A method of analyzing cultivar x location x year experiments: a new stability parameter

Summary Assessment of cultivar performance in a cultivar x location x year experiment is often difficult because of the presence of a location x year interaction. Our objective is to demonstrate a method on separation of environment effects (location x year) into predictable and unpredictabel components. The analysis consists of two parts: (1) a regression analysis based on location effects (averaged over years), assuming that the location means represent predictable environmental variation; and (2) the estimation of stability (denoted type 4) based on the years within location mean squares, assuming that years within location represent unpredictable environmental variation. From the regression analysis in (1), a breeder can determine the optimum range of locations in which a cultivar is well suited, and from (2) he can choose the most stable cultivars. The advantage of type 4 stability is that it is independent of the other cultivars included in the test and of the regression coefficient estimated for predictable variation. Three sets of published data are used to illustrate the analysis. Type 4 stability is compared with type 3 stability (deviation mean square from regression on environmental index) for genetic consistency. The analyses suggest that type 4 stability is consistent and is therefore a potential genetic parameter, but type 3 stability is not.Contribution No. I-806 from Engineering and Statistical Research Centre, Research Branch, Agriculture Canada, Ottawa, K1A OC6, Canada     

Regression analysis of yield stability is strongly affected by companion test varieties and locations — examples from a study of Nordic barley lines

The suitability of regression analysis for studying the phenotypic stability of grain yield was investigated using a collection of 220 Nordic barley lines. Linear regression explained 26–52% of the genotype x environment (GE) interactions in different groupings of the material. The regression coefficient, b _i , measures the yield response of the i-th genotype to improved environmental conditions. Deviations from regression, S _di ² , have been used to estimate Tai's stability parameter, _i , which is a measure of the phenotypic yield stability in the agronomic sense. Repeatability of b _i , _i , and grain yield was studied by means of correlations between estimates obtained in each experimental year. Yield had the highest repeatability, with correlations between years ranging from 0.57 to 0.85. In this study, regression coefficients and _i -values were not repeatable, i.e. genotypes reacted differentially to the yearly climatic variations. Six-rowed (6r) barleys had higher responsiveness, but lower mean yields, than two-rowed (2r) barleys. This is partly due to the history of selection of 6r-barleys, which mainly originate from regions with low potential yield levels, i.e. Finland and Norway. In general, responsiveness and stability were not correlated with yield. The highest-yielding lines had b _i 1. The response pattern of the different types of barleys used in this study show that responsiveness can be changed by recombination.     

Interrelationships among stabilities of important agronomic traits in sugarcane

Summary The stability-variance statistic, s _i ² , measures the contribution of the i^th genotype to genotype x environment interaction. In addition to the knowledge of cultivar stability for an agronomic trait, information on whether stability of one trait can be used to predict stability of another should be useful to breeders. Three separate groups of data, respectively involving CP 79 series, CP 80 series, and CP 81 series experimental clones of sugarcane (Saccharum spp.) were used in this study. Rank-correlation coefficients (r_s) between ranks of genotypes for s _i ² 's for paired traits indicated in both plant-cane and ratoon crops that stability of tons per hectare of sugar can be predicted from the stability of tons per hectare of cane (THC) and also, to a lesser extent, from the stability of stalk number. The stability of THC also can be reasonably well predicted from the stability of stalk number. Brix stability may give some indication of the stabilities for percentage sucrose and sugar concentration (SC). The s _i ² 's for percentage sucrose and SC were almost identical in the CP 79 and CP 81 series (r_s varied from 0.93, P<0.01, in plant-cane crop for CP 79 series to 0.98, P<0.01, in plant-cane crop for CP 81 series). Whether correlations were based on s _i ² 's estimated across locations within crops or across crops, the magnitude of r_s was about the same. Means of various traits were not correlated with their respective s _i ² 's (for CP 81 series), indicating that identification and selection of high-yielding sugarcane genotypes with a relatively high degree of stability of performance across test environments should be possible.Cooperative investigation of the Univ. of Florida, Everglades Research and Education Center, Belle Glade, FL, USA; Louisiana Agricultural Experiment Station, LSU Agricultural Center, Baton Rouge, LA, USA; and Sugarcane Field Station, Canal Point, FL, USA. The field work reported in this study was done when the senior author was affiliated with the University of Florida. Florida Agric. Exp. Stns. Journal Series No. 5933     

