution is given byk = 4 N _e s ₁ v, whereN _e is the effective population number,s ₁ is the selective advantage of the mutants, andv is the mutation rate per gamete for such advantageous mutants (assuming that 4N _e s ₁ 1). On the other hand, if the substitutions are mainly carried out by random fixation of selectively neutral or nearly neutral mutants, we havek = v, wherev is the mutation rate per gamete for such mutants.Reasons were presented for the view that evolutionary change of amino acids in proteins has been mainly caused by random fixation of neutral mutants rather than by natural selection.It was concluded that if this view is correct, we should expect that genes of living fossils have undergone almost as many DNA base replacements as the corresponding genes of more rapidly evolving species.Contribution No. 789 from the National Institute of Genetics, Mishima, Shizuokaken 411 Japan. Aided in part by a grant-in-aid from the Ministry of Education, Japan.     

Sociality and the rate of molecular evolution

The molecular clock does not tick at a uniform rate in all taxa but may be influenced by species characteristics. Eusocial species (those with reproductive division of labor) have been predicted to have faster rates of molecular evolution than their nonsocial relatives because of greatly reduced effective population size; if most individuals in a population are nonreproductive and only one or few queens produce all the offspring, then eusocial animals could have much lower effective population sizes than their solitary relatives, which should increase the rate of substitution of "nearly neutral" mutations. An earlier study reported faster rates in eusocial honeybees and vespid wasps but failed to correct for phylogenetic nonindependence or to distinguish between potential causes of rate variation. Because sociality has evolved independently in many different lineages, it is possible to conduct a more wide-ranging study to test the generality of the relationship. We have conducted a comparative analysis of 25 phylogenetically independent pairs of social lineages and their nonsocial relatives, including bees, wasps, ants, termites, shrimps, and mole rats, using a range of available DNA sequences (mitochondrial and nuclear DNA coding for proteins and RNAs, and nontranslated sequences). By including a wide range of social taxa, we were able to test whether there is a general influence of sociality on rates of molecular evolution and to test specific predictions of the hypothesis: (1) that social species have faster rates because they have reduced effective population sizes; (2) that mitochondrial genes would show a greater effect of sociality than nuclear genes; and (3) that rates of molecular evolution should be correlated with the degree of sociality. We find no consistent pattern in rates of molecular evolution between social and nonsocial lineages and no evidence that mitochondrial genes show faster rates in social taxa. However, we show that the most highly eusocial Hymenoptera do have faster rates than their nonsocial relatives. We also find that social parasites (that utilize the workers from related species to produce their own offspring) have faster rates than their social relatives, which is consistent with an effect of lower effective population size on rate of molecular evolution. Our results illustrate the importance of allowing for phylogenetic nonindependence when conducting investigations of determinants of variation in rate of molecular evolution.     

Estimating the genomewide rate of adaptive protein evolution in Drosophila

When polymorphism and divergence data are available for multiple loci, extended forms of the McDonald-Kreitman test can be used to estimate the average proportion of the amino acid divergence due to adaptive evolution--a statistic denoted alpha. But such tests are subject to many biases. Most serious is the possibility that high estimates of alpha reflect demographic changes rather than adaptive substitution. Testing for between-locus variation in alpha is one possible way of distinguishing between demography and selection. However, such tests have yielded contradictory results, and their efficacy is unclear. Estimates of alpha from the same model organisms have also varied widely. This study clarifies the reasons for these discrepancies, identifying several method-specific biases in widely used estimators and assessing the power of the methods. As part of this process, a new maximum-likelihood estimator is introduced. This estimator is applied to a newly compiled data set of 115 genes from Drosophila simulans, each with each orthologs from D. melanogaster and D. yakuba. In this way, it is estimated that alpha approximately 0.4+/-0.1, a value that does not vary substantially between different loci or over different periods of divergence. The implications of these results are discussed.     

