Journal articles on the topic 'Quantitative Genetics Model'
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1
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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Tachida, H., and C. C. Cockerham. "A building block model for quantitative genetics." Genetics 121, no. 4 (April 1, 1989): 839–44. http://dx.doi.org/10.1093/genetics/121.4.839.
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Abstract We introduce a quantitative genetic model for multiple alleles which permits the parameterization of the degree, D, of dominance of favorable or unfavorable alleles. We assume gene effects to be random from some distribution and independent of the D's. We then fit the usual least-squares population genetic model of additive and dominance effects in an infinite equilibrium population to determine the five genetic components--additive variance sigma 2 a, dominance variance sigma 2 d, variance of homozygous dominance effects d2, covariance of additive and homozygous dominance effects d1, and the square of the inbreeding depression h--required to treat finite populations and large populations that have been through a bottleneck or in which there is inbreeding. The effects of dominance can be summarized as functions of the average, D, and the variance, sigma 2 D. An important distinction arises between symmetrical and nonsymmetrical distributions of gene effects. With symmetrical distributions d1 = -d2/2 which is always negative, and the contribution of dominance to sigma 2 a is equal to d2/2. With nonsymmetrical distributions there is an additional contribution H to sigma 2 a and -H/2 to d1, the sign of H being determined by D and the skew of the distribution. Some numerical evaluations are presented for the normal and exponential distributions of gene effects, illustrating the effects of the number of alleles and of the variation in allelic frequencies. Random additive by additive (a*a) epistatic effects contribute to sigma 2 a and to the a*a variance, sigma 2/aa, the relative contributions depending on the number of alleles and the variation in allelic frequencies.(ABSTRACT TRUNCATED AT 250 WORDS)
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Zhivotovsky, L. A., and M. W. Feldman. "On models of quantitative genetic variability: a stabilizing selection-balance model." Genetics 130, no. 4 (April 1, 1992): 947–55. http://dx.doi.org/10.1093/genetics/130.4.947.
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Abstract A model of stabilizing selection on a multilocus character is proposed that allows the maintenance of stable allelic polymorphism and linkage disequilibrium. The model is a generalization of Lerner's model of homeostasis in which heterozygotes are less susceptible to environmental variation and hence are superior to homozygotes under phenotypic stabilizing selection. The analysis is carried out for weak selection with a quadratic-deviation model for the stabilizing selection. The stationary state is characterized by unequal allele frequencies, unequal proportions of complementary gametes, and a reduction of the genetic (and phenotypic) variance by the linkage disequilibrium. The model is compared with Mather's polygenic balance theory, with models that include mutation-selection balance, and others that have been proposed to study the role of linkage disequilibrium in quantitative inheritance.
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Kao, Chen-Hung, and Zhao-Bang Zeng. "Modeling Epistasis of Quantitative Trait Loci Using Cockerham's Model." Genetics 160, no. 3 (March 1, 2002): 1243–61. http://dx.doi.org/10.1093/genetics/160.3.1243.
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AbstractWe use the orthogonal contrast scales proposed by Cockerham to construct a genetic model, called Cockerham's model, for studying epistasis between genes. The properties of Cockerham's model in modeling and mapping epistatic genes under linkage equilibrium and disequilibrium are investigated and discussed. Because of its orthogonal property, Cockerham's model has several advantages in partitioning genetic variance into components, interpreting and estimating gene effects, and application to quantitative trait loci (QTL) mapping when compared to other models, and thus it can facilitate the study of epistasis between genes and be readily used in QTL mapping. The issues of QTL mapping with epistasis are also addressed. Real and simulated examples are used to illustrate Cockerham's model, compare different models, and map for epistatic QTL. Finally, we extend Cockerham's model to multiple loci and discuss its applications to QTL mapping.
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Hill, William G. "Sewall Wright and quantitative genetics." Genome 31, no. 1 (January 1, 1989): 190–95. http://dx.doi.org/10.1139/g89-033.
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Some aspects of Wright's great contribution to quantitative genetics and animal breeding are reviewed in relation to current research and practice. Particular aspects discussed are as follows: the utility of his definition of inbreeding coefficient in terms of the correlation of uniting gametes; the maintenance of genetic variation in the optimum model; the inter-relations between past and present animal-breeding practice and the shifting-balance theory of evolution.Key words: quantitative genetics, inbreeding coefficient, genetic variation, evolution.
