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PubMed1991

Statistical models of the overdispersed molecular clock.

The most commonly used statistical model to describe the rate constancy of molecular evolution (molecular clock) is a simple Poisson process in which the variance of the number of amino acid or nucleotide substitutions in a particular gene should be equal to the mean and henceforth the dispersion index, the ratio of the variance to the mean, should be equal to one. Recent sequence data, however, have shown that the substitutional process in molecular evolution is often considerably overdispersed and have called into question the generality of using a simple Poisson process. Several efforts have been made to develop more realistic models of molecular evolution. In this paper, I will show that the spatial (site-specific) variation in the rate of molecular evolution is an improbable cause of the overdispersion and then review various statistical models which take the temporal variation into account. Although these models do not immediately specify what the mechanisms of molecular evolution might be, they do make qualitatively different predictions and give some insight into their inference. One way to distinguish them is suggested. In addition, effects of selected substitutions that presumably occur after a major change in a molecule are quasi-quantitatively examined. It is most likely that the overdispersion of molecular clock is due either to a major molecular reconfiguration (fluctuating neutral space) led by a series of subliminal neutral changes or to selected substitutions fine-tuning a molecule after a major molecular change. Although the latter possibility, of course, violates the simplest neutrality assumption, it would not impair the neutral theory as a whole.

Biological Evolution↗

PubMed2004

Molecular clock fork phylogenies: closed form analytic maximum likelihood solutions.

Maximum likelihood (ML) is increasingly used as an optimality criterion for selecting evolutionary trees, but finding the global optimum is a hard computational task. Because no general analytic solution is known, numeric techniques such as hill climbing or expectation maximization (EM) are used in order to find optimal parameters for a given tree. So far, analytic solutions were derived only for the simplest model-three-taxa, two-state characters, under a molecular clock. Quoting Ziheng Yang, who initiated the analytic approach,"this seems to be the simplest case, but has many of the conceptual and statistical complexities involved in phylogenetic estimation."In this work, we give general analytic solutions for a family of trees with four-taxa, two-state characters, under a molecular clock. The change from three to four taxa incurs a major increase in the complexity of the underlying algebraic system, and requires novel techniques and approaches. We start by presenting the general maximum likelihood problem on phylogenetic trees as a constrained optimization problem, and the resulting system of polynomial equations. In full generality, it is infeasible to solve this system, therefore specialized tools for the molecular clock case are developed. Four-taxa rooted trees have two topologies-the fork (two subtrees with two leaves each) and the comb (one subtree with three leaves, the other with a single leaf). We combine the ultrametric properties of molecular clock fork trees with the Hadamard conjugation to derive a number of topology dependent identities. Employing these identities, we substantially simplify the system of polynomial equations for the fork. We finally employ symbolic algebra software to obtain closed formanalytic solutions (expressed parametrically in the input data). In general, four-taxa trees can have multiple ML points. In contrast, we can now prove that each fork topology has a unique(local and global) ML point.

Animals↗

PubMed2006

Variable molecular clocks in hominoids.

Generation time is an important determinant of a neutral molecular clock. There are several human-specific life history traits that led to a substantially longer generation time in humans than in other hominoids. Indeed, a long generation time is considered an important trait that distinguishes humans from their closest relatives. Therefore, humans may exhibit a significantly slower molecular clock as compared to other hominoids. To investigate this hypothesis, we performed a large-scale analysis of lineage-specific rates of single-nucleotide substitutions among hominoids. We found that humans indeed exhibit a significant slowdown of molecular evolution compared to chimpanzees and other hominoids. However, the amount of fixed differences between humans and chimpanzees appears extremely small, suggesting a very recent evolution of human-specific life history traits. Notably, chimpanzees also exhibit a slower rate of molecular evolution compared to gorillas and orangutans in the regions analyzed.

Animals↗

PubMed2003

Testing a molecular clock without an outgroup: derivations of induced priors on branch-length restrictions in a Bayesian framework.

