Journal articles: 'Statistical and quantitative genetics'

1

Sen, Śaunak, and Gary A. Churchill. "A Statistical Framework for Quantitative Trait Mapping." Genetics 159, no. 1 (September 1, 2001): 371–87. http://dx.doi.org/10.1093/genetics/159.1.371.

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AbstractWe describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.

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Neher, Richard A., and Boris I. Shraiman. "Statistical genetics and evolution of quantitative traits." Reviews of Modern Physics 83, no. 4 (November 10, 2011): 1283–300. http://dx.doi.org/10.1103/revmodphys.83.1283.

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Sorensen, Daniel. "Developments in statistical analysis in quantitative genetics." Genetica 136, no. 2 (August 21, 2008): 319–32. http://dx.doi.org/10.1007/s10709-008-9303-5.

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Zou, Fei, Brian S. Yandell, and Jason P. Fine. "Rank-Based Statistical Methodologies for Quantitative Trait Locus Mapping." Genetics 165, no. 3 (November 1, 2003): 1599–605. http://dx.doi.org/10.1093/genetics/165.3.1599.

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Abstract This article addresses the identification of genetic loci (QTL and elsewhere) that influence nonnormal quantitative traits with focus on experimental crosses. QTL mapping is typically based on the assumption that the traits follow normal distributions, which may not be true in practice. Model-free tests have been proposed. However, nonparametric estimation of genetic effects has not been studied. We propose an estimation procedure based on the linear rank test statistics. The properties of the new procedure are compared with those of traditional likelihood-based interval mapping and regression interval mapping via simulations and a real data example. The results indicate that the nonparametric method is a competitive alternative to the existing parametric methodologies.

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Ye, Shuyun, Rhonda Bacher, Mark P. Keller, Alan D. Attie, and Christina Kendziorski. "Statistical Methods for Latent Class Quantitative Trait Loci Mapping." Genetics 206, no. 3 (May 26, 2017): 1309–17. http://dx.doi.org/10.1534/genetics.117.203885.

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Chen, Meng, and Christina Kendziorski. "A Statistical Framework for Expression Quantitative Trait Loci Mapping." Genetics 177, no. 2 (July 29, 2007): 761–71. http://dx.doi.org/10.1534/genetics.107.071407.

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Barton, N. H., and H. P. de Vladar. "Statistical Mechanics and the Evolution of Polygenic Quantitative Traits." Genetics 181, no. 3 (December 15, 2008): 997–1011. http://dx.doi.org/10.1534/genetics.108.099309.

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Zou, Fei, Brian S. Yandell, and Jason P. Fine. "Statistical Issues in the Analysis of Quantitative Traits in Combined Crosses." Genetics 158, no. 3 (July 1, 2001): 1339–46. http://dx.doi.org/10.1093/genetics/158.3.1339.

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Abstract We consider some practical statistical issues in QTL analysis where several crosses originate in multiple inbred parents. Our results show that ignoring background polygenic variation in different crosses may lead to biased interval mapping estimates of QTL effects or loss of efficiency. Threshold and power approximations are derived by extending earlier results based on the Ornstein-Uhlenbeck diffusion process. The results are useful in the design and analysis of genome screen experiments. Several common designs are evaluated in terms of their power to detect QTL.

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Mitchell-Olds, T., and J. Bergelson. "Statistical genetics of an annual plant, Impatiens capensis. I. Genetic basis of quantitative variation." Genetics 124, no. 2 (February 1, 1990): 407–15. http://dx.doi.org/10.1093/genetics/124.2.407.

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Abstract Analysis of quantitative genetics in natural populations has been hindered by computational and methodological problems in statistical analysis. We developed and validated a jackknife procedure to test for existence of broad sense heritabilities and dominance or maternal effects influencing quantitative characters in Impatiens capensis. Early life cycle characters showed evidence of dominance and/or maternal effects, while later characters exhibited predominantly environmental variation. Monte Carlo simulations demonstrate that these jackknife tests of variance components are extremely robust to heterogeneous error variances. Statistical methods from human genetics provide evidence for either a major locus influencing germination date, or genes that affect phenotypic variability per se. We urge explicit consideration of statistical behavior of estimation and testing procedures for proper biological interpretation of statistical results.

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Hoeschele, I., P. Uimari, F. E. Grignola, Q. Zhang, and K. M. Gage. "Advances in Statistical Methods to Map Quantitative Trait Loci in Outbred Populations." Genetics 147, no. 3 (November 1, 1997): 1445–57. http://dx.doi.org/10.1093/genetics/147.3.1445.

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Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLS on a chromosome as an unknown.

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Dupuis, Josée, and David Siegmund. "Statistical Methods for Mapping Quantitative Trait Loci From a Dense Set of Markers." Genetics 151, no. 1 (January 1, 1999): 373–86. http://dx.doi.org/10.1093/genetics/151.1.373.