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Luo, L., Y.-M. Zhang, and S. Xu. "A quantitative genetics model for viability selection." Heredity 94, no. 3 (November 10, 2004): 347–55. http://dx.doi.org/10.1038/sj.hdy.6800615.
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Nagylaki, T. "Geographical variation in a quantitative character." Genetics 136, no. 1 (January 1, 1994): 361–81. http://dx.doi.org/10.1093/genetics/136.1.361.
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Abstract A model for the evolution of the local averages of a quantitative character under migration, selection, and random genetic drift in a subdivided population is formulated and investigated. Generations are discrete and nonoverlapping; the monoecious, diploid population mates at random in each deme. All three evolutionary forces are weak, but the migration pattern and the local population numbers are otherwise arbitrary. The character is determined by purely additive gene action and a stochastically independent environment; its distribution is Gaussian with a constant variance; and it is under Gaussian stabilizing selection with the same parameters in every deme. Linkage disequilibrium is neglected. Most of the results concern the covariances of the local averages. For a finite number of demes, explicit formulas are derived for (i) the asymptotic rate and pattern of convergence to equilibrium, (ii) the variance of a suitably weighted average of the local averages, and (iii) the equilibrium covariances when selection and random drift are much weaker than migration. Essentially complete analyses of equilibrium and convergence are presented for random outbreeding and site homing, the Levene and island models, the circular habitat and the unbounded linear stepping-stone model in the diffusion approximation, and the exact unbounded stepping-stone model in one and two dimensions.
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Andersson, Leif. "Fisher’s quantitative genetic model and the molecular genetics of multifactorial traits." Journal of Animal Breeding and Genetics 135, no. 6 (October 2018): 391–92. http://dx.doi.org/10.1111/jbg.12362.
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Caballero, A., and P. D. Keightley. "A pleiotropic nonadditive model of variation in quantitative traits." Genetics 138, no. 3 (November 1, 1994): 883–900. http://dx.doi.org/10.1093/genetics/138.3.883.
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Abstract A model of mutation-selection-drift balance incorporating pleiotropic and dominance effects of new mutations on quantitative traits and fitness is investigated and used to predict the amount and nature of genetic variation maintained in segregating populations. The model is based on recent information on the joint distribution of mutant effects on bristle traits and fitness in Drosophila melanogaster from experiments on the accumulation of spontaneous and P element-induced mutations. These experiments suggest a leptokurtic distribution of effects with an intermediate correlation between effects on the trait and fitness. Mutants of large effect tend to be partially recessive while those with smaller effect are on average additive, but apparently with very variable gene action. The model is parameterized with two different sets of information derived from P element insertion and spontaneous mutation data, though the latter are not fully known. They differ in the number of mutations per generation which is assumed to affect the trait. Predictions of the variance maintained for bristle number assuming parameters derived from effects of P element insertions, in which the proportion of mutations with an effect on the trait is small, fit reasonably well with experimental observations. The equilibrium genetic variance is nearly independent of the degree of dominance of new mutations. Heritabilities of between 0.4 and 0.6 are predicted with population sizes from 10(4) to 10(6), and most of the variance for the metric trait in segregating population is due to a small proportion of mutations (about 1% of the total number) with neutral or nearly neutral effects on fitness and intermediate effects on the trait (0.1-0.5 sigma P).(ABSTRACT TRUNCATED AT 250 WORDS)
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Eshel, Ilan, and Carlo Matessi. "Canalization, Genetic Assimilation and Preadaptation: A Quantitative Genetic Model." Genetics 149, no. 4 (August 1, 1998): 2119–33. http://dx.doi.org/10.1093/genetics/149.4.2119.
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Abstract We propose a mathematical model to analyze the evolution of canalization for a trait under stabilizing selection, where each individual in the population is randomly exposed to different environmental conditions, independently of its genotype. Without canalization, our trait (primary phenotype) is affected by both genetic variation and environmental perturbations (morphogenic environment). Selection of the trait depends on individually varying environmental conditions (selecting environment). Assuming no plasticity initially, morphogenic effects are not correlated with the direction of selection in individual environments. Under quite plausible assumptions we show that natural selection favors a system of canalization that tends to repress deviations from the phenotype that is optimal in the most common selecting environment. However, many experimental results, dating back to Waddington and others, indicate that natural canalization systems may fail under extreme environments. While this can be explained as an impossibility of the system to cope with extreme morphogenic pressure, we show that a canalization system that tends to be inactivated in extreme environments is even more advantageous than rigid canalization. Moreover, once this adaptive canalization is established, the resulting evolution of primary phenotype enables substantial preadaptation to permanent environmental changes resembling extreme niches of the previous environment.
