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0000-0001-7190-5104
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University of Oxford
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University of Oxford University College Oxford
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Publisher: Wiley
Date: 04-1971
Publisher: Elsevier BV
Date: 05-1986
Publisher: Springer New York
Date: 1997
Publisher: Informa UK Limited
Date: 1998
Publisher: Elsevier BV
Date: 04-1982
Publisher: Elsevier BV
Date: 09-2003
DOI: 10.1016/S0040-5809(03)00075-3
Abstract: General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a s le of n genes. A general formula is derived for the frequency spectrum of a mutation in a s le. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.
Publisher: Elsevier BV
Date: 04-1992
DOI: 10.1016/0888-7543(92)90293-2
Abstract: There are many situations in which grain distributions resulting from in situ hybridization of radioactively labeled probes to unique genes should be subjected to a statistical analysis. However, the problems posed by analysis of in situ hybridization data are not straightforward, and no completely satisfying method is currently available. We have developed a procedure in which the major and any number of minor site(s) of hybridization may be specifically located and the significance of each tested. This zmax procedure first tests the overall distribution for departure from randomness and then identifies significantly overlabeled whole chromosomes (or chromosome arms or other large segments), a process that may be repeated to pinpoint significantly overlabeled regions within these chromosomes. We describe in detail the derivation of the zmax statistic, present tables of significant zmax levels, and show with ex les how zmax is used in tests of significance of in situ hybridization data.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2021
Publisher: Canadian Mathematical Society
Date: 06-1974
Abstract: The permanent of an n × n matrix A = ( a ij ) is defined as where S n is the symmetric group of order n . For a survey article on permanents the reader is referred to [2]. An unresolved conjecture due to van der Waerden states that if A is an n × n doubly stochastic matrix then per ( A ) ≧ n !/ n n , with equality if and only if A = J n = (1/ n ).
Publisher: Springer Science and Business Media LLC
Date: 06-1981
DOI: 10.1007/BF00276133
Publisher: Springer New York
Date: 1997
Publisher: Elsevier BV
Date: 12-2009
Publisher: Springer Science and Business Media LLC
Date: 10-1980
DOI: 10.1007/BF00275842
Publisher: Wiley
Date: 08-1972
Publisher: Elsevier BV
Date: 11-2013
Publisher: Elsevier BV
Date: 07-2016
Publisher: Informa UK Limited
Date: 08-06-2016
Publisher: Mary Ann Liebert Inc
Date: 1996
Abstract: The s ling distribution of a collection of DNA sequences is studied under a model where recombination can occur in the ancestry of the sequences. The infinitely-many-sites model of mutation is assumed where there may only be one mutation at a given site. Ancestral inference procedures are discussed for: estimating recombination and mutation rates estimating the times to the most recent common ancestors along the sequences estimating ages of mutations and estimating the number of recombination events in the ancestry of the s le. Inferences are made conditional on the configuration of the pattern of mutations at sites in observed s le sequences. A computational algorithm based on a Markov chain simulation is developed, implemented, and illustrated with ex les for these inference procedures. This algorithm is very computationally intensive.
Publisher: Elsevier BV
Date: 09-1978
Publisher: Elsevier BV
Date: 06-2009
DOI: 10.1016/J.TPB.2009.03.004
Abstract: A coalescent dual process for a multi-type Moran model with genic selection is derived using a generator approach. This leads to an expansion of the transition functions in the Moran model and the Wright-Fisher diffusion process limit in terms of the transition functions for the coalescent dual. A graphical representation of the Moran model (in the spirit of Harris) identifies the dual as a strong dual process following typed lines backwards in time. An application is made to the harmonic measure problem of finding the joint probability distribution of the time to the first loss of an allele from the population and the distribution of the surviving alleles at the time of loss. Our dual process mirrors the Ancestral Selection Graph of [Krone, S. M., Neuhauser, C., 1997. Ancestral processes with selection. Theoret. Popul. Biol. 51, 210-237 Neuhauser, C., Krone, S. M., 1997. The genealogy of s les in models with selection. Genetics 145, 519-534], which allows one to reconstruct the genealogy of a random s le from a population subject to genic selection. In our setting, we follow [Stephens, M., Donnelly, P., 2002. Ancestral inference in population genetics models with selection. Aust. N. Z. J. Stat. 45, 395-430] in assuming that the types of in iduals in the s le are known. There are also close links to [Fearnhead, P., 2002. The common ancestor at a nonneutral locus. J. Appl. Probab. 39, 38-54]. However, our methods and applications are quite different. This work can also be thought of as extending a dual process construction in a Wright-Fisher diffusion in [Barbour, A.D., Ethier, S.N., Griffiths, R.C., 2000. A transition function expansion for a diffusion model with selection. Ann. Appl. Probab. 10, 123-162]. The application to the harmonic measure problem extends a construction provided in the setting of a neutral diffusion process model in [Ethier, S.N., Griffiths, R.C., 1991. Harmonic measure for random genetic drift. In: Pinsky, M.A. (Ed.), Diffusion Processes and Related Problems in Analysis, vol. 1. In: Progress in Probability Series, vol. 22, Birkhäuser, Boston, pp. 73-81].