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Abstract Lander and Botstein introduced statistical methods for searching an entire genome for quantitative trait loci (QTL) in experimental organisms, with emphasis on a backcross design and QTL having only additive effects. We extend their results to intercross and other designs, and we compare the power of the resulting test as a function of the magnitude of the additive and dominance effects, the sample size and intermarker distances. We also compare three methods for constructing confidence regions for a QTL: likelihood regions, Bayesian credible sets, and support regions. We show that with an appropriate evaluation of the coverage probability a support region is approximately a confidence region, and we provide a theroretical explanation of the empirical observation that the size of the support region is proportional to the sample size, not the square root of the sample size, as one might expect from standard statistical theory.

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Lange, Christoph, and John C. Whittaker. "Mapping Quantitative Trait Loci Using Generalized Estimating Equations." Genetics 159, no. 3 (November 1, 2001): 1325–37. http://dx.doi.org/10.1093/genetics/159.3.1325.

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AbstractA number of statistical methods are now available to map quantitative trait loci (QTL) relative to markers. However, no existing methodology can simultaneously map QTL for multiple nonnormal traits. In this article we rectify this deficiency by developing a QTL-mapping approach based on generalized estimating equations (GEE). Simulation experiments are used to illustrate the application of the GEE-based approach.

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Melo, Diogo, Guilherme Garcia, Alex Hubbe, Ana Paula Assis, and Gabriel Marroig. "EvolQG - An R package for evolutionary quantitative genetics." F1000Research 4 (September 30, 2015): 925. http://dx.doi.org/10.12688/f1000research.7082.1.

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We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable. Given this mathematical representation of available variation, the EvolQG package provides functions for calculation of relevant evolutionary statistics, estimation of sampling error, corrections for this error, matrix comparison via correlations and distances, and functions for testing evolutionary hypotheses on taxa diversification.

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Melo, Diogo, Guilherme Garcia, Alex Hubbe, Ana Paula Assis, and Gabriel Marroig. "EvolQG - An R package for evolutionary quantitative genetics." F1000Research 4 (June 27, 2016): 925. http://dx.doi.org/10.12688/f1000research.7082.2.

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We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the EvolQG package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

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Melo, Diogo, Guilherme Garcia, Alex Hubbe, Ana Paula Assis, and Gabriel Marroig. "EvolQG - An R package for evolutionary quantitative genetics." F1000Research 4 (November 8, 2016): 925. http://dx.doi.org/10.12688/f1000research.7082.3.

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We present an open source package for performing evolutionary quantitative genetics analyses in the R environment for statistical computing. Evolutionary theory shows that evolution depends critically on the available variation in a given population. When dealing with many quantitative traits this variation is expressed in the form of a covariance matrix, particularly the additive genetic covariance matrix or sometimes the phenotypic matrix, when the genetic matrix is unavailable and there is evidence the phenotypic matrix is sufficiently similar to the genetic matrix. Given this mathematical representation of available variation, the \textbf{EvolQG} package provides functions for calculation of relevant evolutionary statistics; estimation of sampling error; corrections for this error; matrix comparison via correlations, distances and matrix decomposition; analysis of modularity patterns; and functions for testing evolutionary hypotheses on taxa diversification.

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Jiang, C., and Z. B. Zeng. "Multiple trait analysis of genetic mapping for quantitative trait loci." Genetics 140, no. 3 (July 1, 1995): 1111–27. http://dx.doi.org/10.1093/genetics/140.3.1111.

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Abstract We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.

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Boer, Martin P., Cajo J. F. ter Braak, and Ritsert C. Jansen. "A Penalized Likelihood Method for Mapping Epistatic Quantitative Trait Loci With One-Dimensional Genome Searches." Genetics 162, no. 2 (October 1, 2002): 951–60. http://dx.doi.org/10.1093/genetics/162.2.951.

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AbstractEpistasis is a common and important phenomenon, as indicated by results from a number of recent experiments. Unfortunately, the discovery of epistatic quantitative trait loci (QTL) is difficult since one must search for multiple QTL simultaneously in two or more dimensions. Such a multidimensional search necessitates many statistical tests, and a high statistical threshold must be adopted to avoid false positives. Furthermore, the large number of (interaction) parameters in comparison with the number of observations results in a serious danger of overfitting and overinterpretation of the data. In this article we present a new statistical framework for mapping epistasis in inbred line crosses. It is based on reducing the high dimensionality of the problem in two ways. First, epistatic QTL are mapped in a one-dimensional genome scan for high interactions between QTL and the genetic background. Second, the dimension of the search is bounded by penalized likelihood methods. We use simulated backcross data to illustrate the new approach.

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18

Mezey, Jason G., James M. Cheverud, and Günter P. Wagner. "Is the Genotype-Phenotype Map Modular?: A Statistical Approach Using Mouse Quantitative Trait Loci Data." Genetics 156, no. 1 (September 1, 2000): 305–11. http://dx.doi.org/10.1093/genetics/156.1.305.