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Piepho, Hans-Peter, and Hugh G. Gauch. "Marker Pair Selection for Mapping Quantitative Trait Loci." Genetics 157, no. 1 (January 1, 2001): 433–44. http://dx.doi.org/10.1093/genetics/157.1.433.
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AbstractMapping of quantitative trait loci (QTL) for backcross and F2 populations may be set up as a multiple linear regression problem, where marker types are the regressor variables. It has been shown previously that flanking markers absorb all information on isolated QTL. Therefore, selection of pairs of markers flanking QTL is useful as a direct approach to QTL detection. Alternatively, selected pairs of flanking markers can be used as cofactors in composite interval mapping (CIM). Overfitting is a serious problem, especially if the number of regressor variables is large. We suggest a procedure denoted as marker pair selection (MPS) that uses model selection criteria for multiple linear regression. Markers enter the model in pairs, which reduces the number of models to be considered, thus alleviating the problem of overfitting and increasing the chances of detecting QTL. MPS entails an exhaustive search per chromosome to maximize the chance of finding the best-fitting models. A simulation study is conducted to study the merits of different model selection criteria for MPS. On the basis of our results, we recommend the Schwarz Bayesian criterion (SBC) for use in practice.
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Slatkin, M., and S. A. Frank. "The quantitative genetic consequences of pleiotropy under stabilizing and directional selection." Genetics 125, no. 1 (May 1, 1990): 207–13. http://dx.doi.org/10.1093/genetics/125.1.207.
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Abstract The independence of two phenotypic characters affected by both pleiotropic and nonpleiotropic mutations is investigated using a generalization of M. Slatkin's stepwise mutation model of 1987. The model is used to determine whether predictions of either the multivariate normal model introduced in 1980 by R. Lande or the house-of-cards model introduced in 1985 by M. Turelli can be regarded as typical of models that are intermediate between them. We found that, under stabilizing selection, the variance of one character at equilibrium may depend on the strength of stabilizing selection on the other character (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the types of mutations that can occur. Similarly, under directional selection, the genetic covariance between two characters may increase substantially (as in the house-of-cards model) or not (as in the multivariate normal model) depending on the kinds of mutations that are assumed to occur. Hence, even for the simple model we consider, neither the house-of-cards nor the multivariate normal model can be used to make predictions, making it unlikely that either could be used to draw general conclusions about more complex and realistic models.
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Barton, N. H. "Pleiotropic models of quantitative variation." Genetics 124, no. 3 (March 1, 1990): 773–82. http://dx.doi.org/10.1093/genetics/124.3.773.
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Abstract It is widely held that each gene typically affects many characters, and that each character is affected by many genes. Moreover, strong stabilizing selection cannot act on an indefinitely large number of independent traits. This makes it likely that heritable variation in any one trait is maintained as a side effect of polymorphisms which have nothing to do with selection on that trait. This paper examines the idea that variation is maintained as the pleiotropic side effect of either deleterious mutation, or balancing selection. If mutation is responsible, it must produce alleles which are only mildly deleterious (s approximately 10(-3)), but nevertheless have significant effects on the trait. Balancing selection can readily maintain high heritabilities; however, selection must be spread over many weakly selected polymorphisms if large responses to artificial selection are to be possible. In both classes of pleiotropic model, extreme phenotypes are less fit, giving the appearance of stabilizing selection on the trait. However, it is shown that this effect is weak (of the same order as the selection on each gene): the strong stabilizing selection which is often observed is likely to be caused by correlations with a limited number of directly selected traits. Possible experiments for distinguishing the alternatives are discussed.
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Goffinet, Bruno, and Sophie Gerber. "Quantitative Trait Loci: A Meta-analysis." Genetics 155, no. 1 (May 1, 2000): 463–73. http://dx.doi.org/10.1093/genetics/155.1.463.