Publisher: Cambridge University Press (CUP)
Date: 06-1988
DOI: 10.2307/3214441
Abstract: A probability density function important in the Poisson Dirichlet process of population genetics is studied. An accurate computational algorithm is given for this density and for the marginal distributions of the points in the Poisson Dirichlet process. The distribution of the maximal point of the process is tabulated. Rational polynomial approximations in θ , the mutation parameter, are found for the expected values of the first three maximal points.
Publisher: Elsevier BV
Date: 03-1999
DOI: 10.1086/302282
Publisher: Cambridge University Press (CUP)
Date: 06-1979
DOI: 10.2307/1426801
Publisher: Springer Science and Business Media LLC
Date: 11-2001
Abstract: In this paper a new form of the solution for the Laplace transform and moments of the distribution of the waiting time for two genes to coalescence is presented. The two genes are s led from a sub ided population where migration rates between populations are constant in time. Equal subpopulation size is not assumed. For the special case of an island model with equal migration rates between islands, the Laplace transform of the coalescence time and the first and second moments are found explicitly. The new form of the solutions allows numerical calculation. The connection of how the results relate to a panmictic population when migration rates are large is illustrated using strong-migration-limit theory.
Publisher: Elsevier BV
Date: 06-1987
Publisher: Elsevier BV
Date: 09-2010
DOI: 10.1016/J.TPB.2010.05.004
Abstract: The genealogical structure of neutral populations in which reproductive success is highly-skewed has been the subject of many recent studies. Here we derive a coalescent dual process for a related class of continuous-time Moran models with viability selection. In these models, in iduals can give birth to multiple offspring whose survival depends on both the parental genotype and the brood size. This extends the dual process construction for a multi-type Moran model with genic selection described in Etheridge and Griffiths (2009). We show that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which we call the lamda-Fleming-Viot process with viability selection and we derive a coalescent dual for this process directly from the generator and as a limit from the Moran models. The dual is a branching-coalescing process similar to the Ancestral Selection Graph which follows the typed ancestry of genes backwards in time with real and virtual lineages. As an application, the transition functions of the non-neutral Moran and lamda-coalescent models are expressed as mixtures of the transition functions of the dual process.
Publisher: Institute of Mathematical Statistics
Date: 08-1994
Publisher: Elsevier BV
Date: 04-1981
Publisher: Springer Science and Business Media LLC
Date: 09-1987
DOI: 10.1007/BF00277166
Abstract: A 78-year-old man was admitted to the Department of Otolaryngology of our hospital with bilateral lymph node swelling of the neck. Pathological examination revealed squamous cell carcinoma (SCC). He underwent computed tomography (CT) of the neck and chest, upper gastrointestinal endoscopy and laryngoscopy to locate a primary tumour, however, no obvious tumour was detected. Eight months later, a renal tumour without regional lymph node swelling was found when a chest CT scan was performed again. We then performed a right nephroureterectomy and regional lymphadenectomy. Pathological examination revealed SCC of the renal pelvis, pT3, grade 3, without regional lymph node metastasis. This pathological finding for the kidney was virtually the same as that for cervical lymph nodes. Therefore, it was thought that his cervical tumours had metastasized from the renal pelvic SCC. To the best of our knowledge, there are no reports of renal pelvic carcinoma without regional lymph node metastasis having only cervical lymph node metastasis. This is the first case of isolated cervical lymph node metastasis from renal pelvic SCC.
Publisher: Elsevier BV
Date: 02-1979
Publisher: Springer Science and Business Media LLC
Date: 05-1983
DOI: 10.1007/BF00276111
Abstract: To investigate the genetic causes and clinical characteristics of dominant optic atrophy (DOA) in a Chinese family. A 5-generation pedigree of 35 family members including 12 in iduals affected with DOA was recruited from Shenzhen Eye Hospital, China. Four affected family members and one unaffected family member were selected for whole exome sequencing. Sanger sequencing was used to confirm and screen the identified mutation in 18 members of the family. The disease-causing mutation was identified by bioinformatics analysis and confirmed by segregation analysis. The clinical characteristics of the family members were analyzed. A heterozygous missense mutation (c.1313A>G, p.D438G) in Our results suggest that the p.D438G mutation in
Publisher: Institute of Mathematical Statistics
Date: 1991
Publisher: Informa UK Limited
Date: 22-06-2022
Publisher: Wiley
Date: 29-09-2014
Publisher: Elsevier BV
Date: 02-1983
DOI: 10.1016/0040-5809(83)90003-5
Abstract: A method is developed for simulating the allele frequencies in an equilibrium or transient population under the effects of neutral mutation and random drift. The method is based on diffusion theory and is fast so that it can be used to study in detail the distribution of heterozygosity or any quantity that can be expressed as a function of allele frequencies. It has been applied to study the distribution of heterozygosity and the distribution of the frequencies of the first three most frequent alleles in a population. It also has been applied to study the distribution of the number of alleles shared by two populations that were derived from a common stock.