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Abstract Various theories about the evolution of complex characters make predictions about the statistical distribution of genetic effects on phenotypic characters, also called the genotype-phenotype map. With the advent of QTL technology, data about these distributions are becoming available. In this article, we propose simple tests for the prediction that functionally integrated characters have a modular genotype-phenotype map. The test is applied to QTL data on the mouse mandible. The results provide statistical support for the notion that the ascending ramus region of the mandible is modularized. A data set comprising the effects of QTL on a more extensive portion of the phenotype is required to determine if the alveolar region of the mandible is also modularized.

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Zou, Fei, Jason P. Fine, Jianhua Hu, and D. Y. Lin. "An Efficient Resampling Method for Assessing Genome-Wide Statistical Significance in Mapping Quantitative Trait Loci." Genetics 168, no. 4 (December 2004): 2307–16. http://dx.doi.org/10.1534/genetics.104.031427.

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Lin, Min, Xiang-Yang Lou, Myron Chang, and Rongling Wu. "A General Statistical Framework for Mapping Quantitative Trait Loci in Nonmodel Systems: Issue for Characterizing Linkage Phases." Genetics 165, no. 2 (October 1, 2003): 901–13. http://dx.doi.org/10.1093/genetics/165.2.901.

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Abstract Because of uncertainty about linkage phases of founders, linkage mapping in nonmodel, outcrossing systems using molecular markers presents one of the major statistical challenges in genetic research. In this article, we devise a statistical method for mapping QTL affecting a complex trait by incorporating all possible QTL-marker linkage phases within a mapping framework. The advantage of this model is the simultaneous estimation of linkage phases and QTL location and effect parameters. These estimates are obtained through maximum-likelihood methods implemented with the EM algorithm. Extensive simulation studies are performed to investigate the statistical properties of our model. In a case study from a forest tree, this model has successfully identified a significant QTL affecting wood density. Also, the probability of the linkage phase between this QTL and its flanking markers is estimated. The implications of our model and its extension to more general circumstances are discussed.

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Zhang, Yuan-Ming, and Shizhong Xu. "Mapping Quantitative Trait Loci in F2 Incorporating Phenotypes of F3 Progeny." Genetics 166, no. 4 (April 1, 2004): 1981–93. http://dx.doi.org/10.1093/genetics/166.4.1981.

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AbstractIn plants and laboratory animals, QTL mapping is commonly performed using F2 or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F2 individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F3 progeny derived from selfing F2 plants in place of the F2 phenotype itself. All F3 progeny derived from the same F2 plant belong to the same F2:3 family, denoted by F2:3. If the size of each F2:3 family (the number of F3 progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F2 plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F2 marker genotypes and F3 average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F2:3 strategy. We also propose to combine both the F2 phenotypes and the F2:3 average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F2:3 families of heterozygous F2 plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F2 design, even if only a single F3 progeny is collected from each F2:3 family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.

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Hill, William G. "Understanding and using quantitative genetic variation." Philosophical Transactions of the Royal Society B: Biological Sciences 365, no. 1537 (January 12, 2010): 73–85. http://dx.doi.org/10.1098/rstb.2009.0203.

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Quantitative genetics, or the genetics of complex traits, is the study of those characters which are not affected by the action of just a few major genes. Its basis is in statistical models and methodology, albeit based on many strong assumptions. While these are formally unrealistic, methods work. Analyses using dense molecular markers are greatly increasing information about the architecture of these traits, but while some genes of large effect are found, even many dozens of genes do not explain all the variation. Hence, new methods of prediction of merit in breeding programmes are again based on essentially numerical methods, but incorporating genomic information. Long-term selection responses are revealed in laboratory selection experiments, and prospects for continued genetic improvement are high. There is extensive genetic variation in natural populations, but better estimates of covariances among multiple traits and their relation to fitness are needed. Methods based on summary statistics and predictions rather than at the individual gene level seem likely to prevail for some time yet.

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Camussi, A., E. Ottaviano, T. Calinski, and Z. Kaczmarek. "GENETIC DISTANCES BASED ON QUANTITATIVE TRAITS." Genetics 111, no. 4 (December 1, 1985): 945–62. http://dx.doi.org/10.1093/genetics/111.4.945.

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ABSTRACT Morphological data showing continuous distributions, polygenically controlled, may be particularly useful in intergroup classification below the species level; an appropriate distance analysis based on these traits is an important tool in evolutionary biology and in plant and animal breeding.—The interpretation of morphological distances in genetic terms is not easy because simple phenotypic data may lead to biased estimates of genetic distances. Convenient estimates can be obtained whenever it is possible to breed populations according to a suitable crossing design and to derive information from genetic parameters.—A general method for determining genetic distances is proposed. The procedure of multivariate analysis of variance is extended to estimate appropriate genetic parameters (genetic effects). Not only are optimal statistical estimates of parameters obtained but also the procedure allows the measurement of genetic distances between populations as linear functions of the estimated parameters, providing an appropriate distance matrix that can be defined in terms of these parameters. The use of the T 2 statistic, defined in terms of the vector of contrasts specifying the distance, permits the testing of the significance of any distance between any pair of populations that may be of interest from a genetic point of view.—A numerical example from maize diallel data is reported in order to illustrate the procedure. In particular, heterosis effects are used as the basis for estimates of genetic divergence between populations.