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Abstract This article presents a method to combine QTL results from different independent analyses. This method provides a modified Akaike criterion that can be used to decide how many QTL are actually represented by the QTL detected in different experiments. This criterion is computed to choose between models with one, two, three, etc., QTL. Simulations are carried out to investigate the quality of the model obtained with this method in various situations. It appears that the method allows the length of the confidence interval of QTL location to be consistently reduced when there are only very few “actual” QTL locations. An application of the method is given using data from the maize database available online at http://www.agron.missouri.edu/.
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Yi, Nengjun, Daniel Shriner, Samprit Banerjee, Tapan Mehta, Daniel Pomp, and Brian S. Yandell. "An Efficient Bayesian Model Selection Approach for Interacting Quantitative Trait Loci Models With Many Effects." Genetics 176, no. 3 (May 4, 2007): 1865–77. http://dx.doi.org/10.1534/genetics.107.071365.
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Pérez-Enciso, Miguel, and Luis Varona. "Quantitative Trait Loci Mapping in F2 Crosses Between Outbred Lines." Genetics 155, no. 1 (May 1, 2000): 391–405. http://dx.doi.org/10.1093/genetics/155.1.391.
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Abstract We develop a mixed-model approach for QTL analysis in crosses between outbred lines that allows for QTL segregation within lines as well as for differences in mean QTL effects between lines. We also propose a method called “segment mapping” that is based in partitioning the genome in a series of segments. The expected change in mean according to percentage of breed origin, together with the genetic variance associated with each segment, is estimated using maximum likelihood. The method also allows the estimation of differences in additive variances between the parental lines. Completely fixed random and mixed models together with segment mapping are compared via simulation. The segment mapping and mixed-model behaviors are similar to those of classical methods, either the fixed or random models, under simple genetic models (a single QTL with alternative alleles fixed in each line), whereas they provide less biased estimates and have higher power than fixed or random models in more complex situations, i.e., when the QTL are segregating within the parental lines. The segment mapping approach is particularly useful to determining which chromosome regions are likely to contain QTL when these are linked.
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Moorad, Jacob A., and Daniel E. L. Promislow. "Evolutionary demography and quantitative genetics: age-specific survival as a threshold trait." Proceedings of the Royal Society B: Biological Sciences 278, no. 1702 (July 21, 2010): 144–51. http://dx.doi.org/10.1098/rspb.2010.0992.
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Researchers must understand how mutations affect survival at various ages to understand how ageing evolves. Many models linking mutation to age-specific survival have been proposed but there is little evidence to indicate which model is most appropriate. This is a serious problem because the predicted evolutionary endpoints of ageing depend upon the details of the specific model. We apply an explicitly quantitative genetic perspective to the problem. To determine the inheritance of dichotomous traits (such as survival), quantitative genetics has long employed a threshold model. Beginning from first principles, we show how this is the most defensible mutational model for age-specific survival and how this, relative to the standard model, predicts delayed senescence and mortality deceleration at late age. These are commonly observed patterns of ageing that heretofore have required more complicated survival models. We also show how this model can be developed further to unify quantitative genetics and evolutionary demography into a more complete conceptual framework for understanding the evolution of ageing.
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Xu, S., and W. R. Atchley. "A random model approach to interval mapping of quantitative trait loci." Genetics 141, no. 3 (November 1, 1995): 1189–97. http://dx.doi.org/10.1093/genetics/141.3.1189.
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Abstract Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.
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Yi, Nengjun, Brian S. Yandell, Gary A. Churchill, David B. Allison, Eugene J. Eisen, and Daniel Pomp. "Bayesian Model Selection for Genome-Wide Epistatic Quantitative Trait Loci Analysis." Genetics 170, no. 3 (May 23, 2005): 1333–44. http://dx.doi.org/10.1534/genetics.104.040386.
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Żak, Małgorzata, Andreas Baierl, Małgorzata Bogdan, and Andreas Futschik. "Locating Multiple Interacting Quantitative Trait Loci Using Rank-Based Model Selection." Genetics 176, no. 3 (May 16, 2007): 1845–54. http://dx.doi.org/10.1534/genetics.106.068031.
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Wang, Ping, John A. Dawson, Mark P. Keller, Brian S. Yandell, Nancy A. Thornberry, Bei B. Zhang, I.-Ming Wang, Eric E. Schadt, Alan D. Attie, and C. Kendziorski. "A Model Selection Approach for Expression Quantitative Trait Loci (eQTL) Mapping." Genetics 187, no. 2 (November 29, 2010): 611–21. http://dx.doi.org/10.1534/genetics.110.122796.
