Multiple-Interval Mapping for Quantitative Trait Loci With a Spike in the Trait Distribution

For phenotypic distributions where many individuals share a common value—such as survival time following a pathogenic infection—a spike occurs at that common value. This spike affects quantitative trait loci (QTL) mapping methodologies and causes standard approaches to perform suboptimally. In this article, we develop a multiple-interval mapping (MIM) procedure based on mixture generalized linear models (GLIMs). An extended Bayesian information criterion (EBIC) is used for model selection. To demonstrate its utility, this new approach is compared to single-QTL models that appropriately handle the phenotypic distribution. The method is applied to data from Listeria infection as well as data from simulation studies. Compared to the single-QTL model, the findings demonstrate that the MIM procedure greatly improves the efficiency in terms of positive selection rate and false discovery rate. The method developed has been implemented using functions in R and is freely available to download and use.     

Computation of the Full Likelihood Function for Estimating Variance at a Quantitative Trait Locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n X n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.     

试论种子顽拗性的复合数量性状特征

文章简要概述了从顽拗型种子到顽拗性种子这样一个对顽拗性种子认识提高的过程,在综述了前人关于顽拗性种子数量性状特征论述的基础上,把种子顽拗性的数量性状特征划分为种间、种内和个体发育三个层面,提出种子顽拗性是一种复合性状,其核心至少包括脱水耐性、低温耐性和贮藏耐性三方面的内容,其伴随性状包括种子尺度、千粒重、初始含水量、休眠特性、分类地位、地理分布和保护性物质含量等多方面的内容,而且这些核心内容和伴随性状的每一个方面都具有渐变的、过渡的、数量型的特征,从而阐明种子顽拗性是一种复合数量性状.种子顽拗性的复合数量性状特征的提出及其三个层面的划分,有助于加深对种子顽拗性的认识,并用以指导我们在实践中解决种子顽拗性方面的具体问题.     

On the Use of Variance per Genotype as a Tool to Identify Quantitative Trait Interaction Effects: A Report from the Women's Genome Health Study

Testing for genetic effects on mean values of a quantitative trait has been a very successful strategy. However, most studies to date have not explored genetic effects on the variance of quantitative traits as a relevant consequence of genetic variation. In this report, we demonstrate that, under plausible scenarios of genetic interaction, the variance of a quantitative trait is expected to differ among the three possible genotypes of a biallelic SNP. Leveraging this observation with Levene''s test of equality of variance, we propose a novel method to prioritize SNPs for subsequent gene–gene and gene–environment testing. This method has the advantageous characteristic that the interacting covariate need not be known or measured for a SNP to be prioritized. Using simulations, we show that this method has increased power over exhaustive search under certain conditions. We further investigate the utility of variance per genotype by examining data from the Women''s Genome Health Study. Using this dataset, we identify new interactions between the LEPR SNP rs12753193 and body mass index in the prediction of C-reactive protein levels, between the ICAM1 SNP rs1799969 and smoking in the prediction of soluble ICAM-1 levels, and between the PNPLA3 SNP rs738409 and body mass index in the prediction of soluble ICAM-1 levels. These results demonstrate the utility of our approach and provide novel genetic insight into the relationship among obesity, smoking, and inflammation.     

Isolation by Distance in a Quantitative Trait

Random genetic drift in a quantitative character is modeled for a population with a continuous spatial distribution in an infinite habitat of one or two dimensions. The analysis extends Wright's concept of neighborhood size to spatially autocorrelated sampling variation in the expected phenotype at different locations. Weak stabilizing selection is assumed to operate toward the same optimum phenotype in every locality, and the distribution of dispersal distances from parent to offspring is a (radially) symmetric function. The equilibrium pattern of geographic variation in the expected local phenotype depends on the neighborhood size, the genetic variance within neighborhoods, and the strength of selection, but is nearly independent of the form of the dispersal function. With all else equal, geographic variance is smaller in a two-dimensional habitat than in one dimension, and the covariance between expected local phenotypes decreases more rapidly with the distance separating them in two dimensions than in one. The equilibrium geographic variance is less than the phenotypic variance within localities, unless the neighborhood size is small and selection is extremely weak, especially in two dimensions. Nevertheless, dispersal of geographic variance created by random genetic drift is an important mechanism maintaining genetic variance within local populations. For a Gaussian dispersal function it is shown that, even with a small neighborhood size, a population in a two-dimensional habitat can maintain within neighborhoods most of the genetic variance that would occur in an infinite panmictic population.     

