Genotype by environment interaction for 450-day weight of Nelore cattle analyzed by reaction norm models

Genotype by environment interactions (GEI) have attracted increasing attention in tropical breeding programs because of the variety of production systems involved. In this work, we assessed GEI in 450-day adjusted weight (W450) Nelore cattle from 366 Brazilian herds by comparing traditional univariate single-environment model analysis (UM) and random regression first order reaction norm models for six environmental variables: standard deviations of herd-year (RRMw) and herd-year-season-management (RRMw-m) groups for mean W450, standard deviations of herd-year (RRMg) and herd-year-season-management (RRMg-m) groups adjusted for 365-450 days weight gain (G450) averages, and two iterative algorithms using herd-year-season-management group solution estimates from a first RRMw-m and RRMg-m analysis (RRMITw-m and RRMITg-m, respectively). The RRM results showed similar tendencies in the variance components and heritability estimates along environmental gradient. Some of the variation among RRM estimates may have been related to the precision of the predictor and to correlations between environmental variables and the likely components of the weight trait. GEI, which was assessed by estimating the genetic correlation surfaces, had values < 0.5 between extreme environments in all models. Regression analyses showed that the correlation between the expected progeny differences for UM and the corresponding differences estimated by RRM was higher in intermediate and favorable environments than in unfavorable environments (p < 0.0001).     

Detection and parameter estimation for quantitative trait loci using regression models and multiple markers

A strategy of multi-step minimal conditional regression analysis has been developed to determine the existence of statistical testing and parameter estimation for a quantitative trait locus (QTL) that are unaffected by linked QTLs. The estimation of marker-QTL recombination frequency needs to consider only three cases: 1) the chromosome has only one QTL, 2) one side of the target QTL has one or more QTLs, and 3) either side of the target QTL has one or more QTLs. Analytical formula was derived to estimate marker-QTL recombination frequency for each of the three cases. The formula involves two flanking markers for case 1), two flanking markers plus a conditional marker for case 2), and two flanking markers plus two conditional markers for case 3). Each QTL variance and effect, and the total QTL variance were also estimated using analytical formulae. Simulation data show that the formulae for estimating marker-QTL recombination frequency could be a useful statistical tool for fine QTL mapping. With 1 000 observations, a QTL could be mapped to a narrow chromosome region of 1.5 cM if no linked QTL is present, and to a 2.8 cM chromosome region if either side of the target QTL has at least one linked QTL.     

Genotype by environment interaction for growth of Eucalyptus globulus in Australia

This study assessed the genotype by environment (G × E) interaction for diameter growth in 15 Eucalyptus globulus progeny trials in Australia. Single-site analyses revealed significant subrace and family-within-subrace variance in all trials. Across-site subrace () and family () correlations were estimated by linear mixed model analyses of pairs of trials. Using a factor analytic structure for subrace and family random terms in a multi-environment mixed model analysis, best linear unbiased predictions of subrace effects were obtained for each trial. These were then averaged for each of four states (Victoria, Tasmania, South Australia and Western Australia) and across all sites. Statistically significant G × E interaction was detected, and weighted means across states for and were 0.73 and 0.76, respectively. Nevertheless, the three subraces from the Otway Ranges were both fast growing and relatively stable in their ranks over all sites. We evaluated the sensitivity of subraces to changing environmental conditions, on the basis of random coefficient models regressing subrace performance on selected trial climatic variables. The results suggested differential susceptibility of subraces to water, light and (to a less extent) temperature stresses during summer. Moreover, using multivariate techniques to visualize and interpret the across-site correlation structure for subrace effects, we could identify site clusters of reduced G × E interaction related to soil water availability and evaporative demand during summer. A revised site-type classification using these factors should allow a better capture of genetic gains from breeding and deployment.     

Factor regression for interpreting genotype-environment interaction in bread-wheat trials

Summary The French INRA wheat (Triticum aestivum L. em Thell.) breeding program is based on multilocation trials to produce high-yielding, adapted lines for a wide range of environments. Differential genotypic responses to variable environment conditions limit the accuracy of yield estimations. Factor regression was used to partition the genotype-environment (GE) interaction into four biologically interpretable terms. Yield data were analyzed from 34 wheat genotypes grown in four environments using 12 auxiliary agronomic traits as genotypic and environmental covariates. Most of the GE interaction (91%) was explained by the combination of only three traits: 1,000-kernel weight, lodging susceptibility and spike length. These traits are easily measured in breeding programs, therefore factor regression model can provide a convenient and useful prediction method of yield.     