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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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Xu, Shizhong, and William R. Atchley. "Mapping Quantitative Trait Loci for Complex Binary Diseases Using Line Crosses." Genetics 143, no. 3 (July 1, 1996): 1417–24. http://dx.doi.org/10.1093/genetics/143.3.1417.
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Abstract A composite interval gene mapping procedure for complex binary disease traits is proposed in this paper. The binary trait of interest is assumed to be controlled by an underlying liability that is normally distributed. The liability is treated as a typical quantitative character and thus described by the usual quantitative genetics model. Translation from the liability into a binary (disease) phenotype is through the physiological threshold model. Logistic regression analysis is employed to estimate the effects and locations of putative quantitative trait loci (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). Simulation studies show that properties of this mapping procedure mimic those of the composite interval mapping for normally distributed data. Potential utilization of the QTL mapping procedure for resolving alternative genetic models (e.g., single- or two-trait-locus model) is discussed.
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Harper, A. B. "Evolutionary Stability for Interactions among Kin under Quantitative Inheritance." Genetics 121, no. 4 (April 1, 1989): 877–89. http://dx.doi.org/10.1093/genetics/121.4.877.
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Abstract The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.
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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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Dohm, Michael R., Jack P. Hayes, and Theodore Garland. "The Quantitative Genetics of Maximal and Basal Rates of Oxygen Consumption in Mice." Genetics 159, no. 1 (September 1, 2001): 267–77. http://dx.doi.org/10.1093/genetics/159.1.267.
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Abstract A positive genetic correlation between basal metabolic rate (BMR) and maximal (V.O2max) rate of oxygen consumption is a key assumption of the aerobic capacity model for the evolution of endothermy. We estimated the genetic (VA, additive, and VD, dominance), prenatal (VN), and postnatal common environmental (VC) contributions to individual differences in metabolic rates and body mass for a genetically heterogeneous laboratory strain of house mice (Mus domesticus). Our breeding design did not allow the simultaneous estimation of VD and VN. Regardless of whether VD or VN was assumed, estimates of VA were negative under the full models. Hence, we fitted reduced models (e.g., VA + VN + VE or VA + VE) and obtained new variance estimates. For reduced models, narrow-sense heritability (hN2) for BMR was <0.1, but estimates of hN2 for V.O2max were higher. When estimated with the VA + VE model, the additive genetic covariance between V.O2max and BMR was positive and statistically different from zero. This result offers tentative support for the aerobic capacity model for the evolution of vertebrate energetics. However, constraints imposed on the genetic model may cause our estimates of additive variance and covariance to be biased, so our results should be interpreted with caution and tested via selection experiments.
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Forties, Robert A., Justin A. North, Sarah Javaid, Omar P. Tabbaa, Richard Fishel, Michael G. Poirier, and Ralf Bundschuh. "A quantitative model of nucleosome dynamics." Nucleic Acids Research 39, no. 19 (July 15, 2011): 8306–13. http://dx.doi.org/10.1093/nar/gkr422.
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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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Feenstra, Bjarke, and Ib M. Skovgaard. "A Quantitative Trait Locus Mixture Model That Avoids Spurious LOD Score Peaks." Genetics 167, no. 2 (June 2004): 959–65. http://dx.doi.org/10.1534/genetics.103.025437.
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Zhang, Xu-Sheng, Jinliang Wang, and William G. Hill. "Pleiotropic Model of Maintenance of Quantitative Genetic Variation at Mutation-Selection Balance." Genetics 161, no. 1 (May 1, 2002): 419–33. http://dx.doi.org/10.1093/genetics/161.1.419.
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AbstractA pleiotropic model of maintenance of quantitative genetic variation at mutation-selection balance is investigated. Mutations have effects on a metric trait and deleterious effects on fitness, for which a bivariate gamma distribution is assumed. Equations for calculating the strength of apparent stabilizing selection (Vs) and the genetic variance maintained in segregating populations (VG) were derived. A large population can hold a high genetic variance but the apparent stabilizing selection may or may not be relatively strong, depending on other properties such as the distribution of mutation effects. If the distribution of mutation effects on fitness is continuous such that there are few nearly neutral mutants, or a minimum fitness effect is assumed if most mutations are nearly neutral, VG increases to an asymptote as the population size increases. Both VG and Vs are strongly affected by the shape of the distribution of mutation effects. Compared with mutants of equal effect, allowing their effects on fitness to vary across loci can produce a much higher VG but also a high Vs (Vs in phenotypic standard deviation units, which is always larger than the ratio VP/Vm), implying weak apparent stabilizing selection. If the mutational variance Vm is ∼10-3 Ve (Ve, environmental variance), the model can explain typical values of heritability and also apparent stabilizing selection, provided the latter is quite weak as suggested by a recent review.
