The age of a mutation in a general coalescent tree

Griffiths, R. C.; Tavaré, Simon

doi:10.1080/15326349808807471

Cited by 241 publications

(306 citation statements)

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“…The rarest allele that can be observed in the data of Patil et al (2001) has a frequency of 2/20, which implies a population frequency of 10%. Such alleles are likely to be much older than any of the recent growth scenarios that have been discussed in the literature (Kimura and Ohta 1973;Griffiths and Tavaré 1998). In a sample of size 20, recent growth would mostly affect the relative frequency of the singleton class.…”

Section: Allele-frequency Distributionmentioning

confidence: 98%

The Pattern of Polymorphism on Human Chromosome 21

Innan

Padhukasahasram²,

Nordborg

2003

Genome Res.

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Polymorphism data from 20 partially resequenced copies of human chromosome 21-more than 20,000 polymorphic sites-were analyzed. The allele-frequency distribution shows no deviation from the simplest population genetic model with a constant population size (although we show that our analysis has no power to detect population growth). The average rate of recombination per site is estimated to be roughly one-half of the rate of mutation per site, again in agreement with simple model predictions. However, sliding-window analyses of the amount of polymorphism and the extent of linkage disequilibrium (LD) show significant deviations from standard models. This could be due to the history of selection or demographic change, but it is impossible to draw strong conclusions without much better knowledge of variation in the relationship between genetic and physical distance along the chromosome.[Supplemental material is available online at www.genome.org.]There are essentially two reasons for studying the pattern of genetic polymorphism in population samples. The first is to identify polymorphisms that have important phenotypic effects. The pattern of polymorphism is important when searching for alleles that are statistically associated with phenotypic differences, either because they are directly causative, or because they are in linkage disequilibrium (LD) with variants (at other sites) that are directly causative.The second reason, which is also the focus of this paper, is interest in the evolutionary process that gave rise to the pattern of polymorphism. One may be interested in forces that influence all loci, such as migration, mutation, and recombination, or one may be interested in the history of selection on a particular locus. Many years of research in population genetics (empirical as well as theoretical) have led to a sophisticated mathematical theory for this type of analysis (for review, see Li 1997;Kreitman 2000;Nordborg 2001;Stephens 2001). Arguably the most fundamental insight that has emerged from this work is that in order to overcome the enormous variance that is due to random history and estimate evolutionary parameters accurately, data from surprisingly large numbers of loci are needed. Indeed, it can be said (with only slight exaggeration), that theory has typically told us that in order to answer the questions of interest, more data are required than is feasible to collect.This situation is about to change. As a result of rapid advances in genotyping technology (primarily due to the enormous efforts devoted to finding polymorphisms associated with human diseases), polymorphism data on a genomic scale will soon become common. The most spectacular example to date is provided by Patil et al. (2001), who partially resequenced 20 copies of human chromosome 21. Although their data are in many ways unsuitable for evolutionary genetics (see below), this is to a significant extent compensated for by quantity: over 21,000 polymorphic sites, with enough recombination to ensure that most sites are effectively ind...

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Section: Allele-frequency Distributionmentioning

confidence: 98%

The Pattern of Polymorphism on Human Chromosome 21

Innan

Padhukasahasram²,

Nordborg

2003

Genome Res.

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“…The next result can be deduced from Griffiths and Tavaré (1998) or Stephens (2000). Assume that the mutation D has B ¼ b descendants.…”

Section: Background Resultsmentioning

confidence: 99%

“…; n ÿ b 1 1. The age of the mutation D has been studied by Griffiths and Tavaré (1998), Wiuf and Donnelly (1999), and Stephens (2000). Conditional on B ¼ b, the expected age is given by…”

Section: Background Resultsmentioning

confidence: 99%

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Conditional Coalescent Trees With Two Mutation Rates and Their Application to Genomic Instability