Publisher: Elsevier BV
Date: 02-1990
DOI: 10.1016/0040-5809(90)90029-U
Abstract: The probability distribution and moments of the number of alleles present in a s le of homologous chromosomes are studied. It is assumed that there are multiple copies of the gene on each chromosome. When there are only two copies per chromosome or when there are only two or three chromosomes, it is possible to use analytic methods to tackle the problem. Otherwise, a simulation method is suggested.
Publisher: Elsevier BV
Date: 12-2016
DOI: 10.1016/J.TPB.2016.08.007
Abstract: Duality plays an important role in population genetics. It can relate results from forwards-in-time models of allele frequency evolution with those of backwards-in-time genealogical models a well known ex le is the duality between the Wright-Fisher diffusion for genetic drift and its genealogical counterpart, the coalescent. There have been a number of articles extending this relationship to include other evolutionary processes such as mutation and selection, but little has been explored for models also incorporating crossover recombination. Here, we derive from first principles a new genealogical process which is dual to a Wright-Fisher diffusion model of drift, mutation, and recombination. The process is reminiscent of the ancestral recombination graph, a widely-used multilocus genealogical model, but here ancestral lineages are typed and transition rates are regarded as being conditioned on an observed configuration at the leaves of the genealogy. Our approach is based on expressing a putative duality relationship between two models via their infinitesimal generators, and then seeking an appropriate test function to ensure the validity of the duality equation. This approach is quite general, and we use it to find dualities for several important variants, including both a discrete L-locus model of a gene and a continuous model in which mutation and recombination events are scattered along the gene according to continuous distributions. As an application of our results, we derive a series expansion for the transition function of the diffusion. Finally, we study in further detail the case in which mutation is absent. Then the dual process describes the dispersal of ancestral genetic material across the ancestors of a s le. The stationary distribution of this process is of particular interest we show how duality relates this distribution to haplotype fixation probabilities. We develop an efficient method for computing such probabilities in multilocus models.
Publisher: Elsevier BV
Date: 05-1995
DOI: 10.1016/0025-5564(94)00044-Z
Abstract: The infinitely-many-sites process is often used to model the sequence variability observed in s les of DNA sequences. Despite its popularity, the s ling theory of the process is rather poorly understood. We describe the tree structure underlying the model and show how this may be used to compute the probability of a s le of sequences. We show how to produce the unrooted genealogy from a set of sites in which the ancestral labeling is unknown and from this the corresponding rooted genealogies. We derive recursions for the probability of the configuration of sequences (equivalently, of trees) in both the rooted and unrooted cases. We give a computational method based on Monte Carlo recursion that provides approximates to s ling probabilities for s les of any size. Among several applications, this algorithm may be used to find maximum likelihood estimators of the substitution rate, both when the ancestral labeling of sites is known and when it is unknown.
Publisher: Elsevier BV
Date: 03-2000
Publisher: Springer Science and Business Media LLC
Date: 17-09-2019
DOI: 10.1007/S00285-019-01430-8
Abstract: The transition distribution of a s le taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of the s le up to the most recent common ancestor with additional mutations occurring on the lineage from the most recent common ancestor to the time origin if complete coalescence occurs before the origin. The s ling distribution leads to an approximation for the transition density in the diffusion with small mutation rates. This new solution has interest because the transition density in a Wright-Fisher diffusion with general mutation rates is not known.
Publisher: Cambridge University Press
Date: 15-07-2010
Publisher: Elsevier BV
Date: 04-1996
Publisher: Elsevier BV
Date: 11-2004
DOI: 10.1016/J.TPB.2004.06.006
Abstract: The extent to which natural selection shapes ersity within populations is a key question for population genetics. Thus, there is considerable interest in quantifying the strength of selection. A full likelihood approach for inference about selection at a single site within an otherwise neutral fully linked sequence of sites is described here. A coalescent model of evolution is used to model the ancestry of a s le of DNA sequences which have the selected site segregating. The mutation model, for the selected and neutral sites, is the infinitely many-sites model where there is no back or parallel mutation at sites. A unique perfect phylogeny, a gene tree, can be constructed from the configuration of mutations on the s le sequences under this model of mutation. The approach is general and can be used for any bi-allelic selection scheme. Selection is incorporated through modelling the frequency of the selected and neutral allelic classes stochastically back in time, then using a sub ided population model considering the population frequencies through time as variable population sizes. An importance s ling algorithm is then used to explore over coalescent tree space consistent with the data. The method is applied to a simulated data set and the gene tree presented in Verrelli et al. (2002).