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Yi, Nengjun, Shizhong Xu, and David B. Allison. "Bayesian Model Choice and Search Strategies for Mapping Interacting Quantitative Trait Loci." Genetics 165, no. 2 (October 1, 2003): 867–83. http://dx.doi.org/10.1093/genetics/165.2.867.
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AbstractMost complex traits of animals, plants, and humans are influenced by multiple genetic and environmental factors. Interactions among multiple genes play fundamental roles in the genetic control and evolution of complex traits. Statistical modeling of interaction effects in quantitative trait loci (QTL) analysis must accommodate a very large number of potential genetic effects, which presents a major challenge to determining the genetic model with respect to the number of QTL, their positions, and their genetic effects. In this study, we use the methodology of Bayesian model and variable selection to develop strategies for identifying multiple QTL with complex epistatic patterns in experimental designs with two segregating genotypes. Specifically, we develop a reversible jump Markov chain Monte Carlo algorithm to determine the number of QTL and to select main and epistatic effects. With the proposed method, we can jointly infer the genetic model of a complex trait and the associated genetic parameters, including the number, positions, and main and epistatic effects of the identified QTL. Our method can map a large number of QTL with any combination of main and epistatic effects. Utility and flexibility of the method are demonstrated using both simulated data and a real data set. Sensitivity of posterior inference to prior specifications of the number and genetic effects of QTL is investigated.
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Wu, Rongling, Chang-Xing Ma, and George Casella. "A Bivalent Polyploid Model for Mapping Quantitative Trait Loci in Outcrossing Tetraploids." Genetics 166, no. 1 (January 2004): 581–95. http://dx.doi.org/10.1534/genetics.166.1.581.
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Gianola, Daniel, and Henner Simianer. "A Thurstonian Model for Quantitative Genetic Analysis of Ranks: A Bayesian Approach." Genetics 174, no. 3 (September 15, 2006): 1613–24. http://dx.doi.org/10.1534/genetics.106.060673.
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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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Doerge, R. W., and G. A. Churchill. "Permutation Tests for Multiple Loci Affecting a Quantitative Character." Genetics 142, no. 1 (January 1, 1996): 285–94. http://dx.doi.org/10.1093/genetics/142.1.285.
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The problem of detecting minor quantitative trait loci (QTL) responsible for genetic variation not explained by major QTL is of importance in the complete dissection of quantitative characters. Two extensions of the permutation-based method for estimating empirical threshold values are presented. These methods, the conditional empirical threshold (CET) and the residual empirical threshold (RET), yield critical values that can be used to construct tests for the presence of minor QTL effects while accounting for effects of known major QTL. The CET provides a completely nonparametric test through conditioning on markers linked to major QTL. It allows for general nonadditive interactions among QTL, but its practical application is restricted to regions of the genome that are unlinked to the major QTL. The RET assumes a structural model for the effect of major QTL, and a threshold is constructed using residuals from this structural model. The search space for minor QTL is unrestricted, and RET-based tests may be more powerful than the CET-based test when the structural model is approximately true.
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Bryant, Edwin H., Steven A. McCommas, and Lisa M. Combs. "THE EFFECT OF AN EXPERIMENTAL BOTTLENECK UPON QUANTITATIVE GENETIC VARIATION IN THE HOUSEFLY." Genetics 114, no. 4 (December 1, 1986): 1191–211. http://dx.doi.org/10.1093/genetics/114.4.1191.
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ABSTRACT Effects of a population bottleneck (founder-flush cycle) upon quantitative genetic variation of morphometric traits were examined in replicated experimental lines of the housefly founded with one, four or 16 pairs of flies. Heritability and additive genetic variances for eight morphometric traits generally increased as a result of the bottleneck, but the pattern of increase among bottleneck sizes differed among traits. Principal axes of the additive genetic correlation matrix for the control line yielded two suites of traits, one associated with general body size and another set largely independent of body size. In the former set containing five of the traits, additive genetic variance was greatest in the bottleneck size of four pairs, whereas in the latter set of two traits the largest additive genetic variance occurred in the smallest bottleneck size of one pair. One trait exhibited changes in additive genetic variance intermediate between these two major responses. These results were inconsistent with models of additive effects of alleles within loci or of additive effects among loci. An observed decline in viability measures and body size in the bottleneck lines also indicated that there was nonadditivity of allelic effects for these traits. Several possible nonadditive models were explored that increased additive genetic variance as a result of a bottleneck. These included a model with complete dominance, a model with overdominance and a model incorporating multiplicative epistasis.