性状遗传力与QTL方差对标记辅助选择效果的影响

在采用动物模型标记辅助最佳线性无偏预测方法对个体育种值进行估计的基础上,模拟了在一个闭锁群体内连续对单个性状选择10个世代的情形,并系统地比较了性状遗传力和QTL方差对标记辅助选择所获得的遗传进展、QTL增效基因频率和群体近交系数变化的影响。结果表明：在对高遗传力和QTL方差较小的性状实施标记辅助选择时,可望获得更大的遗传进展;遗传力越高,QTL方差越大,则QTL增效基因频率的上升速度越快;遗传力较高时,群体近交系数上升的速度较为缓慢,而QTL方差对群体近交系数上升速度的影响则不甚明显。结合前人关于标记辅助选择相对效率的研究结果,可以认为：当选择性状的遗传力和QTL方差为中等水平时,标记辅助选择可望获得理想的效果。     

Origin and Consequences of the Relationship between Protein Mean and Variance

Cell-to-cell variance in protein levels (noise) is a ubiquitous phenomenon that can increase fitness by generating phenotypic differences within clonal populations of cells. An important challenge is to identify the specific molecular events that control noise. This task is complicated by the strong dependence of a protein''s cell-to-cell variance on its mean expression level through a power-law like relationship (σ²∝μ^1.69). Here, we dissect the nature of this relationship using a stochastic model parameterized with experimentally measured values. This framework naturally recapitulates the power-law like relationship (σ²∝μ^1.6) and accurately predicts protein variance across the yeast proteome (r² = 0.935). Using this model we identified two distinct mechanisms by which protein variance can be increased. Variables that affect promoter activation, such as nucleosome positioning, increase protein variance by changing the exponent of the power-law relationship. In contrast, variables that affect processes downstream of promoter activation, such as mRNA and protein synthesis, increase protein variance in a mean-dependent manner following the power-law. We verified our findings experimentally using an inducible gene expression system in yeast. We conclude that the power-law-like relationship between noise and protein mean is due to the kinetics of promoter activation. Our results provide a framework for understanding how molecular processes shape stochastic variation across the genome.     

一种可用于同时检测过程均值和方差的控制图

针对一元正态分布的过程数据,基于似然比检验思想,应用指数加权移动平均(EWMA)的一步线性预报功能来估计均值和方差,提出了一种同时检测均值变化和方差增大变化的综合控制图,在文章最后给出了本图与已有的一些控制图的模拟比较,数据显示,所设计的控制图能较快的发现过程变化从而减少产品的不合格率.     

Quantitative Trait Evolution and Environmental Change

Background

Given the recent changes in climate, there is an urgent need to understand the evolutionary ability of populations to respond to these changes.

Methodology/Principal Findings

We performed individual-based simulations with different shapes of the fitness curve, different heritabilities, different levels of density compensation, and different autocorrelation of environmental noise imposed on an environmental trend to study the ability of a population to adapt to changing conditions. The main finding is that when there is a positive autocorrelation of environmental noise, the outcome of the evolutionary process is much more unpredictable compared to when the noise has no autocorrelation. In addition, we found that strong selection resulted in a higher load, and more extinctions, and that this was most pronounced when heritability was low. The level of density-compensation was important in determining the variance in load when there was strong selection, and when genetic variance was lower when the level of density-compensation was low.

Conclusions

The strong effect of the details of the environmental fluctuations makes predictions concerning the evolutionary future of populations very hard to make. In addition, to be able to make good predictions we need information on heritability, fitness functions and levels of density compensation. The results strongly suggest that patterns of environmental noise must be incorporated in future models of environmental change, such as global warming.     

Mapping Quantitative Trait Loci onto a Phylogenetic Tree

Despite advances in genetic mapping of quantitative traits and in phylogenetic comparative approaches, these two perspectives are rarely combined. The joint consideration of multiple crosses among related taxa (whether species or strains) not only allows more precise mapping of the genetic loci (called quantitative trait loci, QTL) that contribute to important quantitative traits, but also offers the opportunity to identify the origin of a QTL allele on the phylogenetic tree that relates the taxa. We describe a formal method for combining multiple crosses to infer the location of a QTL on a tree. We further discuss experimental design issues for such endeavors, such as how many crosses are required and which sets of crosses are best. Finally, we explore the method's performance in computer simulations, and we illustrate its use through application to a set of four mouse intercrosses among five inbred strains, with data on HDL cholesterol.     

The Prior Distribution of the Minimum and Maximum Distance between Several Marker Loci and Quantitative Trait Loci

In order to control linkage experiments, exact formulas and approximations are derived for the minimum distance between quantitative trait loci and the nearest marker locus. The locations of the loci are assumed to be uniformly distributed over the genome. The locations of the marker loci may be known or unknown. The number and length of the chromosomes are arbitrary and therefore the results are applicable for all kinds of species. Analogous formulas are derived for the maximum distance between the quantitative trait loci and the nearest marker loci. For the probability of linkage more simple expressions are derived. The accuracy of the approximations is checked by a simulation.     

Multiple Trait Analysis of Genetic Mapping for Quantitative Trait Loci

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.     