Publisher: Institute of Mathematical Statistics
Date: 08-1999
Publisher: Cambridge University Press (CUP)
Date: 09-1988
DOI: 10.2307/1427033
Abstract: In iduals in a population which grows according to the rules defining the simple branching process can mutate to novel allelic forms. We obtain limit theorems for the number of alleles present in any generation, the total number of alleles ever seen and the number of the generation containing the last mutation event. In addition we define a notion of frequency spectrum for each generation as the expected number of alleles having a given number of representatives. As the generation number increases we prove the existence of a limiting notion of the frequency spectrum and discuss its upper tail behaviour. Our results here are incomplete and we make some conjectures which are supported by informal argument and specific ex les.
Publisher: Wiley
Date: 11-1972
Publisher: Birkhäuser Boston
Date: 1990
Publisher: S. Karger AG
Date: 2005
DOI: 10.1159/000088845
Abstract: Large-scale association studies hold promise for discovering the genetic basis of common human disease. These studies will consist of a large number of in iduals, as well as large number of genetic markers, such as single nucleotide polymorphisms (SNPs). The potential size of the data and the resulting model space require the development of efficient methodology to unravel associations between phenotypes and SNPs in dense genetic maps. Our approach uses a genetic algorithm (GA) to construct logic trees consisting of Boolean expressions involving strings or blocks of SNPs. These blocks or nodes of the logic trees consist of SNPs in high linkage disequilibrium (LD), that is, SNPs that are highly correlated with each other due to evolutionary processes. At each generation of our GA, a population of logic tree models is modified using selection, cross-over and mutation moves. Logic trees are selected for the next generation using a fitness function based on the marginal likelihood in a Bayesian regression frame-work. Mutation and cross-over moves use LD measures to pro pose changes to the trees, and facilitate the movement through the model space. We demonstrate our method and the flexibility of logic tree structure with variable nodal lengths on simulated data from a coalescent model, as well as data from a candidate gene study of quantitative genetic variation.
Publisher: Institute of Mathematical Statistics
Date: 07-1993
Publisher: Springer International Publishing
Date: 04-11-2020
Publisher: Cambridge University Press (CUP)
Date: 06-2004
Abstract: Stephens and Donnelly (2000) constructed an efficient sequential importance-s ling proposal distribution on coalescent histories of a s le of genes for computing the likelihood of a type configuration of genes in the s le. In the current paper a characterization of their importance-s ling proposal distribution is given in terms of the diffusion-process generator describing the distribution of the population gene frequencies. This characterization leads to a new technique for constructing importance-s ling algorithms in a much more general framework when the distribution of population gene frequencies follows a diffusion process, by approximating the generator of the process.
Publisher: Elsevier BV
Date: 10-1994
Publisher: Wiley
Date: 11-1970
Publisher: Elsevier BV
Date: 12-2018
DOI: 10.1016/J.TPB.2018.09.004
Abstract: The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for approximating the forward Kolmogorov equation, the stationary distribution is obtained to leading order as a set of line densities on the edges of the s le space, corresponding to states for which one island is bi-allelic and the other island is non-segregating, and a set of point masses at the corners of the s le space, corresponding to states for which both islands are simultaneously non-segregating. Analytic results for the corner probabilities and line densities are verified independently using the backward generator and for the corner probabilities using the coalescent.
Publisher: Elsevier BV
Date: 07-2018
DOI: 10.1016/J.TPB.2017.09.005
Abstract: The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when x=z=0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t∈(0,T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t∈(0,T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching Pólya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting.
Publisher: Cambridge University Press (CUP)
Date: 03-1981
DOI: 10.2307/3213165
Abstract: The transient distribution of the number of segregating sites in a s le from a large population of 2 N genes is found. Segregating sites are split into those in common with the sites segregating in the initial population and those segregating due to new mutations. The waiting time distribution for a population to lose all of its initial sites is also studied. A neutral infinite-sites model with no recombination is used. This paper extends the work of Watterson (1975), from the stationary case and of Li (1977) from the transient distribution in a s le of 2.