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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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Ball, Roderick D. "Bayesian Methods for Quantitative Trait Loci Mapping Based on Model Selection: Approximate Analysis Using the Bayesian Information Criterion." Genetics 159, no. 3 (November 1, 2001): 1351–64. http://dx.doi.org/10.1093/genetics/159.3.1351.
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Abstract We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-δ criterion, with the parameter δ increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.
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Yi, Nengjun, Varghese George, and David B. Allison. "Stochastic Search Variable Selection for Identifying Multiple Quantitative Trait Loci." Genetics 164, no. 3 (July 1, 2003): 1129–38. http://dx.doi.org/10.1093/genetics/164.3.1129.
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AbstractIn this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.
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Keightley, P. D., and W. G. Hill. "Quantitative genetic variation in body size of mice from new mutations." Genetics 131, no. 3 (July 1, 1992): 693–700. http://dx.doi.org/10.1093/genetics/131.3.693.
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Abstract To measure the amount of new genetic variation in 6-week weight of mice arising each generation from mutation, selection lines derived from an initially inbred strain were maintained for 25 generations. An analysis using an animal model with restricted maximum likelihood was applied to estimate a mutational genetic component of variance for the infinitesimal model of many genes of small effect. Assuming that the inbred base population was at a mutation-drift equilibrium, it is estimated that the heritability for body size has increased by 1.0% per generation, with lower and upper confidence limits of 0.6% and 1.6%, respectively. A model which includes a mutational genetic component of variance fits the data much better than one involving only base population genetic variance. A model with no genetic component fits the data very poorly. An environmental covariance of body size of mother and offspring was included in the model and accounts for 10% of the variance. By using information only from the observed response to selection, the estimated increase in heritability from mutation is 0.3% per generation. These values are higher than published estimates for the increase in variance from spontaneous mutations in bristle traits of Drosophila, for which there are extensive data, but similar to estimates for various skeletal traits in mice.
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Rajon, Etienne, and Joshua B. Plotkin. "The evolution of genetic architectures underlying quantitative traits." Proceedings of the Royal Society B: Biological Sciences 280, no. 1769 (October 22, 2013): 20131552. http://dx.doi.org/10.1098/rspb.2013.1552.
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In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in quantitative trait loci mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here, we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions with qualitative trends in the genetics of human traits, and with systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis for traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.
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de Koning, Dirk J., Luc L. G. Janss, Annemieke P. Rattink, Pieter A. M. van Oers, Beja J. de Vries, Martien A. M. Groenen, Jan J. van der Poel, Piet N. de Groot, E. W. (Pim) Brascamp, and Johan A. M. van Arendonk. "Detection of Quantitative Trait Loci for Backfat Thickness and Intramuscular Fat Content in Pigs (Sus scrofa)." Genetics 152, no. 4 (August 1, 1999): 1679–90. http://dx.doi.org/10.1093/genetics/152.4.1679.
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Abstract In an experimental cross between Meishan and Dutch Large White and Landrace lines, 619 F2 animals and their parents were typed for molecular markers covering the entire porcine genome. Associations were studied between these markers and two fatness traits: intramuscular fat content and backfat thickness. Association analyses were performed using interval mapping by regression under two genetic models: (1) an outbred line-cross model where the founder lines were assumed to be fixed for different QTL alleles; and (2) a half-sib model where a unique allele substitution effect was fitted within each of the 19 half-sib families. Both approaches revealed for backfat thickness a highly significant QTL on chromosome 7 and suggestive evidence for a QTL at chromosome 2. Furthermore, suggestive QTL affecting backfat thickness were detected on chromosomes 1 and 6 under the line-cross model. For intramuscular fat content the line-cross approach showed suggestive evidence for QTL on chromosomes 2, 4, and 6, whereas the half-sib analysis showed suggestive linkage for chromosomes 4 and 7. The nature of the QTL effects and assumptions underlying both models could explain discrepancies between the findings under the two models. It is concluded that both approaches can complement each other in the analysis of data from outbred line crosses.
