Molecular‐clock methods for estimating evolutionary rates and timescales

The molecular clock presents a means of estimating evolutionary rates and timescales using genetic data. These estimates can lead to important insights into evolutionary processes and mechanisms, as well as providing a framework for further biological analyses. To deal with rate variation among genes and among lineages, a diverse range of molecular‐clock methods have been developed. These methods have been implemented in various software packages and differ in their statistical properties, ability to handle different models of rate variation, capacity to incorporate various forms of calibrating information and tractability for analysing large data sets. Choosing a suitable molecular‐clock model can be a challenging exercise, but a number of model‐selection techniques are available. In this review, we describe the different forms of evolutionary rate heterogeneity and explain how they can be accommodated in molecular‐clock analyses. We provide an outline of the various clock methods and models that are available, including the strict clock, local clocks, discrete clocks and relaxed clocks. Techniques for calibration and clock‐model selection are also described, along with methods for handling multilocus data sets. We conclude our review with some comments about the future of molecular clocks.     

Bayesian random local clocks,or one rate to rule them all

Background  

Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 2^2n-2 possible rate models available for averaging with 1, 2, ..., 2n - 2 different rate categories.     

Correcting for Purifying Selection: An Improved Human Mitochondrial Molecular Clock

There is currently no calibration available for the whole human mtDNA genome, incorporating both coding and control regions. Furthermore, as several authors have pointed out recently, linear molecular clocks that incorporate selectable characters are in any case problematic. We here confirm a modest effect of purifying selection on the mtDNA coding region and propose an improved molecular clock for dating human mtDNA, based on a worldwide phylogeny of > 2000 complete mtDNA genomes and calibrating against recent evidence for the divergence time of humans and chimpanzees. We focus on a time-dependent mutation rate based on the entire mtDNA genome and supported by a neutral clock based on synonymous mutations alone. We show that the corrected rate is further corroborated by archaeological dating for the settlement of the Canary Islands and Remote Oceania and also, given certain phylogeographic assumptions, by the timing of the first modern human settlement of Europe and resettlement after the Last Glacial Maximum. The corrected rate yields an age of modern human expansion in the Americas at ∼15 kya that—unlike the uncorrected clock—matches the archaeological evidence, but continues to indicate an out-of-Africa dispersal at around 55–70 kya, 5–20 ky before any clear archaeological record, suggesting the need for archaeological research efforts focusing on this time window. We also present improved rates for the mtDNA control region, and the first comprehensive estimates of positional mutation rates for human mtDNA, which are essential for defining mutation models in phylogenetic analyses.     

Quantitative genetic variation and developmental clocks

It is well-known that most genetic variation affects quantitative traits, and natural or artificial selection can act to change quantitative features of organisms more rapidly than qualitative ones. Surprisingly, variability is not confined to outbred species, but also occurs in inbred mice at a much higher rate than expected from known mutation rates. The size and shape of organisms and their constituent parts are, at least in part, controlled by the number of cell divisions, and there is published evidence for the existence of developmental clocks, which may count cell divisions. A molecular model for a developmental clock was previously proposed. It depends on the DNA methylation of repeated sequences of DNA, where the methylation of each additional sequence is tied to DNA synthesis and therefore cell division. The number of repeats specifies the number of divisions which will occur before a signal is produced which can activate or inactivate one or more genes. It is known that crossing over occurs between sister chromatids, and where tandemly repeated sequences occur unequal exchange can generate a larger or smaller number of repeats. An example of this is seen in the well-known variability of "minisatellite" sequences in human DNA. Unequal sister chromatid exchange can occur in mitotic and meiotic cells in the germ line, and in the case of developmental clock sequences could generate variation in clock length which in turn would directly affect quantitative traits. These events can be regarded as a special case of molecular drive during evolution.     

Calibration of multiple poliovirus molecular clocks covering an extended evolutionary range

