Determining the linkage of disease-resistance genes to molecular markers: the LOD-SCORE method revisited with regard to necessary sample sizes

Some approaches to molecular marker-assisted linkage detection for a dominant disease-resistance trait based on a segregating F₂ population are discussed. Analysis of two-point linkage is carried out by the traditional measure of maximum lod score. It depends on (1) the maximum-likelihood estimate of the recombination fraction between the marker and the disease-resistance gene locus, (2) the observed absolute frequencies, and (3) the unknown number of tested individuals. If one replaces the absolute frequencies by expressions depending on the unknown sample size and the maximum-likelihood estimate of recombination value, the conventional rule for significant linkage (maximum lod score exceeds a given linkage threshold) can be resolved for the sample size. For each sub-population used for linkage analysis [susceptible (= recessive) individuals, resistant (= dominant) individuals, complete F₂] this approach gives a lower bound for the necessary number of individuals required for the detection of significant two-point linkage by the lod-score method.     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. I. Prior knowledge

Summary Prior information on gene effects at individual quantitative trait loci (QTL) and on recombination rates between marker loci and QTL is derived. The prior distribution of QTL gene effects is assumed to be exponential with major effects less likely than minor ones. The prior probability of linkage between a marker and another single locus is a function of the number and length of chromosomes, and of the map function relating recombination rate to genetic distance among loci. The prior probability of linkage between a marker locus and a quantitative trait depends additionally on the number of detectable QTL, which may be determined from total additive genetic variance and minimum detectable QTL effect. The use of this prior information should improve linkage tests and estimates of QTL effects.     

Trait-based analyses for the detection of linkage between marker loci and quantitative trait loci in crosses between inbred lines

Summary Methods are presented for determining linkage between a marker locus and a nearby locus affecting a quantitative trait (quantitative trait locus=QTL), based on changes in the marker allele frequencies in selection lines derived from the F-2 of a cross between inbred lines, or in the high and low phenotypic classes of an F-2 or BC population. The power of such trait-based (TB) analyses was evaluated and compared with that of methods for determining linkage based on the mean quantitative trait value of marker genotypes in F-2 or BC populations [marker-based (MB) analyses]. TB analyses can be utilized for marker-QTL linkage determination in situations where the MB analysis is not applicable, including analysis of polygenic resistance traits where only a part of the population survives exposure to the Stressor and analysis of marker-allele frequency changes in selection lines. TB analyses may be a useful alternative to MB analyses when interest is centered on a single quantitative trait only and costs of scoring for markers are high compared with costs of raising and obtaining quantitative trait information on F-2 or BC individuals. In this case, a TB analysis will enable equivalent power to be obtained with fewer individuals scored for the marker, but more individuals scored for the quantitative trait. MB analyses remain the method of choice when more than one quantitative trait is to be analyzed in a given population.Contribution from the ARO, Bet Dagan, Israel. No. 1698-E, 1986 series     

Power analysis to determine sample size for monitoring vegetation change in salt marsh habitats

Numerous initiatives are underway throughout New England and elsewhere to quantify salt marsh vegetation change, mostly in response to habitat restoration, sea level rise, and nutrient enrichment. To detect temporal changes in vegetation at a marsh or to compare vegetation among different marshes with a degree of statistical certainty an adequate sample size is required. Based on sampling 1 m² vegetation plots from 11 New England salt marsh data sets, we conducted a power analysis to determine the minimum number of samples that were necessary to detect change between vegetation communities. Statistical power was determined for sample sizes of 5, 10, 15, and 20 vegetation plots at an alpha level of 0.05. Detection of subtle differences between vegetation data sets (e.g., comparing vegetation in the same marsh over two consecutive years) can be accomplished using a sample size of 20 plots with a reasonable probability of detecting a difference when one truly exists. With a lower sample size, and thus lower power, there is an increased probability of not detecting a difference when one exists (e.g., Type II error). However, if investigators expect to detect major changes in vegetation (e.g., such as those between an un-impacted and a highly impacted marsh) then a sample size of 5, 10, or 15 plots may be appropriate while still maintaining adequate power. Due to the relative ease of collecting vegetation data, we suggest a minimum sample size of 20 randomly located 1 m² plots when developing monitoring designs to detect vegetation community change of salt marshes. The sample size of 20 plots per New England salt marsh is appropriate regardless of marsh size or permanency (permanent or non-permanent) of the plots.     

Expression genetics and haplotype analysis reveal cis regulation of serine carboxypeptidase I (Cxp1), a candidate gene for malting quality in barley (Hordeum vulgare L.)