Publisher: Springer New York
Date: 1993
Publisher: Springer Science and Business Media LLC
Date: 03-1982
DOI: 10.1007/BF00276292
Publisher: Elsevier BV
Date: 02-1980
Publisher: Cambridge University Press (CUP)
Date: 06-2006
Abstract: We study identities for the distribution of the number of edges at time t back (i.e. measured backwards) in a coalescent tree whose subtrees have no mutations. This distribution is important in the infinitely-many-alleles model of mutation, where every mutation is unique. The model includes, as a special case, the number of edges in a coalescent tree at time t back when mutation is ignored. The identities take the form of expected values of functions of Z t =e i X t , where X t is distributed as standard Brownian motion. Associated identities are also found for the distributions of the time to the most recent common ancestor, the time until loss of ancestral lines by coalescence or mutation, and the age of a mutation. Hypergeometric functions play an important role in the identities. The identities are of mathematical interest, as well as potentially being formulae to use for numerical integration or simulation to compute distributions that are usually expressed as alternating-sign series expansions, which are difficult to compute.
Publisher: Cambridge University Press (CUP)
Date: 06-1982
DOI: 10.2307/1426518
Abstract: A study is made of the joint distribution of the number of alleles and segregating sites in a random s le of genes from the infinite-alleles model of population genetics. Tables of the joint distribution are given for representative values of the mutation parameter. A conclusion is that each segregating site has a high probability of delineating an allele type.
Publisher: Cambridge University Press (CUP)
Date: 12-1990
DOI: 10.1017/S0001867800023120
Abstract: The neutral two-locus model in population genetics is reformulated as a measure-valued diffusion process and is shown under certain conditions to have a unique stationary distribution and be weakly ergodic. The limits of the process and its stationary distribution as the recombination parameter tends to infinity are found. Genealogies are incorporated into the model, and it is shown that a random s le of size n from the population at stationarity has a common ancestor.
Publisher: Springer Science and Business Media LLC
Date: 1997
DOI: 10.1007/PL00000063
Abstract: We have analyzed allelic sequence variation in sixty-one 3-kb beta-globin sequences from the Melanesian population of Vanuatu to demonstrate the value of (1) turning to the autosomal nuclear genome for studies on the evolution of modern humans and (2) using new analytical methods based on a coalescent model. After excluding recombination events, beta-globin sequence variants were connected in a unique gene tree. A gene tree provides more information for inferences on the population genealogy than simple summary statistics such as the average pairwise sequence difference. Estimates of the time to the most recent common ancestor (MRCA) and of the ages of each mutation, conditional on the gene tree, were made using new maximum likelihood methods assuming a coalescent model. We found that allelic beta-globin variation coalesces to a single shared ancestral haplotype over a time scale of approximately 900,000 years. Three major haplotypes (A1, B1, C3) that are older than 200,000 years identify ancestral ersity contemporaneous with the single MRCA for mitochondrial variation.
Publisher: Institute of Mathematical Statistics
Date: 02-2000
Publisher: Cambridge University Press (CUP)
Date: 12-1990
DOI: 10.2307/1427561
Abstract: The neutral two-locus model in population genetics is reformulated as a measure-valued diffusion process and is shown under certain conditions to have a unique stationary distribution and be weakly ergodic. The limits of the process and its stationary distribution as the recombination parameter tends to infinity are found. Genealogies are incorporated into the model, and it is shown that a random s le of size n from the population at stationarity has a common ancestor.
Publisher: MDPI AG
Date: 09-05-2016
DOI: 10.3390/SYM8050033
Publisher: John Wiley & Sons, Inc.
Date: 15-10-2004
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Date: 08-2011
DOI: 10.3150/10-BEJ305
Publisher: Cambridge University Press (CUP)
Date: 12-2014
Abstract: The d -dimensional Λ-Fleming-Viot generator acting on functions g ( x ), with x being a vector of d allele frequencies, can be written as a Wright-Fisher generator acting on functions g with a modified random linear argument of x induced by partitioning occurring in the Λ-Fleming-Viot process. The eigenvalues and right polynomial eigenvectors are easy to see from this representation. The two-dimensional process, which has a one-dimensional generator, is considered in detail. A nonlinear equation is found for the Green's function. In a model with genic selection a proof is given that there is a critical selection value such that if the selection coefficient is greater than or equal to the critical value then fixation, when the boundary 1 is hit, has probability 1 beginning from any nonzero frequency. This is an analytic proof different from the proofs of Der, Epstein and Plotkin (2011) and Foucart (2013). An application in the infinitely-many-alleles Λ-Fleming-Viot process is finding an interesting identity for the frequency spectrum of alleles that is based on size biasing. The moment dual process in the Fleming-Viot process is the usual Λ-coalescent tree back in time. The Wright-Fisher representation using a different set of polynomials g n ( x ) as test functions produces a dual death process which has a similarity to the Kingman coalescent and decreases by units of one. The eigenvalues of the process are analogous to the Jacobi polynomials when expressed in terms of g n ( x ), playing the role of x n . Under the stationary distribution when there is mutation, is analogous to the n th moment in a beta distribution. There is a d -dimensional version g n ( X ), and even an intriguing Ewens' s ling formula analogy when d → ∞.