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Álvarez-Castro, José M., and Örjan Carlborg. "A Unified Model for Functional and Statistical Epistasis and Its Application in Quantitative Trait Loci Analysis." Genetics 176, no. 2 (April 3, 2007): 1151–67. http://dx.doi.org/10.1534/genetics.106.067348.

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Schliekelman, Paul. "Statistical Power of Expression Quantitative Trait Loci for Mapping of Complex Trait Loci in Natural Populations." Genetics 178, no. 4 (February 3, 2008): 2201–16. http://dx.doi.org/10.1534/genetics.107.076687.

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Zeng, Z. B., and C. C. Cockerham. "Mutation models and quantitative genetic variation." Genetics 133, no. 3 (March 1, 1993): 729–36. http://dx.doi.org/10.1093/genetics/133.3.729.

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Abstract Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, gamma, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When gamma = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as gamma changes. The effects of gamma on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.

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GIANOLA, DANIEL, and GUSTAVO de los CAMPOS. "Inferring genetic values for quantitative traits non-parametrically." Genetics Research 90, no. 6 (December 2008): 525–40. http://dx.doi.org/10.1017/s0016672308009890.

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SummaryInferences about genetic values and prediction of phenotypes for a quantitative trait in the presence of complex forms of gene action, issues of importance in animal and plant breeding, and in evolutionary quantitative genetics, are discussed. Current methods for dealing with epistatic variability via variance component models are reviewed. Problems posed by cryptic, non-linear, forms of epistasis are identified and discussed. Alternative statistical procedures are suggested. Non-parametric definitions of additive effects (breeding values), with and without employing molecular information, are proposed, and it is shown how these can be inferred using reproducing kernel Hilbert spaces regression. Two stylized examples are presented to demonstrate the methods numerically. The first example falls in the domain of the infinitesimal model of quantitative genetics, with additive and dominance effects inferred both parametrically and non-parametrically. The second example tackles a non-linear genetic system with two loci, and the predictive ability of several models is evaluated.

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Zeng, Z. B. "Precision mapping of quantitative trait loci." Genetics 136, no. 4 (April 1, 1994): 1457–68. http://dx.doi.org/10.1093/genetics/136.4.1457.

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Abstract Adequate separation of effects of possible multiple linked quantitative trait loci (QTLs) on mapping QTLs is the key to increasing the precision of QTL mapping. A new method of QTL mapping is proposed and analyzed in this paper by combining interval mapping with multiple regression. The basis of the proposed method is an interval test in which the test statistic on a marker interval is made to be unaffected by QTLs located outside a defined interval. This is achieved by fitting other genetic markers in the statistical model as a control when performing interval mapping. Compared with the current QTL mapping method (i.e., the interval mapping method which uses a pair or two pairs of markers for mapping QTLs), this method has several advantages. (1) By confining the test to one region at a time, it reduces a multiple dimensional search problem (for multiple QTLs) to a one dimensional search problem. (2) By conditioning linked markers in the test, the sensitivity of the test statistic to the position of individual QTLs is increased, and the precision of QTL mapping can be improved. (3) By selectively and simultaneously using other markers in the analysis, the efficiency of QTL mapping can be also improved. The behavior of the test statistic under the null hypothesis and appropriate critical value of the test statistic for an overall test in a genome are discussed and analyzed. A simulation study of QTL mapping is also presented which illustrates the utility, properties, advantages and disadvantages of the method.

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Wu, Rongling, Chang-Xing Ma, Maria Gallo-Meagher, Ramon C. Littell, and George Casella. "Statistical Methods for Dissecting Triploid Endosperm Traits Using Molecular Markers: An Autogamous Model." Genetics 162, no. 2 (October 1, 2002): 875–92. http://dx.doi.org/10.1093/genetics/162.2.875.

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AbstractThe endosperm, a result of double fertilization in flowering plants, is a triploid tissue whose genetic composition is more complex than diploid tissue. We present a new maximum-likelihood-based statistical method for mapping quantitative trait loci (QTL) underlying endosperm traits in an autogamous plant. Genetic mapping of quantitative endosperm traits is qualitatively different from traits for other plant organs because the endosperm displays complicated trisomic inheritance and represents a younger generation than its mother plant. Our endosperm mapping method is based on two different experimental designs: (1) a one-stage design in which marker information is derived from the maternal genome and (2) a two-stage hierarchical design in which marker information is derived from both the maternal and offspring genomes (embryos). Under the one-stage design, the position and additive effect of a putative QTL can be well estimated, but the estimates of the dominant and epistatic effects are upward biased and imprecise. The two-stage hierarchical design, which extracts more genetic information from the material, typically improves the accuracy and precision of the dominant and epistatic effects for an endosperm trait. We discuss the effects on the estimation of QTL parameters of different sampling strategies under the two-stage hierarchical design. Our method will be broadly useful in mapping endosperm traits for many agriculturally important crop plants and also make it possible to study the genetic significance of double fertilization in the evolution of higher plants.

