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Article ; Online: An estimator for the recombination rate from a continuously observed diffusion of haplotype frequencies.

Griffiths, Robert C / Jenkins, Paul A

2023 Volume 86, Issue 6, Page(s) 98

Abstract: Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are ... ...

Abstract	Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are usually based on the idea of integrating over the unobserved possible evolutionary histories of a sample, can therefore be noisy. Here we consider a related question: how would an estimator behave if the evolutionary history actually was observed? This would offer an upper bound on the performance of estimators used in practice. In this paper we derive an expression for the maximum likelihood estimator for the recombination rate based on a continuously observed, multi-locus, Wright-Fisher diffusion of haplotype frequencies, complementing existing work for an estimator of selection. We show that, contrary to selection, the estimator has unusual properties because the observed information matrix can explode in finite time whereupon the recombination parameter is learned without error. We also show that the recombination estimator is robust to the presence of selection in the sense that incorporating selection into the model leaves the estimator unchanged. We study the properties of the estimator by simulation and show that its distribution can be quite sensitive to the underlying mutation rates.
MeSH term(s)	Haplotypes ; Computer Simulation ; Biological Evolution ; Recombination, Genetic ; Models, Genetic
Language	English
Publishing date	2023-05-26
Publishing country	Germany
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	187101-8
ISSN	1432-1416 ; 0303-6812
ISSN (online)	1432-1416
ISSN	0303-6812
DOI	10.1007/s00285-023-01931-7
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Book ; Online: Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection

Favero, Martina / Jenkins, Paul A.

2023

Abstract: Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling ... ...

Abstract	Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. Under a finite-allele mutation model, with possibly parent-dependent mutation, we consider the asymptotic regime where the selective advantage of one allele grows to infinity, while the other parameters remain fixed. In this regime, we show that the Wright-Fisher diffusion can be approximated either by a Gaussian process or by a process whose components are independent continuous-state branching processes with immigration, aligning with analogous results for Wright-Fisher models but employing different methods. While the first process becomes degenerate at stationarity, the latter does not and provides a simple, analytic approximation for the leading term of the sampling probability. Furthermore, using another approach based on a recursion formula, we characterise all remaining terms to provide a full asymptotic expansion for the sampling probability. Finally, we study the asymptotic behaviour of the rates of the block-counting process of the conditional ancestral selection graph and establish an asymptotic duality relationship between this and the diffusion. Comment: 41 pages
Keywords	Mathematics - Probability ; Quantitative Biology - Populations and Evolution
Subject code	519
Publishing date	2023-12-28
Publishing country	us
Document type	Book ; Online
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Book ; Online: An estimator for the recombination rate from a continuously observed diffusion of haplotype frequencies

Griffiths, Robert C. / Jenkins, Paul A.

2022

Abstract	Recombination is a fundamental evolutionary force, but it is difficult to quantify because the effect of a recombination event on patterns of variation in a sample of genetic data can be hard to discern. Estimators for the recombination rate, which are usually based on the idea of integrating over the unobserved possible evolutionary histories of a sample, can therefore be noisy. Here we consider a related question: how would an estimator behave if the evolutionary history actually was observed? This would offer an upper bound on the performance of estimators used in practice. In this paper we derive an expression for the maximum likelihood estimator for the recombination rate based on a continuously observed, multi-locus, Wright--Fisher diffusion of haplotype frequencies, complementing existing work for an estimator of selection. We show that, contrary to selection, the estimator has unusual properties because the observed information matrix can explode in finite time whereupon the recombination parameter is learned without error. We also show that the recombination estimator is robust to the presence of selection in the sense that incorporating selection into the model leaves the estimator unchanged. We study the properties of the estimator by simulation and show that its distribution can be quite sensitive to the underlying mutation rates. Comment: 28 pages, 3 figures
Keywords	Quantitative Biology - Populations and Evolution ; Mathematics - Probability ; Mathematics - Statistics Theory ; 92D15 (Primary) 62M05 (Secondary)
Subject code	519
Publishing date	2022-12-15
Publishing country	us
Document type	Book ; Online
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Article ; Online: EWF: simulating exact paths of the Wright-Fisher diffusion.

Sant, Jaromir / Jenkins, Paul A / Koskela, Jere / Spanò, Dario

Bioinformatics (Oxford, England)

2023 Volume 39, Issue 1

Abstract: Motivation: The Wright-Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation and genetic drift. Simulating the paths ... ...