Publisher: Oxford University Press (OUP)
Date: 02-1997
DOI: 10.1093/GENETICS/145.2.505
Abstract: The paper is concerned with methods for the estimation of the coalescence time (time since the most recent common ancestor) of a s le of intraspecies DNA sequences. The methods take advantage of prior knowledge of population demography, in addition to the molecular data. While some theoretical results are presented, a central focus is on computational methods. These methods are easy to implement, and, since explicit formulae tend to be either unavailable or unilluminating, they are also more useful and more informative in most applications. Extensions are presented that allow for the effects of uncertainty in our knowledge of population size and mutation rates, for variability in population sizes, for regions of different mutation rate, and for inference concerning the coalescence time of the entire population. The methods are illustrated using recent data from the human Y chromosome.
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Date: 05-2013
DOI: 10.3150/11-BEJ403
Publisher: Cambridge University Press (CUP)
Date: 06-1979
DOI: 10.2307/1426843
Abstract: The exact transient s ling distribution is found for the infinite neutral alleles model with mutation, thus extending the stationary distribution found by Ewens (1972). The first eigenfunction in the s ling distribution depends only on the homozygosity. In a large s le the expected number of allele types is close to the expected number in a stationary distribution and depends little on the initial frequencies or the time of s ling. The expected number of types in a s le for a non-stationary population is tabulated. The s ling distribution from a population with no mutation is found. The probability that the population is monomorphic given that the s le contains only one type is tabulated, where initially the population has a large number of alleles with equal frequencies. A study is made of the joint distribution of the allele frequencies in two s les taken time t apart from a stationary population. Of particular interest is the number of allele types in common in two such s les. The distribution of the number of types in common in a population viewed at time t apart is also found and tabulated for different mutation rates and time. The expected frequency of the allele types in common is tabulated. The distribution of allele frequencies in two ergent populations of common ancestry is shown to be the same as the distribution of frequencies in a single population at two time points 2 t apart. A sufficient statistic for the time of ergence is shown to be the paired frequencies of the allele types in common. The expected waiting time until the populations have no allele types in common is tabulated.
Publisher: Springer International Publishing
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 08-1991
DOI: 10.1007/BF00160191
Publisher: Cambridge University Press (CUP)
Date: 06-2008
Abstract: The diffusion-generator approximation technique developed by De Iorio and Griffiths (2004a) is a very useful method of constructing importance-s ling proposal distributions. Being based on general mathematical principles, the method can be applied to various models in population genetics. In this paper we extend the technique to the neutral coalescent model with recombination, thus obtaining novel s ling distributions for the two-locus model. We consider the case with sub ided population structure, as well as the classic case with only a single population. In the latter case we also consider the importance-s ling proposal distributions suggested by Fearnhead and Donnelly (2001), and show that their two-locus distributions generally differ from ours. In the case of the infinitely-many-alleles model, our approximate s ling distributions are shown to be generally closer to the true distributions than are Fearnhead and Donnelly's.
Publisher: Elsevier BV
Date: 06-1991
DOI: 10.1016/0040-5809(91)90023-9
Abstract: Watterson's formulae for the distribution, mean, and variance of the number of alleles in common on two chromosomes with multigene families are derived as simpler forms, and extended to chromosomes with an infinite number of genes, each evolving as in an infinitely many alleles model.
Publisher: Institute of Mathematical Statistics
Date: 08-1969
Publisher: Wiley
Date: 06-1980
Publisher: Springer Science and Business Media LLC
Date: 11-1989
DOI: 10.1007/BF00276949
Abstract: Drug therapies for advanced breast cancer in hormone-receptor-positive disease include both hormonal and chemotherapies. Current UK practice is to minimise toxicity by using sequential hormonal agents for as long as clinically appropriate. A Markov model was developed to investigate the cost effectiveness of different sequences of therapies, particularly exploring the effects of adding an additional hormonal agent, fulvestrant, to the treatment pathway. A systematic review was undertaken and a panel of seven UK oncologists validated assumptions used for treatment efficacy, treatment pathways and resources used. Fulvestrant was found to be a cost-effective treatment option when added to the treatment sequence as a second- or third-line hormonal therapy for advanced disease. For a cohort of 1000 patients, fulvestrant as a second-line hormone therapy provided an additional 47 life years and 41 quality-adjusted life years (QALYs), at an additional cost of pound 301 359. This equated to pound 6500 per life years gained and pound 7500 per QALY. When used as a third-line option, the fulvestrant arm was dominant providing an increase in health benefit of 27 QALYs for the whole cohort, at a mean overall cost reduction of pound 430 per patient. Sensitivity analyses showed these results to be robust, demonstrating that fulvestrant is an economically viable additional endocrine option in the United Kingdom for the treatment of hormone responsive advanced breast cancer.