Emily¹,

Ochsenbein²

2006

Genetics

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Humans have invested several genes in DNA repair and fidelity replication. To account for the disparity between the rarity of mutations in normal cells and the large number of mutations present in cancer, an hypothesis is that cancer cells must exhibit a mutator phenotype (genomic instability) during tumor progression, with the initiation of abnormal mutation rates caused by the loss of mismatch repair. In this study we introduce a stochastic model of mutation in tumor cells with the aim of estimating the amount of genomic instability due to the alteration of DNA repair genes. Our approach took into account the difficulties generated by sampling within tumoral clones and the fact that these clones must be difficult to isolate. We provide corrections to two classical statistics to obtain unbiased estimators of the raised mutation rate, and we show that large statistical errors may be associated with such estimators. The power of these new statistics to reject genomic instability is assessed and proved to increase with the intensity of mutation rates. In addition, we show that genomic instability cannot be detected unless the raised mutation rates exceed the normal rates by a factor of at least 1000. D NA replication in normal human cells is an extremely accurate process. During the cell division cycle, copy errors occur with probabilities ,10 ÿ9 -10 ÿ10 per nucleotide. In contrast, the malignant cells that constitute cancer tissues are markedly heterogeneous and exhibit alterations in the nucleotide sequence of DNA (e.g., Bielas and Loeb 2005). To account for the disparity between the rarity of mutations in normal cells and the large numbers of mutations present in cancer, Loeb et al. (1974) hypothesized that during tumor progression, cancer cells must exhibit a mutator phenotype (see the review by Loeb et al. 2003). It is still a matter of debate to know exactly which event initiates tumorigenesis. But one hypothesis for the initiation of abnormal mutation rates in tumors is the loss of mismatch repair (MMR). For instance, this phenomenon may follow from the inactivation of the genes hMSH2 and hMLH1 involved in hereditary nonpolyposis colorectal cancers (HNPCC) (Fishel et al. 1993;Leach et al. 1993;Lindblom et al. 1993). In normal conditions, the MMR repair system involves a complex interaction among the protein products of hMSH2 and hMLH1 genes. The result is to eliminate $99.9% of the errors in DNA replication, reducing errors to a rate of $1/10 12 bp in genes that regulate the apoptosis or the cell cycle duration. HNPCC is inherited in an autosomal dominant fashion. One copy of the mutant allele is defective and is inherited in the germline. The loss of MMR may start when the second mutation occurs somatically as a consequence of the two-hits theory (Moolgavkar and Knudson 1981).Widespread genomic instability seems associated with MMR-defective genes. For example, microsatellite instability is associated with HNPCC (Ionov et al. 1993;Peltomaki et al. 1993;Thibodeau et al. 1993). Detection of DNA insta...

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“…Maximum likelihood 63,000 (40,000-100,000) Tang et al (2002) 63,000 (29,000-98,000) Thomson et al (2000) 70,000 (10,000-130,000) genetree (constant population) 84,000 (55,000-149,000) genetree (exponential growth) 59,000 (40,000-140,000) of mutations 1 and 2 were estimated by Thomson et al (2000) using genetree, under the assumption of constant population size and also using the number of segregating sites within the sequences that contained each mutation (Griffiths and Tavaré 1998). Our estimates are for the coalescence times and hence the numbers in Table 7 are not directly comparable.…”

Section: Tablementioning

confidence: 99%

Maximum-Likelihood Estimation of Coalescence Times in Genealogical Trees

Meligkotsidou

Fearnhead

2005

Genetics

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We develop a method for maximum-likelihood estimation of coalescence times in genealogical trees, based on population genetics data. For this purpose, a Viterbi-type algorithm is constructed to maximize the joint likelihood of the coalescence times. Marginal confidence intervals for the coalescence times based on the profile likelihoods are also computed. Our method of finding MLEs and calculating C.I.'s appears to be more accurate than alternative numerical maximization methods, and maximum-likelihood inference appears to be more accurate than other existing model-free approaches to estimating coalescent times. We demonstrate the method on two different data sets: human Y chromosome DNA data and fungus DNA data. W E study the evolutionary history of a sample of nonrecombining DNA sequences, from a given population, which exhibits variation. The ancestral relationships of the individuals in the sample can be depicted by a rooted genealogical tree. Interest lies in estimating the coalescence times in the tree and, in particular, the time to the most recent common ancestor (TMRCA) of the sample.Currently there are two distinct approaches for estimating coalescence times, which we call model-based and model-free. Both approaches use similar models for the mutation process, but differ in whether or not they assume a model for the genealogy.Model-based approaches use coalescence models (Kingman 1982;Nordborg 2001) for the underlying genealogy of the sample. These approaches require specific assumptions about the demography (e.g., the presence of random mating, how population size has varied over time, etc.) to be made. Both Bayesian (Tavaré et al. 1997;Pritchard et al. 1999) and empirical Bayes (Griffiths and Tavaré 1994) methods for performing such inferences exist.Model-free approaches do not assume any model for the genealogy. There are two such existing approaches for estimating the TMRCA, both based on method-ofmoments estimators. Tang et al. (2002) partition the observed sequences into two subsets, corresponding to two clades that have diverged from the sample TMRCA, and use the number of nucleotide differences between pairs of sequences in different clades to obtain an estimator of the sample TMRCA. (This is an extension and significant improvement on an earlier approach by Templeton 1993). Alternatively Thomson et al. (2000) proposed a method, which uses the numbers of mutational differences between the observed DNA sequences and the sequence of the MRCA.Which of the model-free and model-based approaches performs best will depend crucially on the validity of the demographic assumptions made in the model-based methods (for a comparative discussion, see Stumpf and Goldstein 2001). If they are correct, then model-based approaches will be more accurate; however, Tang et al. (2002) give evidence for the lack of robustness of model-based approaches to misspecification of the demographic model. One advantage of the current model-based approaches is that they enable inference for all coalescence times, wherea...

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The age of a mutation in a general coalescent tree

Cited by 241 publications

References 15 publications

The Pattern of Polymorphism on Human Chromosome 21

The Pattern of Polymorphism on Human Chromosome 21

Conditional Coalescent Trees With Two Mutation Rates and Their Application to Genomic Instability

Maximum-Likelihood Estimation of Coalescence Times in Genealogical Trees

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