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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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Lebreton, Claude M., and Peter M. Visscher. "Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model." Genetics 148, no. 1 (January 1, 1998): 525–35. http://dx.doi.org/10.1093/genetics/148.1.525.
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Abstract Several nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.
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Mutshinda, Crispin M., and Mikko J. Sillanpää. "A Decision Rule for Quantitative Trait Locus Detection Under the Extended Bayesian LASSO Model." Genetics 192, no. 4 (September 14, 2012): 1483–91. http://dx.doi.org/10.1534/genetics.111.130278.
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Keightley, P. D. "Models of quantitative variation of flux in metabolic pathways." Genetics 121, no. 4 (April 1, 1989): 869–76. http://dx.doi.org/10.1093/genetics/121.4.869.
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Abstract As a model of variation in a quantitative character, enzyme activity variation segregating in a population is assumed to affect the flux in simple metabolic pathways. The genetic variation of flux is partitioned into additive and nonadditive components. An interaction component of flux variance is present because the effect of an allelic substitution is modified by other substitutions which change the concentrations of shared metabolites. In a haploid population, the the proportion of interaction variance is a function of the gene frequencies at the loci contributing to the flux variation, enzyme activities of mutant and wild type at variable loci and activities at nonvariable loci. The proportion of interaction variance is inversely related to the ratio of mutant to wild-type activities at the loci controlling the enzyme activities. The interaction component as a function of gene frequencies is at a maximum with high mutant allele frequencies. In contrast, the dominance component which would apply to a diploid population is maximal as a proportion of the total when mutant alleles are at low frequencies. Unless there are many loci with large differences in activity between the alleles, the interaction component is a small proportion of the total variance. Data on enzyme activity variation from natural and artificial populations suggest that such variation generates little nonadditive variance despite the highly interactive nature of the underlying biochemical system.
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Revell, Liam J. "ANCESTRAL CHARACTER ESTIMATION UNDER THE THRESHOLD MODEL FROM QUANTITATIVE GENETICS." Evolution 68, no. 3 (November 18, 2013): 743–59. http://dx.doi.org/10.1111/evo.12300.
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Lange, Kenneth. "An Approximate Model of Polygenic Inheritance." Genetics 147, no. 3 (November 1, 1997): 1423–30. http://dx.doi.org/10.1093/genetics/147.3.1423.
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The finite polygenic model approximates polygenic inheritance by postulating that a quantitative trait is determined by n independent, additive loci. The 3n possible genotypes for each person in this model limit its applicability. Cannings, Thompson, and Skolnick suggested a simplified, nongenetic version of the model involving only 2n + 1 genotypes per person. This article shows that this hypergeometric polygenic model also approximates polygenic inheritance well. In particular, for noninbred pedigrees, trait means, variances, covariances, and marginal distributions match those of the ordinary finite polygenic model. Furthermore as n → ∞, the trait values within a pedigree collectively tend toward multivariate normality. The implications of these results for likelihood evaluation under the polygenic threshold and mixed models of inheritance are discussed. Finally, a simple numerical example illustrates the application of the hypergeometric polygenic model to risk prediction under the polygenic threshold model.
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Rodolphe, F., and M. Lefort. "A multi-marker model for detecting chromosomal segments displaying QTL activity." Genetics 134, no. 4 (August 1, 1993): 1277–88. http://dx.doi.org/10.1093/genetics/134.4.1277.
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Abstract A statistical method is presented for detecting quantitative trait loci (QTLs), based on the linear model. Unlike methods able to detect a few well separated QTLs and to estimate their effects and positions, this method considers the genome as a whole and enables the detection of chromosomal segments involved in the differences between two homozygous lines, and their backcross, doubled haploid, or F2 progenies, for a quantitative trait. Genetic markers must be codominant, but missing markers are accepted, provided they are missing independently from the experiment. Asymptotic properties, which are of practical use, are developed. This method does not rely on strong genetic hypotheses, and thus does not permit any precise genetic analysis of the trait under study, but it does assess which regions of the genome are involved, whatever the complexity of the genetic determinism (number, effects and interactions among QTLs). Simultaneous use of several methods, including this one, should lead to better efficiency in QTL detection.
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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.