Mitochondrial whims: metabolic rate,longevity and the rate of molecular evolution

The evolutionary rate of mitochondrial DNA (mtDNA) is highly variable across lineages in animals, and particularly in mammals. This variation has been interpreted as reflecting variations in metabolic rate: mitochondrial respiratory activity would tend to generate mutagenic agents, thus increasing the mutation rate. Here we review recent evidence suggesting that a direct, mechanical effect of species metabolic rate on mtDNA evolutionary rate is unlikely. We suggest that natural selection could act to reduce the (somatic) mtDNA mutation rate in long-lived species, in agreement with the mitochondrial theory of ageing.     

Remarkably high rate of molecular evolution of ruminant placental lactogens

The sequences of ovine and bovine placental lactogens (based on published cDNA sequences) are remarkably different, indicating a very rapid rate of evolution. Analysis of the cDNA sequences indicates that the rate of nonsynonymous substitution in these proteins is considerably greater than the rate of synonymous substitution. This is an unusual situation, which suggests that the observed rapid rate of evolution is due to incorporation of adaptive rather than neutral mutations.     

Evidence for a slowed rate of molecular evolution in the order acipenseriformes

A test of the hypothesis that the members of the order Acipenseriformes (sturgeons and paddlefishes) possess a slowed rate of molecular evolution was carried out by conducting relative-rate comparisons with representatives of four groups of teleost fishes (Cypriniformes, Elopomorpha, Salmonidae, and Percomorpha) using 21 nuclear or mitochondrial protein loci and the nuclear and mitochondrial small subunit rRNA genes, obtained from the literature or our own research. In 70 out of 81 comparisons between individual taxa (86%), acipenseriform sequences showed slower rates of change than the homologous teleost loci examined. When teleost sequences are considered together, 21 of the 23 loci show slower rates of substitution in the acipenseriform lineage. Teleost proteins show 1.85 times as many unique amino acid differences as acipenseriform proteins, when both are compared with outlier sequences. These results support a hypothesis of slowed molecular evolutionary rate in the Acipenseriformes.     

Time scale of eutherian evolution estimated without assuming a constant rate of molecular evolution

Controversies over the molecular clock hypothesis were reviewed. Since it is evident that the molecular clock does not hold in an exact sense, accounting for evolution of the rate of molecular evolution is a prerequisite when estimating divergence times with molecular sequences. Recently proposed statistical methods that account for this rate variation are overviewed and one of these procedures is applied to the mitochondrial protein sequences and to the nuclear gene sequences from many mammalian species in order to estimate the time scale of eutherian evolution. This Bayesian method not only takes account of the variation of molecular evolutionary rate among lineages and among genes, but it also incorporates fossil evidence via constraints on node times. With denser taxonomic sampling and a more realistic model of molecular evolution, this Bayesian approach is expected to increase the accuracy of divergence time estimates.     

The rate of molecular evolution of alpha-fetoprotein approaches that of pseudogenes

We conducted the present study in an attempt to correlate function with the rate of molecular evolution for serum albumin and alpha-fetoprotein. We found a high rate of silent substitution (between 5 X 10(-9) and 7 X 10(-9)/site/year) for both the albumin and alpha-fetoprotein genes, perhaps the highest so far reported for an expressed nuclear gene. The rates of effective substitution and amino acid changes were also very high, but in contrast to silent substitutions, they are higher for alpha-fetoprotein than for albumin by approximately 70%. For alpha-fetoprotein, the rate of effective substitution (1.5 X 10(-9)/site/year) may be approaching that for nonfunctional pseudogenes (about 3 X 10(-9)/site/year). Evolutionary divergence was also estimated at the amino acid level. It was found that the rate of change of alpha-fetoprotein (55% amino acids replaced in 100 Myr) approaches that of the fastest-evolving fibrinopeptides (92% amino acids replaced in 100 Myr). This high rate may indicate that alpha-fetoprotein can tolerate a great deal of molecular variation without its function being impaired in the process. Albumin evolves at a slower rate (39% amino acids replaced in 100 Myr), although still faster than either hemoglobin (17% amino acids replaced in 100 Myr) or cytochrome c (5% amino acids replaced in 100 Myr). The slower evolutionary rate may indicate that albumin has more refined functional specifications and hence can tolerate fewer mutational changes. The latter conclusion remains, however, to be reconciled with the condition of inherited analbuminemia, where a virtually complete absence of albumin produces surprisingly few symptoms.     