We have calibrated five different molecular clocks for circulating poliovirus based upon the rates of fixation of total substitutions (K(t)), synonymous substitutions (K(s)), synonymous transitions (A(s)), synonymous transversions (B(s)), and nonsynonymous substitutions (K(a)) into the P1/capsid region (2,643 nucleotides). Rates were determined over a 10-year period by analysis of sequences of 31 wild poliovirus type 1 isolates representing a well-defined phylogeny derived from a common imported ancestor. Similar rates were obtained by linear regression, the maximum likelihood/single-rate dated-tip method, and Bayesian inference. The very rapid K(t) [(1.03 +/- 0.10) x 10(-2) substitutions/site/year] and K(s) [(1.00 +/- 0.08) x 10(-2)] clocks were driven primarily by the A(s) clock [(0.96 +/- 0.09) x 10(-2)], the B(s) clock was approximately 10-fold slower [(0.10 +/- 0.03) x 10(-2)], and the more stochastic K(a) clock was approximately 30-fold slower [(0.03 +/- 0.01) x 10(-2)]. Nonsynonymous substitutions at all P1/capsid sites, including the neutralizing antigenic sites, appeared to be constrained by purifying selection. Simulation of the evolution of third-codon positions suggested that saturation of synonymous transitions would be evident at 10 years and complete at approximately 65 years of independent transmission. Saturation of synonymous transversions was predicted to be minimal at 20 years and incomplete at 100 years. The rapid evolution of the K(t), K(s), and A(s) clocks can be used to estimate the dates of divergence of closely related viruses, whereas the slower B(s) and K(a) clocks may be used to explore deeper evolutionary relationships within and across poliovirus genotypes.     

Molecular clocks and evolutionary relationships: Possible distortions due to horizontal gene flow

Summary This paper discusses recent evidence suggesting that genetic information from one species occasionally transfers to another remotely related species. Besides addressing the issue of whether or not the molecular data are consistent with a wide-spread influence of horizontal gene transfer, the paper shows that horizontal gene flow would not necessarily preclude a linear molecular clock or change the rate of molecular evolution (assuming the neutral allele theory). A pervasive influence of horizontal gene transfer is more than just consistent with the data of molecular evolution, it also provides a unique explanation for a number of possibly conflicting phylogenies and contradictory clocks. This phenomenon might explain why some protein clocks are linear while the superoxide dismutase clock is not, how the molecular data on the phylogeny of apes and Australian song birds are not necessarily in conflict with those based on morphology, and, finally, why the mycoplasmas have an accelerated molecular clock.     

Improved integration time estimation of endogenous retroviruses with phylogenetic data

Background

Endogenous retroviruses (ERVs) are genetic fossils of ancient retroviral integrations that remain in the genome of many organisms. Most loci are rendered non-functional by mutations, but several intact retroviral genes are known in mammalian genomes. Some have been adopted by the host species, while the beneficial roles of others remain unclear. Besides the obvious possible immunogenic impact from transcribing intact viral genes, endogenous retroviruses have also become an interesting and useful tool to study phylogenetic relationships. The determination of the integration time of these viruses has been based upon the assumption that both 5′ and 3′ Long Terminal Repeats (LTRs) sequences are identical at the time of integration, but evolve separately afterwards. Similar approaches have been using either a constant evolutionary rate or a range of rates for these viral loci, and only single species data. Here we show the advantages of using different approaches.

Results

We show that there are strong advantages in using multiple species data and state-of-the-art phylogenetic analysis. We incorporate both simple phylogenetic information and Monte Carlo Markov Chain (MCMC) methods to date the integrations of these viruses based on a relaxed molecular clock approach over a Bayesian phylogeny model and applied them to several selected ERV sequences in primates. These methods treat each ERV locus as having a distinct evolutionary rate for each LTR, and make use of consensual speciation time intervals between primates to calibrate the relaxed molecular clocks.

Conclusions

The use of a fixed rate produces results that vary considerably with ERV family and the actual evolutionary rate of the sequence, and should be avoided whenever multi-species phylogenetic data are available. For genome-wide studies, the simple phylogenetic approach constitutes a better alternative, while still being computationally feasible.     

MAXIMUM-LIKELIHOOD ESTIMATES OF SELECTION COEFFICIENTS FROM DNA SEQUENCE DATA

Selection can have a significant effect on sequence evolution and this will be reflected in the information contained within the phylogenetic relationships between species. Selection will reduce the frequency of any deleterious nucleotides, and this can be used to test for the presence of selection. The frequencies of different nucleotides can be predicted theoretically and compared to observed values. If a sample of sequences has an usually low frequency of a particular nucleotide then selection might be inferred to have acted upon these sequences. This conclusion can be true only if the sequences are not too closely related and if sufficient mutations have occurred during their evolution. Otherwise, the unusual pattern of nucleotides in the sequences may be caused by recent common ancestry. An algorithm is presented to obtain maximum-likelihood estimates of selection coefficients using the phylogenetic information contained within sequence data. A k-allele model is developed that uses the phylogeny to measure relative mutation rates and degrees of relatedness and to evaluate the likelihood in the presence of selection. The method is illustrated with examples from the NS2 genes of influenza viruses and the MHC genes of mice. It is shown that the maximum-likelihood estimate for mutation rates are very large for. influenza viruses and that statistically significant selection acts to maintain a specific coding sequence. Overall, the MHC genes also have significant selection to preserve the coding sequence, but at the antigen recognition site, this selection is reversed to promote genetic variation. Maximum-likelihood estimates of these selection coefficients are provided.     