Abstract	Motivation: The Wright-Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation and genetic drift. Simulating the paths of the process is challenging due to the form of the transition density. We present EWF, a robust and efficient sampler which returns exact draws for the diffusion and diffusion bridge processes, accounting for general models of selection including those with frequency dependence. Results: Given a configuration of selection, mutation and endpoints, EWF returns draws at the requested sampling times from the law of the corresponding Wright-Fisher process. Output was validated by comparison to approximations of the transition density via the Kolmogorov-Smirnov test and QQ plots. Availability and implementation: All softwares are available at https://github.com/JaroSant/EWF. Supplementary information: Supplementary data are available at Bioinformatics online.
MeSH term(s)	Models, Genetic ; Gene Frequency ; Genetics, Population ; Genetic Drift ; Mutation ; Selection, Genetic
Language	English
Publishing date	2023-01-26
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	1422668-6
ISSN	1367-4811 ; 1367-4803
ISSN (online)	1367-4811
ISSN	1367-4803
DOI	10.1093/bioinformatics/btad017
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Article ; Online: Ongoing Recombination in SARS-CoV-2 Revealed through Genealogical Reconstruction.

Ignatieva, Anastasia / Hein, Jotun / Jenkins, Paul A

Molecular biology and evolution

2022 Volume 39, Issue 2

Abstract: The evolutionary process of genetic recombination has the potential to rapidly change the properties of a viral pathogen, and its presence is a crucial factor to consider in the development of treatments and vaccines. It can also significantly affect the ...

Abstract	The evolutionary process of genetic recombination has the potential to rapidly change the properties of a viral pathogen, and its presence is a crucial factor to consider in the development of treatments and vaccines. It can also significantly affect the results of phylogenetic analyses and the inference of evolutionary rates. The detection of recombination from samples of sequencing data is a very challenging problem and is further complicated for SARS-CoV-2 by its relatively slow accumulation of genetic diversity. The extent to which recombination is ongoing for SARS-CoV-2 is not yet resolved. To address this, we use a parsimony-based method to reconstruct possible genealogical histories for samples of SARS-CoV-2 sequences, which enables us to pinpoint specific recombination events that could have generated the data. We propose a statistical framework for disentangling the effects of recurrent mutation from recombination in the history of a sample, and hence provide a way of estimating the probability that ongoing recombination is present. We apply this to samples of sequencing data collected in England and South Africa and find evidence of ongoing recombination.
MeSH term(s)	COVID-19 ; Genome, Viral ; Humans ; Mutation ; Phylogeny ; Recombination, Genetic ; SARS-CoV-2
Language	English
Publishing date	2022-02-21
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	998579-7
ISSN	1537-1719 ; 0737-4038
ISSN (online)	1537-1719
ISSN	0737-4038
DOI	10.1093/molbev/msac028
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Book ; Online: EWF

Sant, Jaromir / Jenkins, Paul A. / Koskela, Jere / Spanò, Dario

simulating exact paths of the Wright--Fisher diffusion

2023

Abstract: The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of the process ... ...

Abstract	The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of the process is challenging due to the form of the transition density. We present EWF, a robust and efficient sampler which returns exact draws for the diffusion and diffusion bridge processes, accounting for general models of selection including those with frequency-dependence. Given a configuration of selection, mutation, and endpoints, EWF returns draws at the requested sampling times from the law of the corresponding Wright--Fisher process. Output was validated by comparison to approximations of the transition density via the Kolmogorov--Smirnov test and QQ plots. All software is available at https://github.com/JaroSant/EWF Comment: 34 pages, 12 figures
Keywords	Quantitative Biology - Populations and Evolution ; Mathematics - Probability ; Quantitative Biology - Quantitative Methods ; Statistics - Applications ; Statistics - Computation ; 92D25 ; 60J70 ; 65C99 ; 60J60
Subject code	519
Publishing date	2023-01-13
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: A characterisation of the reconstructed birth-death process through time rescaling.

Ignatieva, Anastasia / Hein, Jotun / Jenkins, Paul A

Theoretical population biology

2020 Volume 134, Page(s) 61–76

Abstract: The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death process, started ...

Abstract	The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death process, started at a random time in the past, and conditioned to have n sampled individuals at the present. The genealogy of individuals sampled at the present time is then described by the reversed reconstructed process (RRP), which traces the ancestry of the sample backwards from the present. We show that a simple, analytic, time rescaling of the RRP provides a straightforward way to derive its inter-event times. The same rescaling characterises other distributions underlying this process, obtained elsewhere in the literature via more cumbersome calculations. We also consider the case of incomplete sampling of the population, in which each leaf of the genealogy is retained with an independent Bernoulli trial with probability ψ, and we show that corresponding results for Bernoulli-sampled RRPs can be derived using time rescaling, for any values of the underlying parameters. A central result is the derivation of a scaling limit as ψ approaches 0, corresponding to the underlying population growing to infinity, using the time rescaling formalism. We show that in this setting, after a linear time rescaling, the event times are the order statistics of n logistic random variables with mode log(1∕ψ); moreover, we show that the inter-event times are approximately exponentially distributed.
MeSH term(s)	Humans ; Population Density ; Probability
Language	English
Publishing date	2020-05-18
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	3948-2
ISSN	1096-0325 ; 0040-5809
ISSN (online)	1096-0325
ISSN	0040-5809
DOI	10.1016/j.tpb.2020.05.001
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Article ; Online: KwARG: parsimonious reconstruction of ancestral recombination graphs with recurrent mutation.