Detection and modelling of time-dependent QTL in animal populations

A longitudinal approach is proposed to map QTL affecting function-valued traits and to estimate their effect over time. The method is based on fitting mixed random regression models. The QTL allelic effects are modelled with random coefficient parametric curves and using a gametic relationship matrix. A simulation study was conducted in order to assess the ability of the approach to fit different patterns of QTL over time. It was found that this longitudinal approach was able to adequately fit the simulated variance functions and considerably improved the power of detection of time-varying QTL effects compared to the traditional univariate model. This was confirmed by an analysis of protein yield data in dairy cattle, where the model was able to detect QTL with high effect either at the beginning or the end of the lactation, that were not detected with a simple 305 day model.     

Genotype by environment interaction for adult body weights of shrimp Penaeus vannamei when grown at low and high densitie

Shrimp is one of few marine species cultured worldwide for which several selective breeding programs are being conducted. One environmental factor that can affect the response to selection in breeding programs is the density at which the shrimp are cultured (low-medium-high). Phenotypic plasticity in the growth response to different densities might be accompanied by a significant genotype by environment interaction, evidenced by a change in heritabilities between environments and by a genetic correlation less than one for a unique trait between environments. Our goal was to understand whether different growth densities affect estimates of those genetic parameters for adult body weight (BW) in the Pacific white shrimp (Penaeus vannamei). BW heritabilities were significantly different between environments, with the largest at high density. These differences resulted from both an increased additive genetic variance and a decreased environmental variance when grown at high density. The genetic correlation between BWs at the two environmental conditions was significantly less than one. Whereas these results might be suggestive for carrying out shrimp selective breeding for BW under high density conditions, further understanding of genetic correlations between growth and reproductive traits within a given environment is necessary, as there are indications of reduced reproductive fitness for shrimp grown at high densities.     

Random regression analyses using B-splines to model growth of Australian Angus cattle

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error.     

Combining genotype, environment and attribute variables in regression models for predicting the cell-means of multi-environment cultivar trials

 The main objectives of this study were: (1) to develop models which combine variables of genotype, environment and attribute in regression models (GEAR) for increasing the accuracy of predicted cell-means of the genotype×environment two-way table, and (2) to compare GEAR models with the additive main effects and multiplicative interaction (AMMI) model. GEAR models were developed by regressing the observed values on principal components of genotypes (PCG) and environments (PCE). Genetic and environmental attributes were also added to the GEAR models. GEAR and AMMI models were applied to multi-environment trials of triticale (trial 1), maize (trial 2) and broad beans (trial 3). The random data-splitting and cross-validation procedure was used and the root mean square-predicted difference (RMSPD) was computed to validate each model. GEAR models increased the accuracy of predicted cell-means. Attribute variables, such as soil pH, rainfall, altitude and class of genotype, did not improve the best GEAR model of trial 1, but they increased the predictive value of other models. Two iterations of the computer program further refined the best GEAR model. Based on the RMSPD criterion, GEAR models were as good as, or better than, some AMMI truncated models for predicting cell-means. The approximate accuracy gain factors (GF) of the best GEAR model over the raw data were 2.08, 3.02 and 2.22, for trials 1, 2 and 3, respectively. The GF of the best AMMI model were 1.74, 2.28 and 2.32 for trials 1, 2 and 3, respectively. The analysis of variance of the predicted cell means showed that the genotype×environment interaction (GEI) variance was reduced by about 20% in trial 1 and 81% in trial 2. A bias associated with the predicted cell reduced the GEI variability. Advantages of using GEAR models in muti-environment cultivar trials are that they: (1) increase the precision of cell-mean estimates and (2) reduce the GEI variance and increase trait heritability. Received: 15 August 1997 / Accepted: 28 October 1997     