Understanding Neutral Genomic Molecular Clocks

The molecular clock hypothesis is a central concept in molecular evolution and has inspired much research into why evolutionary rates vary between and within genomes. In the age of modern comparative genomics, understanding the neutral genomic molecular clock occupies a critical place. It has been demonstrated that molecular clocks run differently between closely related species, and generation time is an important determinant of lineage specific molecular clocks. Moreover, it has been repeatedly shown that regional molecular clocks vary even within a genome, which should be taken into account when measuring evolutionary constraint of specific genomic regions. With the availability of a large amount of genomic sequence data, new insights into the patterns and causes of variation in molecular clocks are emerging. In particular, factors such as nucleotide composition, molecular origins of mutations, weak selection and recombination rates are important determinants of neutral genomic molecular clocks.     

The role of DNA replication and isochores in generating mutation and silent substitution rate variance in mammals.

It has been suggested that isochores are maintained by mutation biases, and that this leads to variation in the rate of mutation across the genome. A model of DNA replication is presented in which the probabilities of misincorporation and proofreading are affected by the composition and concentration of the free nucleotide pools. The relationship between sequence G+C content and the mutation rate is investigated. It is found that there is very little variation in the mutation rate between sequences of different G+C contents if the total concentration of the free nucleotides remains constant. However, variation in the mutation rate can be arbitrarily large if some mismatches are proofread and the total concentration of free nucleotides varies. Hence the model suggests that the maintenance of isochores by the replication of DNA in free nucleotide pools of biased composition does not lead per se to mutation rate variance. However, it is possible that changes in composition could be accompanied by changes in concentration, thus generating mutation rate variance. Furthermore, there is the possibility that germ-line selection could lead to alterations in the overall free nucleotide concentration through the cell cycle. These findings are discussed with reference to the variance in mammalian silent substitution rates.     

Models of coding sequence evolution

Probabilistic models of sequence evolution are in widespreaduse in phylogenetics and molecular sequence evolution. Thesemodels have become increasingly sophisticated and combined withstatistical model comparison techniques have helped to shedlight on how genes and proteins evolve. Models of codon evolutionhave been particularly useful, because, in addition to providinga significant improvement in model realism for protein-codingsequences, codon models can also be designed to test hypothesesabout the selective pressures that shape the evolution of thesequences. Such models typically assume a phylogeny and canbe used to identify sites or lineages that have evolved adaptively.Recently some of the key assumptions that underlie phylogenetictests of selection have been questioned, such as the assumptionthat the rate of synonymous changes is constant across sitesor that a single phylogenetic tree can be assumed at all sitesfor recombining sequences. While some of these issues have beenaddressed through the development of novel methods, others remainas caveats that need to be considered on a case-by-case basis.Here, we outline the theory of codon models and their applicationto the detection of positive selection. We review some of themore recent developments that have improved their power andutility, laying a foundation for further advances in the modelingof coding sequence evolution.      