A likelihood method for detecting trait-dependent shifts in the rate of molecular evolution

Rate heterogeneity within groups of organisms is known to exist even when closely related taxa are examined. A wide variety of phylogenetic and dating methods have been developed that aim either to test for the existence of rate variation or to correct for its bias. However, none of the existing methods track the evolution of features that account for observed rate heterogeneity. Here, we present a likelihood model that assumes that rate variation is caused, in part, by species' intrinsic characteristics, such as a particular life-history trait, morphological feature, or habitat association. The model combines models of sequence and character state evolution such that rates of sequence change depend on the character state of a lineage at each point in time. We test, using simulations, the power and accuracy of the model to determine whether rates of molecular evolution depend on a particular character state and demonstrate its utility using an empirical example with halophilic and freshwater daphniids.     

Why do species vary in their rate of molecular evolution?

Despite hopes that the processes of molecular evolution would be simple, clock-like and essentially universal, variation in the rate of molecular evolution is manifest at all levels of biological organization. Furthermore, it has become clear that rate variation has a systematic component: rate of molecular evolution can vary consistently with species body size, population dynamics, lifestyle and location. This suggests that the rate of molecular evolution should be considered part of life-history variation between species, which must be taken into account when interpreting DNA sequence differences between lineages. Uncovering the causes and correlates of rate variation may allow the development of new biologically motivated models of molecular evolution that may improve bioinformatic and phylogenetic analyses.     

Estimating the rate of photorespiration in leaves

The influence of Li⁺ on the circumnutations of hypocotyls of Helianthus annuus L . cv. Californicus was investigated. LiCl at concentration levels from 0 to 40 m M (lethal) was added to intact hypocotyls grown in liquid nutrient medium. The Li⁺ concentration in the hypocotyls was measured by flame photometry. The growth of the hypocotyls was not affected by the LiCl.
Amplitude and frequency of the circumnutations were determined by correlation analysis. The oscillatory pattern of the movements became less regular at concentrations above 10 m M LiCl. The amplitude of the movements was reduced for concentrations above 7 m M LiCl. The frequency of the movements was reduced when LiCl was increased from 0 to 10 m M . Above 10 m M LiCl the frequency of the circumnutations was higher than for control plants. The results showed that circumnutations of sunflower hypocotyls can be added to the group of oscillators in biological organisms that are affected by Li⁺.     

A generation‐time effect on the rate of molecular evolution in bacteria

Molecular evolutionary rate varies significantly among species and a strict global molecular clock has been rejected across the tree of life. Generation time is one primary life‐history trait that influences the molecular evolutionary rate. Theory predicts that organisms with shorter generation times evolve faster because of the accumulation of more DNA replication errors per unit time. Although the generation‐time effect has been demonstrated consistently in plants and animals, the evidence of its existence in bacteria is lacking. The bacterial phylum Firmicutes offers an excellent system for testing generation‐time effect because some of its members can enter a dormant, nonreproductive endospore state in response to harsh environmental conditions. It follows that spore‐forming bacteria would—with their longer generation times—evolve more slowly than their nonspore‐forming relatives. It is therefore surprising that a previous study found no generation‐time effect in Firmicutes. Using a phylogenetic comparative approach and leveraging on a large number of Firmicutes genomes, we found sporulation significantly reduces the genome‐wide spontaneous DNA mutation rate and protein evolutionary rate. Contrary to the previous study, our results provide strong evidence that the evolutionary rates of bacteria, like those of plants and animals, are influenced by generation time.     