We propose a Bayesian method for testing molecular clock hypotheses for use with aligned sequence data from multiple taxa. Our method utilizes a nonreversible nucleotide substitution model to avoid the necessity of specifying either a known tree relating the taxa or an outgroup for rooting the tree. We employ reversible jump Markov chain Monte Carlo to sample from the posterior distribution of the phylogenetic model parameters and conduct hypothesis testing using Bayes factors, the ratio of the posterior to prior odds of competing models. Here, the Bayes factors reflect the relative support of the sequence data for equal rates of evolutionary change between taxa versus unequal rates, averaged over all possible phylogenetic parameters, including the tree and root position. As the molecular clock model is a restriction of the more general unequal rates model, we use the Savage-Dickey ratio to estimate the Bayes factors. The Savage-Dickey ratio provides a convenient approach to calculating Bayes factors in favor of sharp hypotheses. Critical to calculating the Savage-Dickey ratio is a determination of the prior induced on the modeling restrictions. We demonstrate our method on a well-studied mtDNA sequence data set consisting of nine primates. We find strong support against a global molecular clock, but do find support for a local clock among the anthropoids. We provide mathematical derivations of the induced priors on branch length restrictions assuming equally likely trees. These derivations also have more general applicability to the examination of prior assumptions in Bayesian phylogenetics.

Animals↗

PubMed1987

On the overdispersed molecular clock.

Rates of molecular evolution at some loci are more irregular than described by simple Poisson processes. Three situations under which molecular evolution would not follow simple Poisson processes are reevaluated from the viewpoint of the neutrality hypothesis: concomitant or multiple substitutions in a gene, fluctuating substitution rates in time caused by coupled effects of deleterious mutations and bottlenecks, and changes in the degree of selective constraints against a gene (neutral space) caused by successive substitutions. The common underlying assumption that these causes are lineage nonspecific excludes the case where mutation rates themselves change systematically among lineages or taxonomic groups, and severely limits the extent of variation in the number of substitutions among lineages. Even under this stringent condition, however, the third hypothesis, the fluctuating neutral space model, can generate fairly large variation. This is described by a time-dependent renewal process, which does not exhibit any episodic nature of molecular evolution. It is argued that the observed elevated variances in the number of nucleotide or amino acid substitutions do not immediately call for positive Darwinian selection in molecular evolution.

Animals↗

PubMedDate not supplied

Calibration and error in placental molecular clocks: a conservative approach using the cetartiodactyl fossil record.

The nature of the molecular and fossil record and their limitations must be ascertained in order to gain the most precise and accurate evolutionary timescale using genetic information. Yet the majority of such timescales are based on point estimates using fossils or the molecular clock. Here we document from the primary literature minimum and maximum fossil age estimates of the divergence of whales from artiodactyls, a commonly used anchor point for calibrating both mitogenomic and nucleogenomic placental timescales. We applied these reestimates to the most recently established placental timescale based on mitochondrial rRNA and several nuclear loci, and present an attempt to account for both genetic and fossil uncertainty. Our results indicate that disregard for fossil calibration error may inflate the power of the molecular clock when testing the time of ordinal diversification in context with the K-T boundary. However, the early history of placentals, including their superordinal diversification, remained in the Cretaceous despite a conservative approach. Our conclusions need corroboration across other frequently used fossil anchor points, but also with more genetic partitions on the linear relationship between molecular substitutions and geologic time.

Animals↗

PubMed2006

Dates from the molecular clock: how wrong can we be?

Large discrepancies have been found in dates of evolutionary events obtained using the molecular clock. Twofold differences have been reported between the dates estimated from molecular data and those from the fossil record; furthermore, different molecular methods can give dates that differ 20-fold. New software attempts to incorporate appropriate allowances for this uncertainty into the calculation of the accuracy of date estimates. Here, we propose that these innovations represent welcome progress towards obtaining reliable dates from the molecular clock, but warn that they are currently unproven, given that the causes and pattern of the discrepancies are the subject of ongoing research. This research implies that many previous studies, even some of those using recently developed methods, might have placed too much confidence in their date estimates, and their conclusions might need to be revised.