Biological timing and the clock metaphor: oscillatory and hourglass mechanisms

Living organisms have developed a multitude of timing mechanisms--"biological clocks." Their mechanisms are based on either oscillations (oscillatory clocks) or unidirectional processes (hourglass clocks). Oscillatory clocks comprise circatidal, circalunidian, circadian, circalunar, and circannual oscillations--which keep time with environmental periodicities--as well as ultradian oscillations, ovarian cycles, and oscillations in development and in the brain, which keep time with biological timescales. These clocks mainly determine time points at specific phases of their oscillations. Hourglass clocks are predominantly found in development and aging and also in the brain. They determine time intervals (duration). More complex timing systems combine oscillatory and hourglass mechanisms, such as the case for cell cycle, sleep initiation, or brain clocks, whereas others combine external and internal periodicities (photoperiodism, seasonal reproduction). A definition of a biological clock may be derived from its control of functions external to its own processes and its use in determining temporal order (sequences of events) or durations. Biological and chemical oscillators are characterized by positive and negative feedback (or feedforward) mechanisms. During evolution, living organisms made use of the many existing oscillations for signal transmission, movement, and pump mechanisms, as well as for clocks. Some clocks, such as the circadian clock, that time with environmental periodicities are usually compensated (stabilized) against temperature, whereas other clocks, such as the cell cycle, that keep time with an organismic timescale are not compensated. This difference may be related to the predominance of negative feedback in the first class of clocks and a predominance of positive feedback (autocatalytic amplification) in the second class. The present knowledge of a compensated clock (the circadian oscillator) and an uncompensated clock (the cell cycle), as well as relevant models, are briefly re viewed. Hourglass clocks are based on linear or exponential unidirectional processes that trigger events mainly in the course of development and aging. An important hourglass mechanism within the aging process is the limitation of cell division capacity by the length of telomeres. The mechanism of this clock is briefly reviewed. In all clock mechanisms, thresholds at which "dependent variables" are triggered play an important role.     

On the Organization of Higher Chromosomes

OHTA and Kimura¹ have argued that only about 6% of the sequences in mammalian DNA can be under the intense selection that has characterized the evolutionary history of the cytochromes c, the globin chains and the histones. From the calculated mutation rate of fibrinopeptides A and B they show that if all genes are subjected to the same mutation rate 8.3 mutations would accumulate per genome per generation. Because 0,5 deleterious mutations per genome per generation is the maximum allowable in an equilibrium population², they conclude that the amount of DNA that codes for informational sequences such as the cytochromes, globins and histones must be no more than 0.5/8.3, or 6%. We are therefore left with the interesting observation that 94% of mammalian nuclear DNA serves a function not under strong selection. These authors make several assumptions, one of which is that the spontaneous mutation rate characteristic of a species is constant over all nucleotide sequences. I suggest here that this assumption is incorrect, for a variety of reasons and that by assuming that spontaneous mutation rates vary sequence by sequence, one can arrive at a plausible organizing principle for the structure of higher chromosomes.     

Temporal patterns of fruit fly (Drosophila) evolution revealed by mutation clocks

Drosophila melanogaster has been a canonical model organism to study genetics, development, behavior, physiology, evolution, and population genetics for nearly a century. Despite this emphasis and the completion of its nuclear genome sequence, the timing of major speciation events leading to the origin of this fruit fly remain elusive because of the paucity of extensive fossil records and biogeographic data. Use of molecular clocks as an alternative has been fraught with non-clock-like accumulation of nucleotide and amino-acid substitutions. Here we present a novel methodology in which genomic mutation distances are used to overcome these limitations and to make use of all available gene sequence data for constructing a fruit fly molecular time scale. Our analysis of 2977 pairwise sequence comparisons from 176 nuclear genes reveals a long-term fruit fly mutation clock ticking at a rate of 11.1 mutations per kilobase pair per Myr. Genomic mutation clock-based timings of the landmark speciation events leading to the evolution of D. melanogaster show that it shared most recent common ancestry 5.4 MYA with D. simulans, 12.6 MYA with D. erecta+D. orena, 12.8 MYA with D. yakuba+D. teisseri, 35.6 MYA with the takahashii subgroup, 41.3 MYA with the montium subgroup, 44.2 MYA with the ananassae subgroup, 54.9 MYA with the obscura group, 62.2 MYA with the willistoni group, and 62.9 MYA with the subgenus Drosophila. These and other estimates are compatible with those known from limited biogeographic and fossil records. The inferred temporal pattern of fruit fly evolution shows correspondence with the cooling patterns of paleoclimate changes and habitat fragmentation in the Cenozoic.     

Molecular dating in the genomic era

The comparison of DNA and protein sequences of extant species might be informative for reconstructing the chronology of evolutionary events on Earth. A phylogenetic tree inferred from molecular data directly depicts the evolutionary affinities of species and indirectly allows estimating the age of their origin and diversification. Molecular dating is achieved by assuming the molecular clock hypothesis, i.e., that the rate of change of nucleotide and amino acid sequences is on average constant over geological time. If paleontological calibrations are available, then absolute divergence times of species can be estimated. However, three major difficulties potentially hamper molecular dating : (1) a limited sample of genes and organisms, (2) a limited number of fossil references, and (3) pervasive variations of molecular evolutionary rates among genomes and species. To circumvent these problems, different solutions have been recently proposed. Larger data sets are built with more genes and more species sampled through the mining of an increasing number of genomes. Moreover, independent key fossils are identified to calibrate molecular clocks, and the uncertainty on their age is integrated in subsequent analyses. Finally, models of molecular rate variations are constructed, and incorporated in the so-called relaxed molecular clock approaches. As an illustration of these improvements, we mention that the debated age of the animal (bilaterian metazoans) diversification may have occurred between 642-761 million years ago (Mya), roughly 100 Ma before the Cambrian explosion. Among mammals, the initial diversification of major placental groups may have taken place around 100 Mya, well before the Cretaceous/Tertiary boundary marking the extinction of dinosaurs.     

