Maximum-Likelihood Estimation of Coalescence Times in Genealogical Trees

Meligkotsidou, Loukia; Fearnhead, Paul

doi:10.1534/genetics.105.043067

Cited by 9 publications

(7 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such an approach (i) obtains an estimate of the coalescent timest using the genetic data and (ii) bases inference on the conditional likelihood pðx jt; sÞ. We used the maximum-likelihood estimator oft (which for these models can be calculated using the method of Meligkotsidou and Fearnhead 2005).…”

Section: Tablementioning

confidence: 99%

Postprocessing of Genealogical Trees

Meligkotsidou

Fearnhead

2007

Genetics

Self Cite

View full text Add to dashboard Cite

We consider inference for demographic models and parameters based upon postprocessing the output of an MCMC method that generates samples of genealogical trees (from the posterior distribution for a specific prior distribution of the genealogy). This approach has the advantage of taking account of the uncertainty in the inference for the tree when making inferences about the demographic model and can be computationally efficient in terms of reanalyzing data under a wide variety of models. We consider a (simulation-consistent) estimate of the likelihood for variable population size models, which uses importance sampling, and propose two new approximate likelihoods, one for migration models and one for continuous spatial models. . Often this approach is applied informally, with the qualitative features of the inferred tree being used to suggest plausible demographic histories for the sample (e.g., Shen et al. 2000).The second approach involves joint inference of the genealogical tree and the parameters. In many cases the genealogical tree is a nuisance parameter, and calculation of the likelihood for the parameters involves integrating out the unknown tree, for example, in inference about various demographic models under a coalescent prior, including variable population sizes (Griffiths and Tavaré 1994a;Kuhner et al. 1998;Drummond et al. 2005) and population structure (Bahlo and Griffiths 1998;Beerli and Felsenstein 1999), inference for selection (Coop and Griffiths 2004), dispersal of a population (Brooks et al. 2007), and inference for recombination rates (Griffiths and Marjoram 1996;Kuhner et al. 2000;Fearnhead and Donnelly 2002). (In the latter case the genealogical information is contained in a graph and not in a tree.)The advantage of the second approach is that, assuming the model for the genealogical tree is reasonable, the uncertainty in this genealogy is correctly incorporated into the inference about the parameters of interest. This is particularly important for data where there is considerable uncertainty in the genealogy (which is common for many data sets). The first approach of conditioning on a single estimate of the genealogy can sometimes lead to biases in estimates and, more generally, to underestimates of the uncertainty in the parameters. These problems often mean that analysis conditional on the tree is often used primarily to test hypotheses (Templeton et al. 1987;French et al. 2005), rather than for estimating parameters of appropriate models.However, implementing the second approach is considerably more challenging and generally requires the use of modern computationally intensive statistical methods (Stephens and Donnelly 2000). In particular, this often requires the development of customized programs to analyze the data under the specific model or models of interest, and the application of this approach can be limited by the availability of suitable software.In this article we consider a new approach, which lies between these two approaches. The basic idea is (i) to perform infer...

show abstract

Section: Tablementioning

confidence: 99%

Postprocessing of Genealogical Trees

Meligkotsidou

Fearnhead

2007

Genetics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many methods to exploit this pattern have been developed in an effort to identify loci under recent positive selection [Tajima, 1989, Fu and Li, 1993, Hudson et al, 1994, Kelly, 1997,Depaulis et al, 1998,Andolfatto et al, 1999, Fay and Wu, 2000, Sabeti et al, 2002, Kim and Stephan, 2002, Kim and Nielsen, 2004, Nielsen et al, 2005, Toomajian et al, 2006, Voight et al, 2006, Tang et al, 2007, Sabeti et al, 2007, Williamson et al, 2007, Pickrell et al, 2009, Chen et al, 2010, Grossman et al, 2013, Chen et al, 2015]. A parallel effort has focused on quantifying specific properties of the signature to infer the age of the selected allele [Serre et al, 1990, Kaplan et al, 1994, Risch et al, 1995, Goldstein et al, 1999, Guo and Xiong, 1997, Slatkin and Rannala, 1997, Stephens et al, 1998, Reich and Goldstein, 1999, Thomson et al, 2000, Slatkin, 2002, Tang et al, 2002, Innan and Nordborg, 2003, Przeworski, 2003, Toomajian et al, 2003, Meligkotsidou and Fearnhead, 2005, Tishkoff et al, 2007, Bryk et al, 2008, Coop et al, 2008, Slatkin, 2008, Peter et al, 2012, Beleza et al, 2013b, Chen and Slatkin, 2013, Chen et al, 2015, Nakagome et al, 2015].…”

Section: Introductionmentioning

confidence: 99%

“…One category of methods used to estimate allele age relies on a point estimate of the mean length of the selected haplotype, or a count of derived mutations within an arbitrary cutoff distance from the selected site [Thomson et al, 2000, Tang et al, 2002, Meligkotsidou and Fearnhead, 2005, Hudson, 2007, Coop et al, 2008]. These approaches ignore uncertainty in the extent of the selected haplotype on each chromosome, leading to inflated confidence in the point estimates.…”

