Smooth Descent: a Ploidy-Aware Algorithm To Improve Linkage Mapping In The Presence of Genotyping Errors

Abstract Linkage mapping is an approach to order markers based on recombination events. Mapping algorithms cannot easily handle genotyping errors, which are common in high-throughput genotyping data. To solve this issue, strategies have been developed, aimed mostly at identifying and eliminating these errors. One such strategy is SMOOTH (van Os et al. 2005), an iterative algorithm to detect genotyping errors. Unlike other approaches, SMOOTH can also be used to impute the most probable alternative genotypes, but its application is limited to diploid species and to markers heterozygous in only one of the parents. In this study we adapted SMOOTH to expand its use to any marker type and to autopolyploids with the use of identity-by-descent probabilities, naming the updated algorithm Smooth Descent (SD). We applied SD to real and simulated data, showing that in the presence of genotyping errors this method produces better genetic maps in terms of marker order and map length. SD is particularly useful for error rates between 5% and 20% and when error rates are not homogeneous among markers or individuals. Moreover, the simplicity of the algorithm allows thousands of markers to be efficiently processed, thus being particularly useful for error detection in high-density datasets. We have implemented this algorithm in the R package SmoothDescent.

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Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽

10.1038/s41586-021-03588-y ◽

2021 ◽

Vol 595 (7867) ◽

pp. 383-387

Author(s):

◽

Zijun Chen ◽

Kevin J. Satzinger ◽

Juan Atalaya ◽

Alexander N. Korotkov ◽

...

Keyword(s):

Error Correction ◽

Error Detection ◽

Fault Tolerant ◽

Error Rates ◽

Quantum Error Correction ◽

Superconducting Qubits ◽

Two Dimensional ◽

Logical Error ◽

Quantum Error ◽

Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

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Constructing Large-Scale Genetic Maps Using an Evolutionary Strategy Algorithm

Genetics ◽

10.1093/genetics/165.4.2269 ◽

2003 ◽

Vol 165 (4) ◽

pp. 2269-2282

Author(s):

D Mester ◽

Y Ronin ◽

D Minkov ◽

E Nevo ◽

A Korol

Keyword(s):

Discrete Optimization ◽

High Performance ◽

Large Scale ◽

Simulated Data ◽

Real Data ◽

Genetic Maps ◽

Chromosome 1 ◽

Evolutionary Strategy ◽

Group A ◽

The One

Abstract This article is devoted to the problem of ordering in linkage groups with many dozens or even hundreds of markers. The ordering problem belongs to the field of discrete optimization on a set of all possible orders, amounting to n!/2 for n loci; hence it is considered an NP-hard problem. Several authors attempted to employ the methods developed in the well-known traveling salesman problem (TSP) for multilocus ordering, using the assumption that for a set of linked loci the true order will be the one that minimizes the total length of the linkage group. A novel, fast, and reliable algorithm developed for the TSP and based on evolution-strategy discrete optimization was applied in this study for multilocus ordering on the basis of pairwise recombination frequencies. The quality of derived maps under various complications (dominant vs. codominant markers, marker misclassification, negative and positive interference, and missing data) was analyzed using simulated data with ∼50-400 markers. High performance of the employed algorithm allows systematic treatment of the problem of verification of the obtained multilocus orders on the basis of computing-intensive bootstrap and/or jackknife approaches for detecting and removing questionable marker scores, thereby stabilizing the resulting maps. Parallel calculation technology can easily be adopted for further acceleration of the proposed algorithm. Real data analysis (on maize chromosome 1 with 230 markers) is provided to illustrate the proposed methodology.