Power of QTL detection by either fixed or random models in half-sib designs

The aim of this study was to compare the variance component approach for QTL linkage mapping in half-sib designs to the simple regression method. Empirical power was determined by Monte Carlo simulation in granddaughter designs. The factors studied (base values in parentheses) included the number of sires (5) and sons per sire (80), ratio of QTL variance to total genetic variance (λ = 0.1), marker spacing (10 cM), and QTL allele frequency (0.5). A single bi-allelic QTL and six equally spaced markers with six alleles each were simulated. Empirical power using the regression method was 0.80, 0.92 and 0.98 for 5, 10, and 20 sires, respectively, versus 0.88, 0.98 and 0.99 using the variance component method. Power was 0.74, 0.80, 0.93, and 0.95 using regression versus 0.77, 0.88, 0.94, and 0.97 using the variance component method for QTL variance ratios (λ) of 0.05, 0.1, 0.2, and 0.3, respectively. Power was 0.79, 0.85, 0.80 and 0.87 using regression versus 0.80, 0.86, 0.88, and 0.85 using the variance component method for QTL allele frequencies of 0.1, 0.3, 0.5, and 0.8, respectively. The log₁₀ of type I error profiles were quite flat at close marker spacing (1 cM), confirming the inability to fine-map QTL by linkage analysis in half-sib designs. The variance component method showed slightly more potential than the regression method in QTL mapping.     

Genetic parameters for test day milk yields of first lactation Holstein cows by random regression models

Covariance components for test day milk yield using 263 390 first lactation records of 32 448 Holstein cows were estimated using random regression animal models by restricted maximum likelihood. Three functions were used to adjust the lactation curve: the five-parameter logarithmic Ali and Schaeffer function (AS), the three-parameter exponential Wilmink function in its standard form (W) and in a modified form (W*), by reducing the range of covariate, and the combination of Legendre polynomial and W (LEG+W). Heterogeneous residual variance (RV) for different classes (4 and 29) of days in milk was considered in adjusting the functions. Estimates of RV were quite similar, rating from 4.15 to 5.29 kg². Heritability estimates for AS (0.29 to 0.42), LEG+W (0.28 to 0.42) and W* (0.33 to 0.40) were similar, but heritability estimates used W (0.25 to 0.65) were highest than those estimated by the other functions, particularly at the end of lactation. Genetic correlations between milk yield on consecutive test days were close to unity, but decreased as the interval between test days increased. The AS function with homogeneous RV model had the best fit among those evaluated.     

根据基因表达谱筛选间接互作蛋白质进行蛋白质功能预测

利用基因表达谱数据,通过计算互作蛋白质的表达相关系数,来筛选、优化蛋白质互作网络。结果显示,利用经过筛选的互作数据,根据邻居计数法和卡方法进行功能预测的预测效果明显提高,距离待测蛋白质较远的邻居也包含着与待测蛋白质功能一致的信息。     

Crop diagnosis and probe genotypes for interpreting genotype environment interaction in winter wheat trials

Genotype*environment interaction has been analyzed with 12 genotypes and four probe genotypes in French wheat trials. An integrated approach was developed which combined crop diagnosis with the analysis of interaction by factorial regression. Crop diagnosis was helpful to characterize the environments and to select environmental variables. Such an approach succeeded in providing an agronomic explanation of genotype*environment interaction and in defining the responses or parameters for each genotype and each environment. Earliness at heading, susceptibility to powdery mildew and susceptibility to lodging were the three major genotypic covariates. Interaction could also be related to environment features, measured indirectly by the behavior of the four probe genotypes during the formation of yield, what we called the outputs of a simplified crop diagnosis, or described directly by indicators of yield-limiting factors. Two important crop diagnosis covariates were analyzed in order to characterize interaction during the formation of yield: the reduction in kernel number, which described the time-period until flowering, and the reduction in thousand kernel weight, which corresponded to the period after flowering. These variates were estimated for each probe genotype and allowed us to compare the behavior of the 12 genotypes to that of the probe genotypes. Both periods of the formation of yield contributed to the interaction, and ’Camp-Rémy’ was the probe of particular interest for the comparisons. When true environmental variates were used, factorial regression revealed that water deficits during the formation of grain number and level of nitrogen were predominant. Such an integrated approach could be exploited when varieties are tested in a network where numerous and diverse yield-limiting factors may occur. Received: 3 August 1998 / Accepted: 16 March 1999     

Genotype x environment interaction of crossover type: detecting its presence and estimating the crossover point

