Modeling Epistasis of Quantitative Trait Loci Using Cockerham's Model

Genetics ◽  
2002 ◽  
Vol 160 (3) ◽  
pp. 1243-1261 ◽  
Author(s):  
Chen-Hung Kao ◽  
Zhao-Bang Zeng
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Genetic Variance ◽  
Genetic Model ◽  
Linkage Equilibrium ◽  
Gene Effects ◽  
Multiple Loci ◽  
Trait Loci ◽  
Orthogonal Property

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.

Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory

Genome ◽  
2002 ◽  
Vol 45 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Rongling Wu ◽  
Chang-Xing Ma ◽  
Jun Zhu ◽  
George Casella
Keyword(s):  
Genetic Variation ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Genetic Variance ◽  
Genetic Model ◽  
Epigenetic Modification ◽  
Growth Trait ◽  
Developmental Trajectory ◽  
Growth Trajectory ◽  
Trait Loci

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance–covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t – 1 implies the generation of episodes of new genetic variation arising during the interval t – 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.Key words: epigenetic modification, development, marker, poplar, QTL.

scholarly journals Theoretical basis for separation of multiple linked gene effects in mapping quantitative trait loci

1993 ◽  
Vol 90 (23) ◽  
pp. 10972-10976 ◽  
Author(s):  
Z B Zeng
Keyword(s):  
Regression Analysis ◽  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Multiple Regression Analysis ◽  
Multiple Regression ◽  
Quantitative Trait ◽  
Genetic Background ◽  
Test Statistic ◽  
Gene Effects ◽  
Trait Loci

It is now possible to use complete genetic linkage maps to locate major quantitative trait loci (QTLs) on chromosome regions. The current methods of QTL mapping (e.g., interval mapping, which uses a pair or two pairs of flanking markers at a time for mapping) can be subject to the effects of other linked QTLs on a chromosome because the genetic background is not controlled. As a result, mapping of QTLs can be biased, and the resolution of mapping is not very high. Ideally when we test a marker interval for a QTL, we would like our test statistic to be independent of the effects of possible QTLs at other regions of the chromosome so that the effects of QTLs can be separated. This test statistic can be constructed by using a pair of markers to locate the testing position and at the same time using other markers to control the genetic background through a multiple regression analysis. Theory is developed in this paper to explore the idea of a conditional test via multiple regression analysis. Various properties of multiple regression analysis in relation to QTL mapping are examined. Theoretical analysis indicates that it is advantageous to construct such a testing procedure for mapping QTLs and that such a test can potentially increase the precision of QTL mapping substantially.

scholarly journals On the Differences Between Maximum Likelihood and Regression Interval Mapping in the Analysis of Quantitative Trait Loci

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 855-865 ◽  
Author(s):  
Chen-Hung Kao
Keyword(s):  
Quantitative Trait Loci ◽  
Maximum Likelihood ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Mean Squared Error ◽  
Interval Mapping ◽  
Size Difference ◽  
Ratio Test ◽  
Trait Loci ◽  
Variance Explained

AbstractThe differences between maximum-likelihood (ML) and regression (REG) interval mapping in the analysis of quantitative trait loci (QTL) are investigated analytically and numerically by simulation. The analytical investigation is based on the comparison of the solution sets of the ML and REG methods in the estimation of QTL parameters. Their differences are found to relate to the similarity between the conditional posterior and conditional probabilities of QTL genotypes and depend on several factors, such as the proportion of variance explained by QTL, relative QTL position in an interval, interval size, difference between the sizes of QTL, epistasis, and linkage between QTL. The differences in mean squared error (MSE) of the estimates, likelihood-ratio test (LRT) statistics in testing parameters, and power of QTL detection between the two methods become larger as (1) the proportion of variance explained by QTL becomes higher, (2) the QTL locations are positioned toward the middle of intervals, (3) the QTL are located in wider marker intervals, (4) epistasis between QTL is stronger, (5) the difference between QTL effects becomes larger, and (6) the positions of QTL get closer in QTL mapping. The REG method is biased in the estimation of the proportion of variance explained by QTL, and it may have a serious problem in detecting closely linked QTL when compared to the ML method. In general, the differences between the two methods may be minor, but can be significant when QTL interact or are closely linked. The ML method tends to be more powerful and to give estimates with smaller MSEs and larger LRT statistics. This implies that ML interval mapping can be more accurate, precise, and powerful than REG interval mapping. The REG method is faster in computation, especially when the number of QTL considered in the model is large. Recognizing the factors affecting the differences between REG and ML interval mapping can help an efficient strategy, using both methods in QTL mapping to be outlined.

Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 525-535
Author(s):  
Claude M Lebreton ◽  
Peter M Visscher
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Genetic Factors ◽  
Genetic Model ◽  
Original Data ◽  
Nonparametric Bootstrap ◽  
Test Protocol ◽  
Trait Loci

AbstractSeveral 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.

Bayesian Model Choice and Search Strategies for Mapping Interacting Quantitative Trait Loci

Genetics ◽  
2003 ◽  
Vol 165 (2) ◽  
pp. 867-883 ◽  
Author(s):  
Nengjun Yi ◽  
Shizhong Xu ◽  
David B Allison
Keyword(s):  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Complex Traits ◽  
Bayesian Model ◽  
Genetic Model ◽  
Genetic Effects ◽  
Monte Carlo Algorithm ◽  
Data Set ◽  
Epistatic Effects ◽  
Trait Loci

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.

Letter to the Editor: Methods for mapping quantitative trait loci in autotetraploid species

2020 ◽  
Author(s):  
Jing Chen ◽  
Lindsey J Leach ◽  
Zewei Luo
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Statistical Methods ◽  
Quantitative Trait ◽  
Important Species ◽  
Letter To The Editor ◽  
Trait Loci ◽  
Points Of View

Abstract Mapping quantitative trait loci (QTL) in autotetraploid species represents a timely and challenging task. Two papers published by Wu and his colleagues proposed statistical methods for QTL mapping in these evolutionarily and economically important species. In this Letter to the Editor, we present critical comments on the fundamental conceptual errors involved, from both statistical and genetic points of view.

scholarly journals A method for computing identity by descent probabilities and quantitative trait loci mapping with dominant (AFLP) markers

2002 ◽  
Vol 79 (3) ◽  
pp. 247-258 ◽  
Author(s):  
MIGUEL PÉREZ-ENCISO ◽  
ODILE ROUSSOT
Keyword(s):  
Quantitative Trait Loci ◽  
Qtl Mapping ◽  
Quantitative Trait ◽  
Cost Effective ◽  
Significant Loss ◽  
Outbred Population ◽  
Identity By Descent ◽  
Fluorescent Band ◽  
Length Polymorphisms ◽  
Trait Loci

Amplified fragment length polymorphisms (AFLPs) are a widely used marker system: the technique is very cost-effective, easy and rapid, and reproducibly generates hundreds of markers. Unfortunately, AFLP alleles are typically scored as the presence or absence of a band and, thus, heterozygous and dominant homozygous genotypes cannot be distinguished. This results in a significant loss of information, especially as regards mapping of quantitative trait loci (QTLs). We present a Monte Carlo Markov Chain method that allows us to compute the identity by descent probabilities (IBD) in a general pedigree whose individuals have been typed for dominant markers. The method allows us to include the information provided by the fluorescent band intensities of the markers, the rationale being that homozygous individuals have on average higher band intensities than heterozygous individuals, as well as information from linked markers in each individual and its relatives. Once IBD probabilities are obtained, they can be combined into the QTL mapping strategy of choice. We illustrate the method with two simulated populations: an outbred population consisting of full sib families, and an F2 cross between inbred lines. Two marker spacings were considered, 5 or 20 cM, in the outbred population. There was almost no difference, for the practical purpose of QTL estimation, between AFLPs and biallelic codominant markers when the band density is taken into account, especially at the 5 cM spacing. The performance of AFLPs every 5 cM was also comparable to that of highly polymorphic markers (microsatellites) spaced every 20 cM. In economic terms, QTL mapping with a dense map of AFLPs is clearly better than microsatellite QTL mapping and little is lost in terms of accuracy of position. Nevertheless, at low marker densities, AFLPs or other biallelic markers result in very inaccurate estimates of QTL position.

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