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Simianer, H., G. J. M. Rosa, and A. Mäki-Tanila. "Special Issue: Quantitative and statistical genetics-papers in honour of Daniel Gianola." Journal of Animal Breeding and Genetics 134, no. 3 (May 15, 2017): 173–74. http://dx.doi.org/10.1111/jbg.12279.

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Kao, Chen-Hung, Zhao-Bang Zeng, and Robert D. Teasdale. "Multiple Interval Mapping for Quantitative Trait Loci." Genetics 152, no. 3 (July 1, 1999): 1203–16. http://dx.doi.org/10.1093/genetics/152.3.1203.

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Abstract A new statistical method for mapping quantitative trait loci (QTL), called multiple interval mapping (MIM), is presented. It uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. With the MIM approach, the precision and power of QTL mapping could be improved. Also, epistasis between QTL, genotypic values of individuals, and heritabilities of quantitative traits can be readily estimated and analyzed. Using the MIM model, a stepwise selection procedure with likelihood ratio test statistic as a criterion is proposed to identify QTL. This MIM method was applied to a mapping data set of radiata pine on three traits: brown cone number, tree diameter, and branch quality scores. Based on the MIM result, seven, six, and five QTL were detected for the three traits, respectively. The detected QTL individually contributed from ∼1 to 27% of the total genetic variation. Significant epistasis between four pairs of QTL in two traits was detected, and the four pairs of QTL contributed ∼10.38 and 14.14% of the total genetic variation. The asymptotic variances of QTL positions and effects were also provided to construct the confidence intervals. The estimated heritabilities were 0.5606, 0.5226, and 0.3630 for the three traits, respectively. With the estimated QTL effects and positions, the best strategy of marker-assisted selection for trait improvement for a specific purpose and requirement can be explored. The MIM FORTRAN program is available on the worldwide web (http://www.stat.sinica.edu.tw/~chkao/).

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Xu, Shizhong. "Mapping Quantitative Trait Loci Using Multiple Families of Line Crosses." Genetics 148, no. 1 (January 1, 1998): 517–24. http://dx.doi.org/10.1093/genetics/148.1.517.

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Abstract To avoid a loss in statistical power as a result of homozygous individuals being selected as parents of a mapping population, one can use multiple families of line crosses for quantitative trait genetic linkage analysis. Two strategies of combining data are investigated: the fixed-model and the random-model strategies. The fixed-model approach estimates and tests the average effect of gene substitution for each parent, while the random-model approach treats each effect of gene substitution as a random variable and directly estimates and tests the variance of gene substitution. Extensive Monte Carlo simulations verify that the two strategies perform equally well, although the random model is preferable in combining data from a large number of families. Simulations also show that there may be an optimal sampling strategy (number of families vs. number of individuals per family) in which QTL mapping reaches its maximum power and minimum estimation error. Deviation from the optimal strategy reduces the efficiency of the method.

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Kendziorski, Christina, and Ping Wang. "A review of statistical methods for expression quantitative trait loci mapping." Mammalian Genome 17, no. 6 (June 2006): 509–17. http://dx.doi.org/10.1007/s00335-005-0189-6.

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Jansen, Ritsert C. "A General Monte Carlo Method for Mapping Multiple Quantitative Trait Loci." Genetics 142, no. 1 (January 1, 1996): 305–11. http://dx.doi.org/10.1093/genetics/142.1.305.

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In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm for fitting multiple-QTL models to such data. Implementation of this algorithm is straightforward in standard statistical software, but computation may take much time. The method may be generalized to cope with more complex models for animal and human pedigrees. A practical example is presented, where a three-QTL model is adopted in an outbreeding situation with dominant markers. The example is concerned with the linkage between randomly amplified polymorphic DNA (RAPD) markers and QTLs for partial resistance to Fusarium oxysporum in lily.

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George, Andrew W., Peter M. Visscher, and Chris S. Haley. "Mapping Quantitative Trait Loci in Complex Pedigrees: A Two-Step Variance Component Approach." Genetics 156, no. 4 (December 1, 2000): 2081–92. http://dx.doi.org/10.1093/genetics/156.4.2081.

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Abstract There is a growing need for the development of statistical techniques capable of mapping quantitative trait loci (QTL) in general outbred animal populations. Presently used variance component methods, which correctly account for the complex relationships that may exist between individuals, are challenged by the difficulties incurred through unknown marker genotypes, inbred individuals, partially or unknown marker phases, and multigenerational data. In this article, a two-step variance component approach that enables practitioners to routinely map QTL in populations with the aforementioned difficulties is explored. The performance of the QTL mapping methodology is assessed via its application to simulated data. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.