Animals↗

PubMed2006

[Regulation of adipose functions by molecular clocks].

Adipocytes play essential metabolic roles, not only serving as massive energy reserves but also secreting hormones and cytokines that regulate metabolic activities. The link between metabolic activity in adipocytes and circadian rhythm has long been studied, e.g., glucose and lipid homeostasis are well known to exhibit circadian variation. Therefore, molecular clock may play important roles in regulation of metabolic activity in adipocytes. In a previous study, we reported that white adipose tissue contains functional molecular clock and expression of several adipocytokines including leptin and plasminogen activator inhibitor-1 displays circadian rhythm. The diurnal rhythm in the level of these molecules suggests that molecular clock is, at least partly, associated with the onset of metabolic syndrome.

ARNTL Transcription Factors↗

PubMed2003

Local molecular clocks in three nuclear genes: divergence times for rodents and other mammals and incompatibility among fossil calibrations.

Reconstructing the chronology of mammalian evolution is a debated issue between molecule- and fossil-based inferences. A methodological limitation of molecules is the evolutionary rate variation among lineages, precluding the application of the global molecular clock. We considered 2422 first and second codon positions of the combined ADRA2B, IRBP, and vWF nuclear genes for a well-documented set of placentals including an extensive sampling of rodents. Using seven independent calibration points and a maximum-likelihood framework, we evaluated whether molecular and paleontological estimates of mammalian divergence dates may be reconciled by the local molecular clocks approach, allowing local constancy of substitution rates with variations at larger phylogenetic scales. To handle the difficulty of choosing among all possible rate assignments for various lineages, local molecular clocks were based on the results of branch-length and two-cluster tests. Extensive lineage-specific variation of evolutionary rates was detected, even among rodents. Cross-calibrations indicated some incompatibilities between divergence dates based on different paleontological references. To decrease the impact of a single calibration point, estimates derived from independent calibrations displaying only slight reciprocal incompatibility were averaged. The divergence dates inferred for the split between mice and rats (approximately 13-19 Myr) was younger than previously published molecular estimates. The most recent common ancestors of rodents, primates and rodents, boreoeutherians, and placentals were estimated to be, respectively, approximately 60, 70, 75, and 78 Myr old. Global clocks, local clocks, and quartet dating analyses suggested a Late Cretaceous origin of the crown placental clades followed by a Tertiary radiation of some placental orders like rodents.

Animals↗

PubMed2025

Detecting Introgression in Shallow Phylogenies: How Minor Molecular Clock Deviations Lead to Major Inference Errors.

Recent theoretical and algorithmic advances in introgression detection, coupled with the growing availability of genome-scale data, have highlighted the widespread occurrence of interspecific gene flow across the tree of life. However, current methods largely depend on the molecular clock assumption-a questionable premise given empirical evidence of substitution rate variation across lineages. While such rate heterogeneity is known to compromise gene flow detection among divergent lineages, its impact on closely related taxa at shallow evolutionary timescales remains poorly understood, likely because these taxa are often assumed to adhere to a molecular clock. To address this gap, we combine theoretical analyses and simulations to evaluate the robustness of widely used site pattern methods (D-statistic and HyDe) to rate variation across phylogenetic timescales. Our results demonstrate that both methods exhibit high sensitivity to even minor deviations from the molecular clock at shallow timescales, complementing previous findings at deeper scales. Specifically, in young phylogenies (with an age of 3 × 105 generations) with small population sizes, weak (17% difference) and moderate (33% difference) rate variation can inflate false-positive rates up to 35% and 100%, respectively, using site pattern counts from a 500 Mb genome. Employing a more distant outgroup intensifies these spurious signals. Our study demonstrates that summary tests for introgression are pervasively vulnerable to minor rate variations and underscores the critical need for advanced methodologies to disentangle genuine introgression from false signals generated by rate heterogeneity.

Phylogeny↗

PubMed1990

Histone deletion mutants challenge the molecular clock hypothesis.