Interval Mapping of Quantitative Trait Loci Employing Correlated Trait Complexes

An approach to increase the resolution power of interval mapping of quantitative trait (QT) loci is proposed, based on analysis of correlated trait complexes. For a given set of QTs, the broad sense heritability attributed to a QT locus (QTL) (say, A/ a) is an increasing function of the number of traits. Thus, for some traits x and y, H(xy)(2) (A/ a) >/= H(x)(2) (A/ a). The last inequality holds even if y does not depend on A/ a at all, but x and y are correlated within the groups AA, Aa and aa due to nongenetic factors and segregation of genes from other chromosomes. A simple relationship connects H(2) (both in single trait and two-trait analysis) with the expected LOD value, ELOD = -1/2N log(1 - H(2)). Thus, situations could exist that from the inequality H(xy)(2) (A/ a) >/= H(x)(2) (A/ a) a higher resolution is provided by the two-trait analysis as compared to the single-trait analysis, in spite of the increased number of parameters. Employing LOD-score procedure to simulated backcross data, we showed that the resolution power of the QTL mapping model can be elevated if correlation between QTs is taken into account. The method allows us to test numerous biologically important hypotheses concerning manifold effects of genomic segments on the defined trait complex (means, variances and correlations).     

Phenotypic Integration Without Modularity: Testing Hypotheses About the Distribution of Pleiotropic Quantitative Trait Loci in a Continuous Space

Theories of phenotypic integration have relied heavily on the concept of modularity in order to model the ways in which traits in an organism correlate and covary. Recent investigations suggest that, while some functional and developmental processes may be morphologically and ontogenetically localized, and thus modular in a developmental sense, there is a great deal of overlap among these influences on patterns of integration in the adult form. This can result in blurry boundaries between hypothesized modules constructed to test hypotheses about phenotypic integration. This investigation tests hypotheses about the contribution of pleiotropic quantitative trait loci (QTL) to phenotypic integration in the mouse mandible without using a priori categorical hypotheses about which traits constitute a module. We ask two main questions: (1) Are the effects of pleiotropic QTL localized to highly correlated traits or more spread out among traits than one might expect by chance? (2) Does the pattern of trait influence when all pleiotropic QTL are considered together deviate from what we might expect if QTL affect traits without regard for the correlations among traits? We find that a large proportion of pleiotropic QTL affect traits that are more highly correlated than we expect by chance with the remainder having effects that are distributed as if by chance. Furthermore, the overall distribution of the effects of pleiotropic QTL differs significantly from the null distribution of no association between pleiotropic effects on traits and correlations among traits. The main modular hypothesis used by earlier studies often does not predict the distribution of sets of traits sharing a common QTL. These results suggest that there is a clear tendency for pleiotropic effects of QTL to be localized but that the localization may be best thought of as occurring in a continuous space rather being clustered in discrete modules.     

Doubled Haploids for Estimating Mean and Variance of Recombination Values

In a diallel cross analysis using doubled haploids, both additive and additive x additive genetic variances can be estimated. In addition, mean and variance of recombination values can also be estimated. Linkage affects the covariance between half-sibs the most, the covariance between grandparent and grand offspring to an intermediate degree and the covariance between full sibs the least. The covariance of parent and offspring is not affected by linkage.     

On the KOLMOGOROV-SMIRNOV Test for the POISSON Distribution with Unknown Mean

The standard tables for the KOLMOGOROV -SMIRNOV test are valid only in the case of testing whether a set of observations is from a completely specified cumulative distribution, F₀(X), with all parameters known. If the parameters are unknown and must be estimated from the sample, then the tables are not valid. A table is given in this paper for use with the KOLMOGOROV -SMIRNOV statistic in the case of testing whether a set of observations is from the POISSON distribution with an unknown mean that must be estimated from the sample. The table is obtained from a Monte Carlo calculation.     

Quantitative Effect of a CNV on a Morphological Trait in Chickens

Copy Number Variation has been associated with morphological traits, developmental defects or disease susceptibility. The autosomal dominant Pea-comb mutation in chickens is due to the massive amplification of a CNV in intron 1 of SOX5 and provides a unique opportunity to assess the effect of variation in the number of repeats on quantitative traits such as comb size and comb mass in Pea-comb chickens. The quantitative variation of comb size was estimated by 2D morphometry and the number of repeats (RQ) was estimated by qPCR, in a total of 178 chickens from 3 experimental lines, two of them showing segregation for the Pea-comb mutation. This study included only Pea-comb chickens. Analysis of variance showed highly significant effects of line and sex on comb measurements. Adult body weight (BW) and RQ were handled as covariates. BW significantly influenced comb mass but not comb size. RQ values significantly influenced comb size, and the linear regression coefficient was highest for heterozygous carriers: the higher the number of repeats, the smaller the comb size. A similar trend was observed for comb mass. The CNV contributed to 3.4% of the phenotypic variance of comb size in heterozygous carriers of the CNV, an order of magnitude frequently encountered for QTLs. Surprisingly, there was no such relationship between RQ values and comb size in the homozygous line. It may be concluded that heterozygosity for a CNV in a non-coding region may contribute to phenotypic plasticity.     

Precision Mapping of Quantitative Trait Loci

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.