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Lan, Hong, Jonathan P. Stoehr, Samuel T. Nadler, Kathryn L. Schueler, Brian S. Yandell, and Alan D. Attie. "Dimension Reduction for Mapping mRNA Abundance as Quantitative Traits." Genetics 164, no. 4 (August 1, 2003): 1607–14. http://dx.doi.org/10.1093/genetics/164.4.1607.

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AbstractThe advent of sophisticated genomic techniques for gene mapping and microarray analysis has provided opportunities to map mRNA abundance to quantitative trait loci (QTL) throughout the genome. Unfortunately, simple mapping of each individual mRNA trait on the scale of a typical microarray experiment is computationally intensive, subject to high sample variance, and therefore underpowered. However, this problem can be addressed by capitalizing on correlation among the large number of mRNA traits. We present a method to reduce the dimensionality for mapping gene expression data as quantitative traits. We used a blind method, principal components, and a sighted method, hierarchical clustering seeded by disease relevant traits, to define new traits composed of a small collection of promising mRNAs. We validated the principle of our approach by mapping the expression levels of metabolism genes in a population of F2-ob/ob mice derived from the BTBR and C57BL/6J strains. We found that lipogenic and gluconeogenic mRNAs, which are known targets of insulin action, were closely associated with the insulin trait. Multiple interval mapping and Bayesian interval mapping of this new trait revealed significant linkages to chromosome regions that were contained in loci associated with type 2 diabetes in this same mouse sample. As a further statistical refinement, we show that principal component analysis also effectively reduced dimensions for mapping phenotypes composed of mRNA abundances.

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Juenger, Thomas, Michael Purugganan, and Trudy F. C. Mackay. "Quantitative Trait Loci for Floral Morphology in Arabidopsis thaliana." Genetics 156, no. 3 (November 1, 2000): 1379–92. http://dx.doi.org/10.1093/genetics/156.3.1379.

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Abstract A central question in biology is how genes control the expression of quantitative variation. We used statistical methods to estimate genetic variation in eight Arabidopsis thaliana floral characters (fresh flower mass, petal length, petal width, sepal length, sepal width, long stamen length, short stamen length, and pistil length) in a cosmopolitan sample of 15 ecotypes. In addition, we used genome-wide quantitative trait locus (QTL) mapping to evaluate the genetic basis of variation in these same traits in the Landsberg erecta × Columbia recombinant inbred line population. There was significant genetic variation for all traits in both the sample of naturally occurring ecotypes and in the Ler × Col recombinant inbred line population. In addition, broad-sense genetic correlations among the traits were positive and high. A composite interval mapping (CIM) analysis detected 18 significant QTL affecting at least one floral character. Eleven QTL were associated with several floral traits, supporting either pleiotropy or tight linkage as major determinants of flower morphological integration. We propose several candidate genes that may underlie these QTL on the basis of positional information and functional arguments. Genome-wide QTL mapping is a promising tool for the discovery of candidate genes controlling morphological development, the detection of novel phenotypic effects for known genes, and in generating a more complete understanding of the genetic basis of floral development.

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BÜRGER, REINHARD, and ALEXANDER GIMELFARB. "Fluctuating environments and the role of mutation in maintaining quantitative genetic variation." Genetical Research 80, no. 1 (August 2002): 31–46. http://dx.doi.org/10.1017/s0016672302005682.

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We study a class of genetic models in which a quantitative trait determined by several additive loci is subject to temporally fluctuating selection. Selection on the trait is assumed to be stabilizing but with an optimum that varies periodically and might be perturbed stochastically. The population mates at random, is infinitely large and has discrete generations. We pursue a statistical and numerical approach, covering a wide range of ecological and genetic parameters, to determine the potential of fluctuating environments to maintain quantitative genetic variation. Whereas, in contrast to some recent claims, this potential seems to be rather limited in the absence of recurrent mutation, fluctuating environments might, in combination with it, often generate high levels of additive genetic variation. We investigate how the genetic variation maintained depends on the ecological parameters and on the underlying genetics.

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Vijayalakshmi, N., Dr P.Sekhar, and Dr G.Mokesh Rayalu. "Estimation of Gene Frequencies in Clinical Research." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 508. http://dx.doi.org/10.14419/ijet.v7i4.10.21213.

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Biometrics is a branch of statistics in which various mathematical and statistical techniques can be applied to biological research problems. These are two main areas of specialization of Biometry namely, Bioassays and Quantitative Genetics. Genetics concerns with Heredity and variation. Quantitative Genetics is concerned with the inheritances of quantitative differences between individuals.The essence of Quantitative Genetics is to estimate the genetic parameters such as Gene frequencies, segregation Ratios, Recombination of Genes and so on. Among them, the estimation of Gene Frequencies in the population is an important one. The proportion or percentage of genes in the population is called gene Frequency. In the present research articles, the ABO blood group system of man has been described by discussing the multiple alleles; genotypes, Frequencies and phenotypes of blood groups. The various estimation methods for estimating gene frequencies have gene presents in the present study.