Cellular and biochemical mechanisms underlying circadian rhythms in vertebrates

Circadian clocks organize neural processes, such as motor activities, into near 24-hour oscillations and adaptively synchronize these rhythms to the solar cycle. Recently, the first mammalian clock genes have been found. Unpredicted diversity in signaling pathways and clock-controlled gating of signals that modulate timekeeping has been discovered. A diffusible clock output has been found to control some behavioral rhythms. Consensus is emerging that circadian mechanisms are conserved across phylogeny, but that mammals have developed a great complexity of controls.     

To be or not to be rhythmic? A review of studies on organisms inhabiting constant environments

Abstract

Circadian clocks are endogenous time keeping mechanisms that drive near 24-h behavioural, physiological and metabolic rhythms in organisms. It is thought that organisms possess circadian clocks to facilitate coordination of essential biological events to the external day and night (extrinsic advantage) so as to enhance Darwinian fitness. However, on Earth, there are a number of habitats that are not subject to such robust daily cycling of geo-physical factors. Do organisms living under such conditions exhibit rhythmic behaviours that are driven by endogenous circadian clocks? We attempt to critically survey studies of rhythms (or the lack of them) in organisms living in a range of constant environments. Many such organisms do show rhythms in behaviour and/or physiological variables. We suggest that such presence of rhythms may be indicative of an underlying clock that facilitates, (a) internal synchrony among rhythms, and (b) temporal partitioning of incompatible cellular processes (intrinsic advantage). We then highlight reasons that limit our interpretations about the presence (or absence) of clocks in such organisms living under constant conditions, and suggest possible methods to conclusively test whether or not rhythms in these organisms are driven by endogenous circadian clocks with the hope that it may enhance our understanding of circadian clocks in organisms under constant environments.     

BIOLOGICAL TIMING AND THE CLOCK METAPHOR: OSCILLATORY AND HOURGLASS MECHANISMS

Living organisms have developed a multitude of timing mechanisms— “biological clocks.” Their mechanisms are based on either oscillations (oscillatory clocks) or unidirectional processes (hourglass clocks). Oscillatory clocks comprise circatidal, circalunidian, circadian, circalunar, and circannual oscillations—which keep time with environmental periodicities—as well as ultradian oscillations, ovarian cycles, and oscillations in development and in the brain, which keep time with biological timescales. These clocks mainly determine time points at specific phases of their oscillations. Hourglass clocks are predominantly found in development and aging and also in the brain. They determine time intervals (duration). More complex timing systems combine oscillatory and hourglass mechanisms, such as the case for cell cycle, sleep initiation, or brain clocks, whereas others combine external and internal periodicities (photoperiodism, seasonal reproduction). A definition of a biological clock may be derived from its control of functions external to its own processes and its use in determining temporal order (sequences of events) or durations. Biological and chemical oscillators are characterized by positive and negative feedback (or feedforward) mechanisms. During evolution, living organisms made use of the many existing oscillations for signal transmission, movement, and pump mechanisms, as well as for clocks. Some clocks, such as the circadian clock, that time with environmental periodicities are usually compensated (stabilized) against temperature, whereas other clocks, such as the cell cycle, that keep time with an organismic timescale are not compensated. This difference may be related to the predominance of negative feedback in the first class of clocks and a predominance of positive feedback (autocatalytic amplification) in the second class. The present knowledge of a compensated clock (the circadian oscillator) and an uncompensated clock (the cell cycle), as well as relevant models, are briefly reviewed. Hourglass clocks are based on linear or exponential unidirectional processes that trigger events mainly in the course of development and aging. An important hourglass mechanism within the aging process is the limitation of cell division capacity by the length of telomeres. The mechanism of this clock is briefly reviewed. In all clock mechanisms, thresholds at which “dependent variables” are triggered play an important role. (Chronobiology International, 18(3), 329–369, 2001)