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Genotyping Error Detection Through Tightly Linked Markers

Genetics ◽

10.1093/genetics/164.3.1161 ◽

2003 ◽

Vol 164 (3) ◽

pp. 1161-1173

Author(s):

Guohua Zou ◽

Deyun Pan ◽

Hongyu Zhao

Keyword(s):

Error Detection ◽

Complex Disease ◽

Disease Genes ◽

Genotyping Error ◽

Genotyping Errors ◽

Detection Rates ◽

Nuclear Families ◽

Additional Information ◽

Number Of Children ◽

Multiple Markers

Abstract The identification of genotyping errors is an important issue in mapping complex disease genes. Although it is common practice to genotype multiple markers in a candidate region in genetic studies, the potential benefit of jointly analyzing multiple markers to detect genotyping errors has not been investigated. In this article, we discuss genotyping error detections for a set of tightly linked markers in nuclear families, and the objective is to identify families likely to have genotyping errors at one or more markers. We make use of the fact that recombination is a very unlikely event among these markers. We first show that, with family trios, no extra information can be gained by jointly analyzing markers if no phase information is available, and error detection rates are usually low if Mendelian consistency is used as the only standard for checking errors. However, for nuclear families with more than one child, error detection rates can be greatly increased with the consideration of more markers. Error detection rates also increase with the number of children in each family. Because families displaying Mendelian consistency may still have genotyping errors, we calculate the probability that a family displaying Mendelian consistency has correct genotypes. These probabilities can help identify families that, although showing Mendelian consistency, may have genotyping errors. In addition, we examine the benefit of available haplotype frequencies in the general population on genotyping error detections. We show that both error detection rates and the probability that an observed family displaying Mendelian consistency has correct genotypes can be greatly increased when such additional information is available.

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MGMM: An R Package for fitting Gaussian Mixture Models on Incomplete Data

10.1101/2019.12.20.884551 ◽

2019 ◽

Cited By ~ 1

Author(s):

Zachary R. McCaw ◽

Hanna Julienne ◽

Hugues Aschard

Keyword(s):

Missing Data ◽

Mixture Models ◽

Gaussian Mixture Models ◽

Model Fitting ◽

Simulated Data ◽

R Package ◽

Gaussian Mixture ◽

Parameter Estimates ◽

Cluster Assignment ◽

Underlying Distribution

AbstractAlthough missing data are prevalent in applications, existing implementations of Gaussian mixture models (GMMs) require complete data. Standard practice is to perform complete case analysis or imputation prior to model fitting. Both approaches have serious drawbacks, potentially resulting in biased and unstable parameter estimates. Here we present MGMM, an R package for fitting GMMs in the presence of missing data. Using three case studies on real and simulated data sets, we demonstrate that, when the underlying distribution is near-to a GMM, MGMM is more effective at recovering the true cluster assignments than state of the art imputation followed by standard GMM. Moreover, MGMM provides an accurate assessment of cluster assignment uncertainty even when the generative distribution is not a GMM. This assessment may be used to identify unassignable observations. MGMM is available as an R package on CRAN: https://CRAN.R-project.org/package=MGMM.

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Supervised linear classification of Gaussian spatio-temporal data

Lietuvos matematikos rinkinys ◽

10.15388/lmr.2021.25214 ◽

2021 ◽

Vol 62 ◽

pp. 9-15

Author(s):

Marta Karaliutė ◽

Kęstutis Dučinskas

Keyword(s):

Time Moment ◽

Gaussian Random Field ◽

Covariance Structure ◽

Simulated Data ◽

Spatial Location ◽

Error Rates ◽

Prior Probabilities ◽

Structure Factors ◽

Spatio Temporal

In this article we focus on the problem of supervised classifying of the spatio-temporal Gaussian random field observation into one of two classes, specified by different mean parameters. The main distinctive feature of the proposed approach is allowing the class label to depend on spatial location as well as on time moment. It is assumed that the spatio-temporal covariance structure factors into a purely spatial component and a purely temporal component following AR(p) model. In numerical illustrations with simulated data, the influence of the values of spatial and temporal covariance parameters to the derived error rates for several prior probabilities models are studied.

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fullsibQTL: an R package for QTL mapping in biparental populations of outcrossing species

10.1101/2020.12.04.412262 ◽

2020 ◽

Author(s):

Rodrigo Gazaffi ◽

Rodrigo R. Amadeu ◽

Marcelo Mollinari ◽

João R. B. F. Rosa ◽

Cristiane H. Taniguti ◽

...