Genotype-environment interaction (GEI) introduces inconsistency in the relative rating of genotypes across environments and plays a key role in formulating strategies for crop improvement. GEI can be either qualitative (i.e., crossover type) or only quantitative (i.e., non-crossover type). Since the presence of crossover-type interaction has a strong implication for breeding for specific adaptation, it is important to assess the frequency of crossover interactions. This paper presents a test for detecting the presence of crossover-type interaction using the response-environment relationship and enumerates the frequency of crossovers and estimation of the crossover point (CP) on the environment axis, which serves as a cut-off point for the two environments groups where different/specific selections can be made. Sixty-four barley lines with various selection histories were grown in northern Syria and Lebanon giving a total of 21 environments (location-year combinations). Linear regression of the genotypic response on the environmental index represented a satisfactory model, and heterogeneity among regressions was significant. At a 5% level of significance, 38% and 19% of the pairs showed crossover interactions when the error variances were considered heterogeneous and homogeneous, respectively, implying that an appreciable number of crossovers took place in the case of barley lines responding to their environments. The CP of 1.64 t/ha, obtained as the CP of regression lines between the genotype numbers 19 and 31, provided maximum genotype x environment-group interaction. Across all environments, genotype nos. 59 and 12 stood first and second for high yield, respectively. The changes in the ranks of genotypes under the groups of environments can be used for selecting specifically adapted genotypes. Received: 25 January 1999 / Accepted: 16 March 1999     

基于随机森林的胃癌微阵列数据基因通路分析

将研究重点从单个基因转移到基因信号通路,结合随机森林与信号通路分析了一组胃癌微阵列数据。通过研究基因在通路中的情况以及通路中的基因对胃癌肠型、弥漫型和正常组织样本的分类能力,扩展了随机森林在生物学中的应用,为胃癌的研究提供了新的思路。     

Determining environmental covariates which explain genotype environment interaction in winter wheat through probe genotypes and biadditive factorial regression

Genotype-environment interaction has been analyzed in a winter-wheat breeding network using bi-additive factorial regression models. This family of models generalizes both factorial regression and biadditive (or AMMI) models; it fits especially well when abundant external information is available on genotypes and/or environments. Our approach, focused on environmental characterization, was performed with two kinds of covariates: (1) deviations of yield components measured on four probe genotypes and (2) usual indicators of yield-limiting factors. The first step was based on the analysis of a crop diagnosis on four probe genotypes. Difference of kernel number to a threshold number (DKN) and reduction of thousand-kernel weight from a potential value (RTKW) were used to characterize the grain-number formation and the grain-filling periods, respectively. Grain yield was analyzed according to a biadditive factorial regression model using eight environmental covariates (DKN and RTKW measured on each of four probe genotypes). In the second step, the usual indicators of yield-limiting factors were too numerous for the analysis of grain yield. Thus a selection of a subset of environmental covariates was performed on the analysis of DKN and RTKW for the four probe genotypes. Biadditive factorial regression models involved environmental covariates related to each deviation and included environmental main effect, sum of water deficits, an indicator of nitrogen stress, sum of daily radiation, high temperature, pressure of powdery mildew and lodging. The correlations of each environmental covariate to the synthetic variates helped to discard those poorly involved in interaction (with | correlation | <0.3). The grain yield of 12 genotypes was interpreted with the retained covariates using biadditive factorial regression. The models explained about 75% of the interaction sums of squares. In addition, the biadditive factorial regression biplot gave relevant information about the interaction of the genotypes (interaction pattern and sensitivities to environmental covariates) with respect to the environmental covariates and proved to be interesting for such an approach. Received: 8 March 1999 / Accepted: 29 July 1999     

利用双单倍体群体剖析水稻产量及其相关性状的遗传基础

主效QTL、上位性效应和它们与环境的互作(QE)都是数量性状的重要遗传因素。利用籼粳交珍汕97／武育粳2号F1植株上的花药进行组织培养得到的190个双单倍体群体和179个微卫星标记,通过两年两重复田间试验,采用混合线性模型方法分析了9个控制水稻产量及其相关性状的遗传效应,得到57个主效QTL,41对上位性互作,8对QTL与环境的互作和7对上位性效应与环境的互作。单个主效QTL解释这些性状1．3％～25．8％的表型方差。各性状QTL的累积表型贡献率达11．5％～66．8％。大多数性状之间具有显著的表型相关性,相关性较高的性状之间常具有较多共同或紧密连锁的QTL。结果表明,基因的多效性或紧密连锁可能是性状相关的重要遗传基础。