Molecular clocks in reptiles: life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between body size and substitution rate for many molecular data sets. Both the generality and the cause of the negative body size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size, age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles, lizards, snakes, crocodile, and tuatara. Although this study was limited by the number of comparisons for which both sequence and life-history data were available, the results suggest that a negative body size trend in rate of molecular evolution may be a general feature of reptile molecular evolution, consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.     

Speciation, introgressive hybridization and nonlinear rate of molecular evolution in flycatchers

Evolutionary history of Muscicapidae flycatchers is inferred from nuclear and mitochondrial DNA (mtDNA) sequence comparisons and population genetic analysis of nuclear and mtDNA markers. Phylogenetic reconstruction based on sequences from the two genomes yielded similar trees with respect to the order at which the species split off. However, the genetic distances fitted a nonlinear, polynomial model reflecting diminishing divergence rate of the mtDNA sequences compared to the nuclear DNA sequences. This could be explained by Haldane's rule because genetic isolation might evolve more rapidly on the mitochondrial rather than the nuclear genome in birds. This is because hybrid sterility of the heterogametic sex (females) would predate that of the homogametic sex (males), leading to sex biased introgression of nuclear genes. Analyses of present hybrid zones of pied (Ficedula hypoleuca) and collared flycatchers (F. albicollis) may indicate a slight sexual bias in rate of introgression, but the introgression rates were too low to allow proper statistical analyses. It is suggested, however, that the observed deviation from linearity can be explained by a more rapid mutational saturation of the mtDNA sequences than of the nuclear DNA sequences, as supported by analyses of third codon position transversions at two protein coding mtDNA genes. A phylogeographic scenario for the black and white flycatcher species is suggested based on interpretation of the genetic data obtained. Four species appear to have diverged from a common ancestor relatively simultaneously during the Pleistocene. After the last glaciation period, pied and collared flycatchers expanded their breeding ranges and eventually came into secondary contact in Central and Eastern Europe and on the Baltic Isles.     

Estimating absolute rates of molecular evolution and divergence times: a penalized likelihood approach.

Rates of molecular evolution vary widely between lineages, but quantification of how rates change has proven difficult. Recently proposed estimation procedures have mainly adopted highly parametric approaches that model rate evolution explicitly. In this study, a semiparametric smoothing method is developed using penalized likelihood. A saturated model in which every lineage has a separate rate is combined with a roughness penalty that discourages rates from varying too much across a phylogeny. A data-driven cross-validation criterion is then used to determine an optimal level of smoothing. This criterion is based on an estimate of the average prediction error associated with pruning lineages from the tree. The methods are applied to three data sets of six genes across a sample of land plants. Optimally smoothed estimates of absolute rates entailed 2- to 10-fold variation across lineages.     

Estimating the division rate for the growth-fragmentation equation

Growth-fragmentation equations arise in many different contexts, ranging from cell division, protein polymerization, neurosciences etc. Direct observation of temporal dynamics being often difficult, it is of main interest to develop theoretical and numerical methods to recover reaction rates and parameters of the equation from indirect observation of the solution. Following the work done in Perthame and Zubelli (Inverse Probl 23:1037–1052, 2007) and Doumic et al. (2009) for the specific case of the cell division equation, we address here the general question of recovering the fragmentation rate of the equation from the observation of the time-asymptotic solution, when the fragmentation kernel and the growth rates are fully general. We give both theoretical results and numerical methods, and discuss the remaining issues.     

Effect of demographic population factors and individual biological parameters on the rate of neutral molecular evolution

The dependence of the rate of neutral molecular evolution on biological parameters and demographic population factors was studied based on actual genetic information as an example and using the individual-oriented model of population dynamics. The first part of the study deals with tracing the neutral evolution occurring in the model concurrently with adaptive speciation. The second part concerns the effect of individual biological parameters and demographic population factors of members of the order Testudines (turtles) on the relative evolution rate of the mitochondrial CytB gene. Demographic population factors and individual biological parameters are shown to affect the rate of molecular evolution.