Keyword(s):

Qtl Mapping ◽

Open Source ◽

Qtl Analysis ◽

Source Code ◽

R Package ◽

Genetic Maps ◽

Linkage Phase ◽

Position Effects ◽

Genetic Features ◽

Outcrossing Species

ABSTRACTAccurate QTL mapping in outcrossing species requires software programs which consider genetic features of these populations, such as markers with different segregation patterns and different level of information. Although the available mapping procedures to date allow inferring QTL position and effects, they are mostly not based on multilocus genetic maps. Having a QTL analysis based in such maps is crucial since they allow informative markers to propagate their information to less informative intervals of the map. We developed fullsibQTL, a novel and freely available R package to perform composite interval QTL mapping considering outcrossing populations and markers with different segregation patterns. It allows to estimate QTL position, effects, segregation patterns, and linkage phase with flanking markers. Additionally, several statistical and graphical tools are implemented, for straightforward analysis and interpretations. fullsibQTL is an R open source package with C and R source code (GPLv3). It is multiplatform and can be installed from https://github.com/augusto-garcia/fullsibQTL.

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debar, a sequence-by-sequence denoiser for COI-5P DNA barcode data

10.1101/2021.01.04.425285 ◽

2021 ◽

Author(s):

Cameron M. Nugent ◽

Tyler A. Elliott ◽

Sujeevan Ratnasingham ◽

Paul D. N. Hebert ◽

Sarah J. Adamowicz

Keyword(s):

High Throughput Sequencing ◽

Dna Barcode ◽

R Package ◽

Error Rates ◽

Real World Data ◽

Species Discovery ◽

Consensus Sequences ◽

In Silico Studies ◽

Coi Sequences

AbstractDNA barcoding and metabarcoding are now widely used to advance species discovery and biodiversity assessments. High-throughput sequencing (HTS) has expanded the volume and scope of these analyses, but elevated error rates introduce noise into sequence records that can inflate estimates of biodiversity. Denoising —the separation of biological signal from instrument (technical) noise—of barcode and metabarcode data currently employs abundance-based methods which do not capitalize on the highly conserved structure of the cytochrome c oxidase subunit I (COI) region employed as the animal barcode. This manuscript introduces debar, an R package that utilizes a profile hidden Markov model to denoise indel errors in COI sequences introduced by instrument error. In silico studies demonstrated that debar recognized 95% of artificially introduced indels in COI sequences. When applied to real-world data, debar reduced indel errors in circular consensus sequences obtained with the Sequel platform by 75%, and those generated on the Ion Torrent S5 by 94%. The false correction rate was less than 0.1%, indicating that debar is receptive to the majority of true COI variation in the animal kingdom. In conclusion, the debar package improves DNA barcode and metabarcode workflows by aiding the generation of more accurate sequences aiding the characterization of species diversity.

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Likelihood-Based Inference for Multi-Color Optical Mapping

Statistical Applications in Genetics and Molecular Biology ◽

10.2202/1544-6115.1266 ◽

2007 ◽

Vol 6 (1) ◽

Cited By ~ 1

Author(s):

Liping Tong ◽

Laurens Mets ◽

Mary Sara McPeek

Keyword(s):

Latent Variable ◽

Optical Mapping ◽

Physical Map ◽

Profile Likelihood ◽

Simulated Data ◽

Likelihood Estimation ◽

Error Rates ◽

Mapping Procedure ◽

Recognition Sites ◽

Estimate Error

Multi-color optical mapping is a new technique being developed to obtain detailed physical maps (indicating relative positions of various recognition sites) of DNA molecules. We consider a study design in which the data consist of noisy observations of multiple copies of a DNA molecule marked with colors at recognition sites. The primary goal is to estimate a physical map. A secondary goal is to estimate error rates associated with the experiment, which are potentially useful for analysis and refinement of the biochemical steps in the mapping procedure. We propose statistical models for various sources of error and use maximum likelihood estimation (MLE) to construct a physical map and estimate error rates. To overcome difficulties arising in the maximization process, a latent-variable Markov chain version of the model is proposed, and the EM algorithm is used for maximization. In addition, a simulated annealing procedure is applied to maximize the profile likelihood over the discrete space of sequences of colors. We apply the methods to simulated data on the bacteriophage lambda genome.