Ignatieva, Anastasia / Lyngsø, Rune B / Jenkins, Paul A / Hein, Jotun

Bioinformatics (Oxford, England)

2021 Volume 37, Issue 19, Page(s) 3277–3284

Abstract: Motivation: The reconstruction of possible histories given a sample of genetic data in the presence of recombination and recurrent mutation is a challenging problem, but can provide key insights into the evolution of a population. We present KwARG, ... ...

Abstract	Motivation: The reconstruction of possible histories given a sample of genetic data in the presence of recombination and recurrent mutation is a challenging problem, but can provide key insights into the evolution of a population. We present KwARG, which implements a parsimony-based greedy heuristic algorithm for finding plausible genealogical histories (ancestral recombination graphs) that are minimal or near-minimal in the number of posited recombination and mutation events. Results: Given an input dataset of aligned sequences, KwARG outputs a list of possible candidate solutions, each comprising a list of mutation and recombination events that could have generated the dataset; the relative proportion of recombinations and recurrent mutations in a solution can be controlled via specifying a set of 'cost' parameters. We demonstrate that the algorithm performs well when compared against existing methods. Availability and implementation: The software is available at https://github.com/a-ignatieva/kwarg. Supplementary information: Supplementary data are available at Bioinformatics online.
Language	English
Publishing date	2021-05-05
Publishing country	England
Document type	Journal Article
ZDB-ID	1422668-6
ISSN	1367-4811 ; 1367-4803
ISSN (online)	1367-4811
ISSN	1367-4803
DOI	10.1093/bioinformatics/btab351
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Article ; Online: Stopping-time resampling and population genetic inference under coalescent models.

Jenkins, Paul A

Statistical applications in genetics and molecular biology

2012 Volume 11, Issue 1, Page(s) Article 9

Abstract: To extract full information from samples of DNA sequence data, it is necessary to use sophisticated model-based techniques such as importance sampling under the coalescent. However, these are limited in the size of datasets they can handle efficiently. ... ...

Abstract	To extract full information from samples of DNA sequence data, it is necessary to use sophisticated model-based techniques such as importance sampling under the coalescent. However, these are limited in the size of datasets they can handle efficiently. Chen and Liu (2000) introduced the idea of stopping-time resampling and showed that it can dramatically improve the efficiency of importance sampling methods under a finite-alleles coalescent model. In this paper, a new framework is developed for designing stopping-time resampling schemes under more general models. It is implemented on data both from infinite sites and stepwise models of mutation, and extended to incorporate crossover recombination. A simulation study shows that this new framework offers a substantial improvement in the accuracy of likelihood estimation over a range of parameters, while a direct application of the scheme of Chen and Liu (2000) can actually diminish the estimate. The method imposes no additional computational burden and is robust to the choice of parameters.
MeSH term(s)	Genetics, Population ; Likelihood Functions ; Models, Genetic ; Mutation ; Recombination, Genetic
Language	English
Publishing date	2012-01-06
Publishing country	Germany
Document type	Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
ISSN	1544-6115
ISSN (online)	1544-6115
DOI	10.2202/1544-6115.1770
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Article ; Online: Evidence of ongoing recombination in SARS-CoV-2 through genealogical reconstruction

Ignatieva, Anastasia / Hein, Jotun / Jenkins, Paul A

bioRxiv

Abstract	The evolutionary process of genetic recombination has the potential to rapidly change the properties of a viral pathogen, and its presence is a crucial factor to consider in the development of treatments and vaccines. It can also significantly affect the results of phylogenetic analyses and the inference of evolutionary rates. The detection of recombination from samples of sequencing data is a very challenging problem, and is further complicated for SARS-CoV-2 by its relatively slow accumulation of genetic diversity. The extent to which recombination is ongoing for SARS-CoV-2 is not yet resolved. To address this, we use a parsimony-based method to reconstruct possible genealogical histories for samples of SARS-CoV-2 sequences, which enables the analysis of recombination events that could have generated the data. We propose a framework for disentangling the effects of recurrent mutation from recombination in the history of a sample, and hence provide a way of estimating the probability that ongoing recombination is present. We apply this to samples of sequencing data collected in England and in South Africa, and find compelling evidence of ongoing recombination.
Keywords	covid19
Language	English
Publishing date	2021-01-21
Publisher	Cold Spring Harbor Laboratory
Document type	Article ; Online
DOI	10.1101/2021.01.21.427579
Database	COVID19

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