Section: Introductionmentioning

confidence: 99%

Estimating time to the common ancestor for a beneficial allele

Smith

Coop

Stephens

et al. 2016

Preprint

View full text Add to dashboard Cite

10The haplotypes of a beneficial allele carry information about its history that can shed light on its age and 11 putative cause for its increase in frequency. Specifically, the signature of an allele's age is contained in 12 the pattern of local ancestry that mutation and recombination impose on its haplotypic background. We 13 provide a method to exploit this pattern and infer the time to the common ancestor of a positively selected 14 allele following a rapid increase in frequency. We do so using a hidden Markov model which leverages 15 the length distribution of the shared ancestral haplotype, the accumulation of derived mutations on 16 the ancestral background, and the surrounding background haplotype diversity. Using simulations, we 17 demonstrate how the inclusion of information from both mutation and recombination events increases 18 accuracy relative to approaches that only consider a single type of event. We also show the behavior of 19 the estimator in cases where data do not conform to model assumptions, and provide some diagnostics 20 for assessing and improving inference. Using the method, we analyze population-specific patterns in 21 the 1000 Genomes Project data to provide a global perspective on the timing of adaptation for several 22 variants which show evidence of recent selection and functional relevance to diet, skin pigmentation, and 23 morphology in humans. 24 Introduction 25 A complete understanding adaptation depends on a description of the genetic mechanisms and selective 26 history that underlies adaptive genetic variation [Radwan and Babik, 2012]. Once a genetic variant 27 underlying a putatively adaptive trait has been identified, several questions remain: What is the molecular 28 mechanism by which the variant affects organismal traits and fitness [Dalziel et al., 2009]?; what is the 29 selective mechanism responsible for allelic differences in fitness?; Did the variant arise by mutation more 30 than once [Elmer and Meyer, 2011]?; when did each unique instance of the variant arise and spread [Slatkin 31 and Rannala, 2000]? Addressing these questions for numerous case studies of beneficial variants across 32 multiple species will be necessary to gain full insight into general properties of adaptation. [Stinchcombe 33 and Hoekstra, 2008] 34Here, our focus is on the the last of the questions given above; that is, when did a mutation arise 35 and spread? Understanding these dates can give indirect evidence regarding the selective pressure that 36 may underlie the adaptation; This is especially useful in cases where it is logistically infeasible to assess 37 fitness consequences of a variant in the field directly [Barrett and Hoekstra, 2011]. In humans, for 38 example, dispersal across the globe has resulted in the occupation of a wide variety of habitats, and in 39 several cases, selection in response to specific ecological pressures appears to have taken place. There 40 are well-documented cases of loci showing evidence of recent selection in addition to being functionall...

show abstract

“…(For more about the model-free approach, see, e.g., Stumpf andGoldstein 2001 andMeligkotsidou andFearnhead 2005, andreferences therein. ) In this model the ancestral tree of a sample is a rootedbifurcating tree with random-joining topological structure, but the time intervals between consecutive coalescent events are parameters.…”

Section: Discussionmentioning

confidence: 99%

Topologies of the Conditional Ancestral Trees and Full-Likelihood-Based Inference in the General Coalescent Tree Framework

Sargsyan

2010

Genetics

View full text Add to dashboard Cite

The general coalescent tree framework is a family of models for determining ancestries among random samples of DNA sequences at a nonrecombining locus. The ancestral models included in this framework can be derived under various evolutionary scenarios. Here, a computationally tractable full-likelihoodbased inference method for neutral polymorphisms is presented, using the general coalescent tree framework and the infinite-sites model for mutations in DNA sequences. First, an exact sampling scheme is developed to determine the topologies of conditional ancestral trees. However, this scheme has some computational limitations and to overcome these limitations a second scheme based on importance sampling is provided. Next, these schemes are combined with Monte Carlo integrations to estimate the likelihood of full polymorphism data, the ages of mutations in the sample, and the time of the most recent common ancestor. In addition, this article shows how to apply this method for estimating the likelihood of neutral polymorphism data in a sample of DNA sequences completely linked to a mutant allele of interest. This method is illustrated using the data in a sample of DNA sequences at the APOE gene locus.T HE interest in analyzing polymorphism data in contemporary samples of DNA sequences under various evolutionary scenarios creates a demand to design computationally tractable full-likelihood-based inference methods. For an evolutionary scenario of interest, an ancestral-mutation model can be used to design such a method. The ancestral-mutation model for a sample of DNA sequences at a nonrecombining locus is a combination of two processes: one is an ancestral process that traces the lineages of the sample back in time until the most recent common ancestor, constructing an ancestral tree for the sample. The second is a mutation process that is superimposed on the ancestral tree. The complexities of ancestralmutation models make the design of such methods challenging. Full data are used instead of summary statistics, which can result in loss of important information in the data (see Felsenstein 1992; Donnelly and Tavaré 1995). In addition, current methods use specific features of the underlying ancestral-mutation models, so they lose flexibility to be applicable to other ancestral-mutation models.More specifically, Griffiths and Tavaré (1994c, 1995) and Kuhner et al. (1995) developed full-likelihood-based inference methods for neutral polymorphisms at a nonrecombining locus. They used the combinations of the standard coalescent (Kingman 1982a,b,c;Hudson 1983;Tajima 1983) with the finite-sites or infinite-sites (Watterson 1975) models as ancestral-mutation models. Stephens and Donnelly (2000) designed an importance sampling method to estimate the full likelihood of the data using the same settings for the ancestralmutation models. Hobolth et al. (2008) provided another importance sampling scheme restricted to the infinite-sites model. The last two methods are computationally more efficient than the first two metho...

show abstract

Maximum-Likelihood Estimation of Coalescence Times in Genealogical Trees

Cited by 9 publications

References 21 publications

Postprocessing of Genealogical Trees

Postprocessing of Genealogical Trees

Estimating time to the common ancestor for a beneficial allele

Topologies of the Conditional Ancestral Trees and Full-Likelihood-Based Inference in the General Coalescent Tree Framework

Contact Info

Product

Resources

About