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Khanzadeh, Hassan, Navid Ghavi Hossein-Zadeh, and Shahrokh Ghovvati. "Statistical power and heritability in whole-genome association studies for quantitative traits." Meta Gene 28 (June 2021): 100869. http://dx.doi.org/10.1016/j.mgene.2021.100869.

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Bedo, Justin, Peter Wenzl, Adam Kowalczyk, and Andrzej Kilian. "Precision-mapping and statistical validation of quantitative trait loci by machine learning." BMC Genetics 9, no. 1 (2008): 35. http://dx.doi.org/10.1186/1471-2156-9-35.

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Wang, Meiyue, and Shizhong Xu. "Statistical power in genome-wide association studies and quantitative trait locus mapping." Heredity 123, no. 3 (March 11, 2019): 287–306. http://dx.doi.org/10.1038/s41437-019-0205-3.

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Lande, R., and R. Thompson. "Efficiency of marker-assisted selection in the improvement of quantitative traits." Genetics 124, no. 3 (March 1, 1990): 743–56. http://dx.doi.org/10.1093/genetics/124.3.743.

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Abstract Molecular genetics can be integrated with traditional methods of artificial selection on phenotypes by applying marker-assisted selection (MAS). We derive selection indices that maximize the rate of improvement in quantitative characters under different schemes of MAS combining information on molecular genetic polymorphisms (marker loci) with data on phenotypic variation among individuals (and their relatives). We also analyze statistical limitations on the efficiency of MAS, including the detectability of associations between marker loci and quantitative trait loci, and sampling errors in estimating the weighting coefficients in the selection index. The efficiency of artificial selection can be increased substantially using MAS following hybridization of selected lines. This requires initially scoring genotypes at a few hundred molecular marker loci, as well as phenotypic traits, on a few hundred to a few thousand individuals; the number of marker loci scored can be greatly reduced in later generations. The increase in selection efficiency from the use of marker loci, and the sample sizes necessary to achieve them, depend on the genetic parameters and the selection scheme.

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Ukai, Yasuo. "History of Statistical Genetics with Special Reference to the Analysis of Quantitative Traits." Japanese Journal of Biometrics 32, Special_Issue (2011): S1—S17. http://dx.doi.org/10.5691/jjb.32.s1.

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Lou, Xiang-Yang, George Casella, Ramon C. Littell, Mark C. K. Yang, Julie A. Johnson, and Rongling Wu. "A Haplotype-Based Algorithm for Multilocus Linkage Disequilibrium Mapping of Quantitative Trait Loci With Epistasis." Genetics 163, no. 4 (April 1, 2003): 1533–48. http://dx.doi.org/10.1093/genetics/163.4.1533.

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AbstractFor tightly linked loci, cosegregation may lead to nonrandom associations between alleles in a population. Because of its evolutionary relationship with linkage, this phenomenon is called linkage disequilibrium. Today, linkage disequilibrium-based mapping has become a major focus of recent genome research into mapping complex traits. In this article, we present a new statistical method for mapping quantitative trait loci (QTL) of additive, dominant, and epistatic effects in equilibrium natural populations. Our method is based on haplotype analysis of multilocus linkage disequilibrium and exhibits two significant advantages over current disequilibrium mapping methods. First, we have derived closed-form solutions for estimating the marker-QTL haplotype frequencies within the maximum-likelihood framework implemented by the EM algorithm. The allele frequencies of putative QTL and their linkage disequilibria with the markers are estimated by solving a system of regular equations. This procedure has significantly improved the computational efficiency and the precision of parameter estimation. Second, our method can detect marker-QTL disequilibria of different orders and QTL epistatic interactions of various kinds on the basis of a multilocus analysis. This can not only enhance the precision of parameter estimation, but also make it possible to perform whole-genome association studies. We carried out extensive simulation studies to examine the robustness and statistical performance of our method. The application of the new method was validated using a case study from humans, in which we successfully detected significant QTL affecting human body heights. Finally, we discuss the implications of our method for genome projects and its extension to a broader circumstance. The computer program for the method proposed in this article is available at the webpage http://www.ifasstat.ufl.edu/genome/~LD.

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Henshall, John M., and Michael E. Goddard. "Multiple-Trait Mapping of Quantitative Trait Loci After Selective Genotyping Using Logistic Regression." Genetics 151, no. 2 (February 1, 1999): 885–94. http://dx.doi.org/10.1093/genetics/151.2.885.