Using a cDNA array-based functional genomics approach in barley, several candidate genes for malting quality including serine carboxypeptidase I (Cxp1) were previously identified (Potokina et al. in Mol Breed 14:153, 2004). The gene was mapped as a single nucleotide polymorphism (SNP) marker on chromosome 3H using the Steptoe (feeding grade) × Morex (malting grade) mapping population. Subsequently, the relative level of Cxp1 expression was determined by real-time RT-PCR for each of the 134 progeny lines and mapped as a quantitative trait. Only one quantitative trait locus (QTL) could be identified that significantly influenced the level of the Cxp1 expression. The expressed QTL maps to the same region on chromosome 3H as does the structural gene and corresponds to a QTL for “diastatic power,” one among several traits measured to assess malting quality. An analysis of 90 barley cultivars sampled from a worldwide collection revealed six SNPs at the Cxp1 locus, three of which display complete linkage disequilibrium and define two haplotypes. The Cxp1 expression level in a set of barley accessions showing haplotype I was significantly higher than that of accessions displaying haplotype II. The data provide evidence that (1) the expression of Cxp1 is regulated in cis and that (2) the level of diastatic power in the barley seed is influenced by the level of Cxp1 expression. Supplementary material is available in the online version of this article at     

利用RFLP进行数量基因定位及效应分析的原理与方法

本文介绍了利用RFLP分子标记进行数量基因定位及效应分析的原理与方法,并讨论了其应用存在的问题．     

基于染色体片段导入系发掘抗玉米丝黑穗病主效QTL

选用抗玉米丝黑穗病自交系Mo17和SH15为供体,与受体感病自交系黄早四和昌7-2构建回交群体(BC3F1BC4F2),通过田间人工接种玉米丝黑穗病原菌鉴定抗病性表现,评价群体抗病性。研究结果显示黄早四×(黄早四×Mo17)BC4F2群体发病率明显高于BC3F1群体;两个BC4F2黄早四×(黄早四×Mo17)和昌7-2×(昌7-2×SH15)群体的发病率差异较大。采用SSR标记分析抗病株的供体染色体导入片段,发现随着回交次数的增多,导入片段数量减少,但不同回交群体中供体导入片段数目明显不同。通过连锁不平衡分析,在染色体2.09和3.04区段发掘和验证2个抗玉米丝黑穗病主效QTL,连锁标记分别为umc2077和phio53或bnlg1965。本文研究结果为抗丝黑穗病基因精细定位和分子聚合育种提供了信息和材料。     

Bayesian analysis of linkage between genetic markers and quantitative trait loci. II. Combining prior knowledge with experimental evidence

Summary A Bayesian method was developed for identifying genetic markers linked to quantitative trait loci (QTL) by analyzing data from daughter or granddaughter designs and single markers or marker pairs. Traditional methods may yield unrealistic results because linkage tests depend on number of markers and QTL gene effects associated with selected markers are overestimated. The Bayesian or posterior probability of linkage combines information from a daughter or granddaughter design with the prior probability of linkage between a marker locus and a QTL. If the posterior probability exceeds a certain quantity, linkage is declared. Upon linkage acceptance, Bayesian estimates of marker-QTL recombination rate and QTL gene effects and frequencies are obtained. The Bayesian estimates of QTL gene effects account for different amounts of information by shrinking information from data toward the mean or mode of a prior exponential distribution of gene effects. Computation of the Bayesian analysis is feasible. Exact results are given for biallelic QTL, and extensions to multiallelic QTL are suggested.     

Linkage and association studies of QTL for nuclear families by mixed models

The transmission disequilibrium test (TDT) has been utilized to test the linkage and association between a genetic trait locus and a marker. Spielman et al. (1993) introduced TDT to test linkage between a qualitative trait and a marker in the presence of association. In the presence of linkage, TDT can be applied to test for association for fine mapping (Martin et al., 1997; Spielman and Ewens, 1996). In recent years, extensive research has been carried out on the TDT between a quantitative trait and a marker locus (Allison, 1997; Fan et al., 2002; George et al., 1999; Rabinowitz, 1997; Xiong et al., 1998; Zhu and Elston, 2000, 2001). The original TDT for both qualitative and quantitative traits requires unrelated offspring of heterozygous parents for analysis, and much research has been carried out to extend it to fit for different settings. For nuclear families with multiple offspring, one approach is to treat each child independently for analysis. Obviously, this may not be a valid method since offspring of one family are related to each other. Another approach is to select one offspring randomly from each family for analysis. However, with this method much information may be lost. Martin et al. (1997, 2000) constructed useful statistical tests to analyse the data for qualitative traits. In this paper, we propose to use mixed models to analyse sample data of nuclear families with multiple offspring for quantitative traits according to the models in Amos (1994). The method uses data of all offspring by taking into account their trait mean and variance-covariance structures, which contain all the effects of major gene locus, polygenic loci and environment. A test statistic based on mixed models is shown to be more powerful than the test statistic proposed by George et al. (1999) under moderate disequilibrium for nuclear families. Moreover, it has higher power than the TDT statistic which is constructed by randomly choosing a single offspring from each nuclear family.     