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An English pronunciation learning system for Japanese students based on diagnosis of critical pronunciation errors

ReCALL ◽

10.1017/s0958344004001314 ◽

2004 ◽

Vol 16 (1) ◽

pp. 173-188 ◽

Cited By ~ 8

Author(s):

YASUSHI TSUBOTA ◽

MASATAKE DANTSUJI ◽

TATSUYA KAWAHARA

Keyword(s):

Error Rate ◽

Error Detection ◽

Native Speakers ◽

Error Rates ◽

Learning System ◽

Second Phase ◽

Acoustic Model ◽

Japanese Students ◽

Speech Data ◽

English Pronunciation

We have developed an English pronunciation learning system which estimates the intelligibility of Japanese learners' speech and ranks their errors from the viewpoint of improving their intelligibility to native speakers. Error diagnosis is particularly important in self-study since students tend to spend time on aspects of pronunciation that do not noticeably affect intelligibility. As a preliminary experiment, the speech of seven Japanese students was scored from 1 (hardly intelligible) to 5 (perfectly intelligible) by a linguistic expert. We also computed their error rates for each skill. We found that each intelligibility level is characterized by its distribution of error rates. Thus, we modeled each intelligibility level in accordance with its error rate. Error priority was calculated by comparing students' error rate distributions with that of the corresponding model for each intelligibility level. As non-native speech is acoustically broader than the speech of native speakers, we developed an acoustic model to perform automatic error detection using speech data obtained from Japanese students. As for supra-segmental error detection, we categorized errors frequently made by Japanese students and developed a separate acoustic model for that type of error detection. Pronunciation learning using this system involves two phases. In the first phase, students experience virtual conversation through video clips. They receive an error profile based on pronunciation errors detected during the conversation. Using the profile, students are able to grasp characteristic tendencies in their pronunciation errors which in effect lower their intelligibility. In the second phase, students practise correcting their individual errors using words and short phrases. They then receive information regarding the errors detected during this round of practice and instructions for correcting the errors. We have begun using this system in a CALL class at Kyoto University. We have evaluated system performance through the use of questionnaires and analysis of speech data logged in the server, and will present our findings in this paper.

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Linkage mapping and QTL analysis of flowering time using ddRAD sequencing with genotype error correction in Brassica napus

BMC Plant Biology ◽

10.1186/s12870-020-02756-y ◽

2020 ◽

Vol 20 (1) ◽

Author(s):

Armin Scheben ◽

Anita A. Severn-Ellis ◽

Dhwani Patel ◽

Aneeta Pradhan ◽

Stephen J. Rae ◽

...

Keyword(s):

Brassica Napus ◽

Error Correction ◽

Flowering Time ◽

Qtl Analysis ◽

Linkage Mapping ◽

Mapping Population ◽

Error Rates ◽

Oilseed Crop ◽

Nucleotide Polymorphisms ◽

Substantial Impact

Abstract Background Brassica napus is an important oilseed crop cultivated worldwide. During domestication and breeding of B. napus, flowering time has been a target of selection because of its substantial impact on yield. Here we use double digest restriction-site associated DNA sequencing (ddRAD) to investigate the genetic basis of flowering in B. napus. An F2 mapping population was derived from a cross between an early-flowering spring type and a late-flowering winter type. Results Flowering time in the mapping population differed by up to 25 days between individuals. High genotype error rates persisted after initial quality controls, as suggested by a genotype discordance of ~ 12% between biological sequencing replicates. After genotype error correction, a linkage map spanning 3981.31 cM and compromising 14,630 single nucleotide polymorphisms (SNPs) was constructed. A quantitative trait locus (QTL) on chromosome C2 was detected, covering eight flowering time genes including FLC. Conclusions These findings demonstrate the effectiveness of the ddRAD approach to sample the B. napus genome. Our results also suggest that ddRAD genotype error rates can be higher than expected in F2 populations. Quality filtering and genotype correction and imputation can substantially reduce these error rates and allow effective linkage mapping and QTL analysis.

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