Publisher: Elsevier BV
Date: 07-2018
DOI: 10.1016/J.TPB.2018.04.006
Abstract: We consider inference about the history of a s le of DNA sequences, conditional upon the haplotype counts and the number of segregating sites observed at the present time. After deriving some theoretical results in the coalescent setting, we implement rejection s ling and importance s ling schemes to perform the inference. The importance s ling scheme addresses an extension of the Ewens S ling Formula for a configuration of haplotypes and the number of segregating sites in the s le. The implementations include both constant and variable population size models. The methods are illustrated by two human Y chromosome datasets.
Publisher: Cambridge University Press (CUP)
Date: 06-1979
DOI: 10.2307/1426842
Abstract: An expansion in orthogonal polynomials is found for the transition density in a neutral multi-allele diffusion model where the mutation rates of allele types A i → A j are assumed to be u j (≥ O). The density is found when the mutation rate is positive for all allele types, and when some or all have zero mutation. The asymptotic conditional density is found for a mixture of positive and zero mutation rates. The infinite alleles limit with equal mutation is studied. Eigenfunctions of the process are derived and the frequency spectrum found. An important result is that the first eigenfunction depends only on the homozygosity. A density for the time to fixation with zero mutation is found for the K allele, and infinite alleles model.
Publisher: Institute of Mathematical Statistics
Date: 2020
DOI: 10.1214/20-ECP357
Publisher: Cambridge University Press (CUP)
Date: 12-1992
DOI: 10.2307/3214710
Abstract: The distribution of the number of alleles in s les from r chromosomes is studied. The stochastic model used includes gene conversion within chromosomes and mutation at loci on the chromosomes. A method is described for simulating the distribution of alleles and an algorithm given for computing lower bounds for the mean number of alleles. A formula is derived for the expected number of s les from r chromosomes which contain the allele type of a locus chosen at random.
Publisher: Elsevier BV
Date: 02-1980
DOI: 10.1016/0040-5809(80)90013-1
Abstract: Since its first appearance in Wuhan, China, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread throughout the world and has become a global pandemic. Several medical comorbidities have been identified as risk factors for coronavirus disease 2019 (COVID-19). However, it remains unclear whether people living with human immunodefeciency virus (PLWH) are at an increased risk of COVID-19 and severe disease manifestation, with controversial suggestion that HIV-infected in iduals could be protected from severe COVID-19 by means of antiretroviral therapy or HIV-related immunosuppression. Several cases of coinfection with HIV and SARS-CoV-2 have been reported from different parts of the globe. This review seeks to provide a holistic overview of SARS-CoV-2 infection in PLWH.
Publisher: Institute of Mathematical Statistics
Date: 04-1987
Publisher: Elsevier BV
Date: 08-1984
Publisher: Elsevier BV
Date: 11-2005
DOI: 10.1016/J.TPB.2005.02.004
Abstract: Ewens' s ling formula, the probability distribution of a configuration of alleles in a s le of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a s le of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.
Publisher: Elsevier BV
Date: 07-2005
DOI: 10.1016/J.TPB.2005.02.001
Abstract: An importance s ling algorithm for computing the likelihood of a s le of genes at loci under a stepwise mutation model in a sub ided population is developed. This allows maximum likelihood estimation of migration rates between subpopulations. The time to the most recent common ancestor of the s le can also be computed. The technique is illustrated by an analysis of a data set of Australian red fox populations.
Publisher: Wiley
Date: 04-1974
Publisher: Cambridge University Press (CUP)
Date: 06-2004
Abstract: De Iorio and Griffiths (2004) developed a new method of constructing sequential importance-s ling proposal distributions on coalescent histories of a s le of genes for computing the likelihood of a type configuration of genes in the s le by simulation. The method is based on approximating the diffusion-process generator describing the distribution of population gene frequencies, leading to an approximate s le distribution and finally to importance-s ling proposal distributions. This paper applies that method to construct an importance-s ling algorithm for computing the likelihood of s les of genes in sub ided population models. The importance-s ling technique of Stephens and Donnelly (2000) is thus extended to models with a Markov chain mutation mechanism between gene types and migration of genes between subpopulations. An algorithm for computing the likelihood of a s le configuration of genes from a sub ided population in an infinitely-many-alleles model of mutation is derived, extending Ewens's (1972) s ling formula in a single population. Likelihood calculation and ancestral inference in gene trees constructed from DNA sequences under the infinitely-many-sites model are also studied. The Griffiths-Tavaré method of likelihood calculation in gene trees of Bahlo and Griffiths (2000) is improved for sub ided populations.