Sample Size Calculation for Intraclass Correlation in the Presence of Random Loss of Sampled Patients

When a trial involves an invasive laboratory test procedure or requires patients to make a commitment to follow a restrictive test schedule, we can often lose a great proportion of our sampled patients due to refusal of participation into our study. Therefore, incorporating the possible loss of patients into sample size calculation is certainly important in the planning stage of a study. In this paper, we have generalized the sample size calculation procedure for intraclass correlation by accounting for the random loss of patients in the beginning of a trial. We have demonstrated that the simple ad hoc procedure, that raises the estimated sample size in the absence of loss of patients by the factor 1/p_o, where p_o is the retention probability for a randomly selected patient, is adequate when p_o is large (=0.80). When p_o is small (i.e., a high refusal rate), however, use of this simple ad hoc procedure tends to underestimate the required sample size. Furthermore, we have found that if the individual retention probability varied substantially among patients, then the magnitude of the above underestimation could even be critical and therefore, the application of the simple direct adjustment procedure in this situation should be avoided.     

Sequential sampling in determining linkage between marker loci and quantitative trait loci

Summary As compared to classical, fixed sample size techniques, simulation studies showed that a proposed sequential sampling procedure can provide a substantial decrease (up to 50%, in some cases) in the mean sample size required for the detection of linkage between marker loci and quantitative trait loci. Sequential sampling with truncation set at the required sample size for the non-sequential test, produced a modest further decrease in mean sample size, accompanied by a modest increase in error probabilities. Sequential sampling with observations taken in groups produced a noticeable increase in mean sample size, with a considerable decrease in error probabilities, as compared to straightforward sequential sampling. It is concluded that sequential sampling has a particularly useful application to experiments aimed at investigating the genetics of differences between lines or strains that differ in some single outstanding trait.     

The Design and Use of Variance Component Models in the Analysis of Human Quantitative Pedigree Data

The use of variance components and multivariate linear models in genetics applications has a long history that dates back to (at least) Fisher's seminal 1918 paper “The correlation between relatives on the supposition of Mendelian inheritance” [Phil. Trans. 52: 399–433]. Although extensions and elaborations of Fisher's insights have been offered in recent times, relatively few studies exist which examine the theoretical and operational properties variance component models possess in complicated genetic analysis settings. In this paper variance component models, as well as some of their properties (e.g., power, efficiency, and sample size considerations) are discussed in the context of each of the following genetic analysis settings: 1. the detection of general polygenic additive and dominance effects; 2. the detection of genetic effects in the presence of environmental effects (and vice versa); 3. the detection of pleiotropic gene action; 4. aspects of the detection of genotype by environment interaction; and 5. sequential tests for general hypotheses framed in the context of settings 1 through 4. Exposition of the proposed methods and results are facilitated through a special emphasis placed on pedigree covariance structure modeling.     

Quantitative trait loci that harbor genes regulating muscle size in (MRL/MPJ x SJL/J) F(2) mice

The genetic mechanisms that determine muscle size have not been elucidated, even though it is a key musculoskeletal parameter that reflects muscle strength. In this study, we performed a high-density genome-wide scan using 633 (MRL/MPJ × SJL/J) F₂ intercross 7-week-old mice to identify quantitative trait loci (QTL) involved in the determination of muscle size. Significant QTL were identified for muscle size and body length. Muscle size (adjusted by body length) QTL were identified on chromosomes 7, 9, 11, 14 (two QTL) and 17, which together explained 19.2% of phenotypic variance in F₂ mice, while body length QTL were located on chromosome 2 (two QTL), 9, 11 and 17 which accounted for 28.3% of phenotypic variance in F₂ mice. Three significant epistatic interactions between different QTL positions from muscle size and body length were identified (P <0.01) on chromosomes 2, 9, 14 and 17, which explained 16.1% of the variance in F₂ mice. Electronic Publication     

BC群体不同连锁模式分子区间标记QTL作图相关方法的精确度分析

该文分析了BC群体不同连锁模式分子区间标记QTL作图相关方法的精确度,提出了相应参数的适用范匿,连锁顺序的检测方法,分析步骤,为QTL作图提供了理论基础。