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Abstract Experiments to map QTL usually measure several traits, and not uncommonly genotype only those animals that are extreme for some trait(s). Analysis of selectively genotyped, multiple-trait data presents special problems, and most simple methods lead to biased estimates of the QTL effects. The use of logistic regression to estimate QTL effects is described, where the genotype is treated as the dependent variable and the phenotype as the independent variable. In this way selection on phenotype does not bias the results. If normally distributed errors are assumed, the logistic-regression analysis is almost equivalent to a maximum-likelihood analysis, but can be carried out with standard statistical packages. Analysis of a simulated half-sib experiment shows that logistic regression can estimate the effect and position of a QTL without bias and confirms the increased power achieved by multiple-trait analysis.

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Xiong, Momiao, and Sun-Wei Guo. "Fine-Scale Mapping of Quantitative Trait Loci Using Historical Recombinations." Genetics 145, no. 4 (April 1, 1997): 1201–18. http://dx.doi.org/10.1093/genetics/145.4.1201.

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With increasing popularity of QTL mapping in economically important animals and experimental species, the need for statistical methodology for fine-scale QTL mapping becomes increasingly urgent. The ability to disentangle several linked QTL depends on the number of recombination events. An obvious approach to increase the recombination events is to increase sample size, but this approach is often constrained by resources. Moreover, increasing the sample size beyond a certain point will not further reduce the length of confidence interval for QTL map locations. The alternative approach is to use historical recombinations. We use analytical methods to examine the properties of fine QTL mapping using historical recombinations that are accumulated through repeated intercrossing from an F2 population. We demonstrate that, using the historical recombinations, both simple and multiple regression models can reduce significantly the lengths of support intervals for estimated QTL map locations and the variances of estimated QTL map locations. We also demonstrate that, while the simple regression model using historical recombinations does not reduce the variances of the estimated additive and dominant effects, the multiple regression model does. We further determine the power and threshold values for both the simple and multiple regression models. In addition, we calculate the Kullback-Leibler distance and Fisher information for the simple regression model, in the hope to further understand the advantages and disadvantages of using historical recombinations relative to F2 data.

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Yi, Nengjun, and Shizhong Xu. "Bayesian Mapping of Quantitative Trait Loci Under Complicated Mating Designs." Genetics 157, no. 4 (April 1, 2001): 1759–71. http://dx.doi.org/10.1093/genetics/157.4.1759.

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AbstractQuantitative trait loci (QTL) are easily studied in a biallelic system. Such a system requires the cross of two inbred lines presumably fixed for alternative alleles of the QTL. However, development of inbred lines can be time consuming and cost ineffective for species with long generation intervals and severe inbreeding depression. In addition, restriction of the investigation to a biallelic system can sometimes be misleading because many potentially important allelic interactions do not have a chance to express and thus fail to be detected. A complicated mating design involving multiple alleles mimics the actual breeding system. However, it is difficult to develop the statistical model and algorithm using the classical maximum-likelihood method. In this study, we investigate the application of a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to QTL mapping under arbitrarily complicated mating designs. We develop the method under a mixed-model framework where the genetic values of founder alleles are treated as random and the nongenetic effects are treated as fixed. With the MCMC algorithm, we first draw the gene flows from the founders to the descendants for each QTL and then draw samples of the genetic parameters. Finally, we are able to simultaneously infer the posterior distribution of the number, the additive and dominance variances, and the chromosomal locations of all identified QTL.

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Uimari, Pekka, Georg Thaller, and Ina Hoeschele. "The Use of Multiple Markers in a Bayesian Method for Mapping Quantitative Trait Loci." Genetics 143, no. 4 (August 1, 1996): 1831–42. http://dx.doi.org/10.1093/genetics/143.4.1831.

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Abstract Information on multiple linked genetic markers was used in a Bayesian method for the statistical mapping of quantitative trait loci (QTL). Bayesian parameter estimation and hypothesis testing were implemented via Markov chain Monte Carlo algorithms. Variables sampled were the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage or nonlinkage, and the parameters. The parameter vector included allele frequencies at the markers and the QTL, map distances of the markers and the QTL, QTL substitution effect, and polygenic and residual variances. The criterion for QTL detection was the marginal posterior probability of a QTL being located on the chromosome carrying the markers, The method was evaluated empirically by analyzing simulated granddaughter designs consisting of 2000 sons, 20 related sires, and their ancestors.

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Zhu, J. "Analysis of conditional genetic effects and variance components in developmental genetics." Genetics 141, no. 4 (December 1, 1995): 1633–39. http://dx.doi.org/10.1093/genetics/141.4.1633.

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Abstract A genetic model with additive-dominance effects and genotype x environment interactions is presented for quantitative traits with time-dependent measures. The genetic model for phenotypic means at time t conditional on phenotypic means measured at previous time (t-1) is defined. Statistical methods are proposed for analyzing conditional genetic effects and conditional genetic variance components. Conditional variances can be estimated by minimum norm quadratic unbiased estimation (MINQUE) method. An adjusted unbiased prediction (AUP) procedure is suggested for predicting conditional genetic effects. A worked example from cotton fruiting data is given for comparison of unconditional and conditional genetic variances and additive effects.

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Journal articles on the topic 'Statistical and quantitative genetics'

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