A basic tenet of the molecular clock hypothesis is that the rate of sequence drift for a protein depends on the number of amino acid residues that are critical for its function. However, recent experiments have determined that, although core histone sequences are highly conserved among eukaryotes, large regions of the proteins are dispensable for growth in yeast.

Amino Acid Sequence↗

PubMed2001

A molecular clock involved in somite segmentation.

Somites are transient embryonic structures that are formed from the unsegmented presomitic mesoderm (PSM) in a highly regulated process called somitogenesis. Somite, formation can be considered as the result of several sequential processes: generation of a basic metameric pattern, specification of the antero-posterior identity of each somite, and, finally, formation of the somitic border. Evidence for the existence of a molecular clock or oscillator linked to somitogenesis has been provided by the discovery of the rhythmic and dynamic expression in the PSM of c-hairy1 and lunatic fringe, two genes potentially related to the Notch signaling pathway. These oscillating expression patterns suggest that an important role of the molecular clock could reside in the temporal control of periodic Notch activation, ultimately resulting in the regular array of the somites. We discuss both the importance of the Notch signaling pathway in the molecular events of somitogenesis and its relationship with the molecular clock, and, finally, in that context we review a number of other genes known to play a role in somitogenesis.

Animals↗

PubMed1985

Dating of the human-ape splitting by a molecular clock of mitochondrial DNA.

A new statistical method for estimating divergence dates of species from DNA sequence data by a molecular clock approach is developed. This method takes into account effectively the information contained in a set of DNA sequence data. The molecular clock of mitochondrial DNA (mtDNA) was calibrated by setting the date of divergence between primates and ungulates at the Cretaceous-Tertiary boundary (65 million years ago), when the extinction of dinosaurs occurred. A generalized least-squares method was applied in fitting a model to mtDNA sequence data, and the clock gave dates of 92.3 +/- 11.7, 13.3 +/- 1.5, 10.9 +/- 1.2, 3.7 +/- 0.6, and 2.7 +/- 0.6 million years ago (where the second of each pair of numbers is the standard deviation) for the separation of mouse, gibbon, orangutan, gorilla, and chimpanzee, respectively, from the line leading to humans. Although there is some uncertainty in the clock, this dating may pose a problem for the widely believed hypothesis that the pipedal creature Australopithecus afarensis, which lived some 3.7 million years ago at Laetoli in Tanzania and at Hadar in Ethiopia, was ancestral to man and evolved after the human-ape splitting. Another likelier possibility is that mtDNA was transferred through hybridization between a proto-human and a proto-chimpanzee after the former had developed bipedalism.

Animals↗

PubMed2005

Molecular clocks: when times are a-changin'.

The molecular clock has proved to be extremely valuable in placing timescales on evolutionary events that would otherwise be difficult to date. However, debate has arisen about the considerable disparities between molecular and palaeontological or archaeological dates, and about the remarkably high mutation rates inferred in pedigree studies. We argue that these debates can be largely resolved by reference to the "time dependency of molecular rates", a recent hypothesis positing that short-term mutation rates and long-term substitution rates are related by a monotonic decline from the former to the latter. Accordingly, the extrapolation of rates across different timescales will result in invalid date estimates. We examine the impact of this hypothesis with respect to various fields, including human evolution, animal domestication and conservation genetics. We conclude that many studies involving recent divergence events will need to be reconsidered.

Animals↗

PubMed2004

Calibration of galliform molecular clocks using multiple fossils and genetic partitions.