Publisher: Elsevier BV
Date: 06-1975
Publisher: Elsevier BV
Date: 04-1999
Abstract: In a s le of DNA sequences where recombination can occur to the ancestors of the s le, distinct parts of the sequences may have different most recent common ancestors. This paper presents a Markov chain Monte Carlo algorithm for computing the expected time to the most recent common ancestor along the sequences, conditional on where the mutations occur on the sequences.
Publisher: Springer Science and Business Media LLC
Date: 12-1984
DOI: 10.1007/BF00275223
Publisher: Oxford University Press (OUP)
Date: 04-1998
DOI: 10.1093/OXFORDJOURNALS.MOLBEV.A025939
Abstract: We surveyed nine diallelic polymorphic sites on the Y chromosomes of 1,544 in iduals from Africa, Asia, Europe, Oceania, and the New World. Phylogenetic analyses of these nine sites resulted in a tree for 10 distinct Y haplotypes with a coalescence time of approximately 150,000 years. The 10 haplotypes were unevenly distributed among human populations: 5 were restricted to a particular continent, 2 were shared between Africa and Europe, 1 was present only in the Old World, and 2 were found in all geographic regions surveyed. The ancestral haplotype was limited to African populations. Random permutation procedures revealed statistically significant patterns of geographical structuring of this paternal genetic variation. The results of a nested cladistic analysis indicated that these geographical associations arose through a combination of processes, including restricted, recurrent gene flow (isolation by distance) and range expansions. We inferred that one of the oldest events in the nested cladistic analysis was a range expansion out of Africa which resulted in the complete replacement of Y chromosomes throughout the Old World, a finding consistent with many versions of the Out of Africa Replacement Model. A second and more recent range expansion brought Asian Y chromosomes back to Africa without replacing the indigenous African male gene pool. Thus, the previously observed high levels of Y chromosomal genetic ersity in Africa may be due in part to bidirectional population movements. Finally, a comparison of our results with those from nested cladistic analyses of human mtDNA and beta-globin data revealed different patterns of inferences for males and females concerning the relative roles of population history (range expansions) and population structure (recurrent gene flow), thereby adding a new sex-specific component to models of human evolution.
Publisher: Wiley
Date: 06-1978
Publisher: Institute of Mathematical Statistics
Date: 2007
DOI: 10.1214/EJP.V12-434
Publisher: Proceedings of the National Academy of Sciences
Date: 26-12-2001
Abstract: Although some mitochondrial, X chromosome, and autosomal sequence ersity data are available for our closest relatives, Pan troglodytes and Pan paniscus , data from the nonrecombining portion of the Y chromosome (NRY) are more limited. We examined ≈3 kb of NRY DNA from 101 chimpanzees, seven bonobos, and 42 humans to investigate: ( i ) relative levels of intraspecific ersity ( ii ) the degree of paternal lineage sorting among species and subspecies of the genus Pan and ( iii ) the date of the chimpanzee/bonobo ergence. We identified 10 informative sequence-tagged sites associated with 23 polymorphisms on the NRY from the genus Pan . Nucleotide ersity was significantly higher on the NRY of chimpanzees and bonobos than on the human NRY. Similar to mtDNA, but unlike X-linked and autosomal loci, lineages defined by mutations on the NRY were not shared among subspecies of P. troglodytes . Comparisons with mtDNA ND2 sequences from some of the same in iduals revealed a larger female versus male effective population size for chimpanzees. The NRY-based ergence time between chimpanzees and bonobos was estimated at ≈1.8 million years ago. In contrast to human populations who appear to have had a low effective size and a recent origin with subsequent population growth, some taxa within the genus Pan may be characterized by large populations of relatively constant size, more ancient origins, and high levels of sub ision.
Publisher: Springer Science and Business Media LLC
Date: 12-1990
DOI: 10.1007/BF00168175
Publisher: Elsevier BV
Date: 12-1996
Abstract: Estimation for an island model where mutation maintains a k-allele neutral polymorphism at a single locus on each island is considered. The likelihood of an observed s le type configuration is obtained by applying a computational algorithm analogous to Griffiths and Tavaré (Theor. Popul. Biol. 46 (1994), 131-159). This allows the computation of s ling distributions in an island model and investigation of their properties. Given a s le type configuration, the maximum likelihood estimate of the migration parameter is obtained by simulating independently the likelihood at a grid of points and, also, using a surface simulation method. The latter method generates the whole likelihood trajectory in a single application of the simulation program. An estimate of variance of the estimate of the migration parameter is obtained using the likelihood trajectory. A comparison of the maximum likelihood estimates of the gene flow between subpopulations is made with those obtained by using Wright's FST statistic.
Publisher: Springer Science and Business Media LLC
Date: 11-02-2022
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Robert Griffiths.