For more than a century, members of the traditional avian order Galliformes (i.e., pheasants, partridges, junglefowl, and relatives) have been among the most intensively studied birds, but still a comprehensive timeframe for their evolutionary history is lacking. Thanks to a number of recent cladistic interpretations for several galliform fossils, candidates now exist that can potentially be used as accurate internal calibrations for molecular clocks. Here, we describe a molecular timescale for Galliformes based on cytochrome b and ND2 using nine mostly internal fossil-based anchorpoints. Beyond application of calibrations spanning the entire evolutionary history of Galliformes, care was taken to investigate the effects of calibration choice, substitution saturation, and rate heterogeneity among lineages on divergence time estimation. Results show broad consistency in time estimation with five out of the nine total calibrations. Our divergence time estimates, based on these anchorpoints, indicate that the early history of Galliformes took place in the Cretaceous, including the origin of the basal-most megapode and perhaps cracid lineages, but that the remaining morphological diversification likely started in the earliest Tertiary. The multi-calibration/multi-genetic partition approach used here highlights the importance of understanding the genetic saturation, variation, and rate constancy spectra for the accurate calculation of divergence times by use of molecular clocks.

Animals↗

PubMed2004

Calibration of molecular clocks and the biogeographic history of Crypteroniaceae.

A recent molecular clock analysis concluded that Gondwanan vicariance and out-of-India dispersal best explained the distribution of Crypteroniaceae and its allies (Conti et al. 2002). A reanalysis of their data using a different molecular dating technique and calibration point is congruent with an alternative hypothesis, namely dispersal between India, Africa, and South America long after the initial break-up of Gondwana.

Biological Clocks↗

PubMed2004

The timing of eukaryotic evolution: does a relaxed molecular clock reconcile proteins and fossils?

The use of nucleotide and amino acid sequences allows improved understanding of the timing of evolutionary events of life on earth. Molecular estimates of divergence times are, however, controversial and are generally much more ancient than suggested by the fossil record. The limited number of genes and species explored and pervasive variations in evolutionary rates are the most likely sources of such discrepancies. Here we compared concatenated amino acid sequences of 129 proteins from 36 eukaryotes to determine the divergence times of several major clades, including animals, fungi, plants, and various protists. Due to significant variations in their evolutionary rates, and to handle the uncertainty of the fossil record, we used a Bayesian relaxed molecular clock simultaneously calibrated by six paleontological constraints. We show that, according to 95% credibility intervals, the eukaryotic kingdoms diversified 950-1,259 million years ago (Mya), animals diverged from choanoflagellates 761-957 Mya, and the debated age of the split between protostomes and deuterostomes occurred 642-761 Mya. The divergence times appeared to be robust with respect to prior assumptions and paleontological calibrations. Interestingly, these relaxed clock time estimates are much more recent than those obtained under the assumption of a global molecular clock, yet bilaterian diversification appears to be approximately 100 million years more ancient than the Cambrian boundary.

Animals↗

PubMed2002

An insect molecular clock dates the origin of the insects and accords with palaeontological and biogeographic landmarks.

A unified understanding of >390 Myr of insect evolution requires insight into their origin. Molecular clocks are widely applied for evolutionary dating, but clocks for the class Insecta have remained elusive. We now define a robust nucleotide and amino acid mitochondrial molecular clock encompassing five insect orders, including the Blattaria (cockroaches), Orthoptera (crickets and locusts), Hemiptera (true bugs), Diptera, and Lepidoptera (butterflies and moths). Calibration of the clock using one of the earliest, most extensive fossil records for insects (the early ancestors of extant Blattaria) was congruent with all available insect fossils, with biogeographic history, with the Cambrian explosion, and with independent dating estimates from Lepidopteran families. In addition, dates obtained from both nucleotide and amino acid clocks were congruent with each other. Of particular interest to vector biology is the early date of the emergence of triatomine bugs (99.8-93.5 MYA), coincident with the formation of the South American continent during the breakup of Gondwanaland. More generally, we reveal the insects arising from a common ancestor with the Anostraca (fairy shrimps) at around the Silurian-Ordovician boundary (434.2-421.1 MYA) coinciding with the earliest plant megafossil. We explore Tilyard's theory proposing that the terrestrial transition of the aquatic arthropod ancestor to the insects is associated with a particular plant group (early vascular plants). The major output of the study is a comprehensive series of dates for deep-branching points within insect evolution that can act as calibration points for further dating studies within insect families and genera.

Animals↗