Selection of test locations for regional trials of barley

Summary Three sets of regional six-row barley (Hordeum vulgare L.) trial data, representing cultivar x location x year, were grouped for locations based on the similarity of genotype x environment (GE) interaction. Locations were selected from each group (cluster) so that the structure of the GE interaction generated by the subsets of the locations would be approximately similar to that of the whole set (all locations). The purpose of this paper is to determine the number of locations where the GE interaction structure generated by these selected locations would be fairly consistent over years. Two statistics were used to measure the success of the selected locations: (1) the ratio of GE mean square (MS) associated with the selected location set relative to that associated with the best set (which gives the highest GE interaction MS) and (2) the rank correlation between the cultivar means averaged over the selected locations and those based on the entire data set. The results show that, for eastern Canada, 10–13 locations based on the cluster method can achieve a fairly consistent GE interaction structure over years.Contribution no. R-078 from Research Program Service, Agriculture Canada, and contribution no. 1352 from Plant Research Centre, Central Experimental Farm     

Choice of selection environment for improving crop yields in saline areas

Spatial variability in salt-affected fields is normally very high. Thus, most salinity affected lands are actually comprised of many micro-environments, ranging from low to high salinity in the same field. The evidence on testing genotypes across a broad range of salinity levels shows that the genotype-by-salinity level interaction is commonly large. Thus, breeding for saline areas can be compared to what has been known as breeding for wide adaptation. The target environments both for breeding for saline soils or for wide adaptation are actually a population of many possible environments, for which there exists a significant component of genotype-by-environment(G x E) interaction. Thus it is possible to study the merit of potential strategies for breeding for salinity tolerance using the tools that have been developed for the study of breeding for wide adaptation. The evidence from selection and breeding experiments for wide adaptation seems to favour testing on a representative subset of environments, including stress and non-stress locations; but the choice of these locations is complicated by the multidimensional nature of G x E. However, in the case of salt stress, the crop-yield response functions to salinity are well known. This paper presents an attempt to systematise the choice of the optimum environment(s) to select for improved yield under saline soil conditions, based on the three-piece linear equation presented by Maas and Hoffman (1977) and the theory of direct and indirect responses to selection. It is proposed that three saline levels should be enough to make a valid estimation of the suitability of a number of selection strategies. A worked example with data from a set of grain sorghum inbred lines tested on ten saline levels shows that the same selection strategies would be chosen using the information from the ten saline levels as that obtained using the two extremes and one intermediate level.     

A parsimonious statistical design and breeding procedure for evaluating and selecting desirable characteristics over environments

The concept of stability as described in the literature does not meet all of the desirable criteria required by growers of cultivars. Various types of possible responses are discussed, and these are divided into those desirable from a grower's viewpoint and those not. Measures of stability appearing in the literature are based on variances, linear regression slopes, and/or deviations from regression. The most desirable response type would be denoted as unstable by current concepts of stability. It is shown how to simulate environments that exceed the ranges found in practice. A statistical design is described which is the height of parsimony and has the advantage that the conditions varied are known. The experimental results can then be interpreted in light of the known conditions. The design is optimally cost effective in terms of funds, material, and personnel. A breeding procedure is presented for such characteristics as desired response, stability under current definitions, tolerance (to pests, cold, drought, etc.), protein, quality, fiber, etc.Technical Report Series No. Bu-960-MA of the Biometrics Unit, Cornell University, Ithaca, N.Y.Liberty Hyde Bailey Professor Emeritus, Biometrics Unit, Department of Plant Breeding and Biometry, Cornell University, Ithaca, NY; Assistant Professor of Vegetable Crops, IFAS, University of Florida, Everglades Research Center, Belle Glade, Fla.     

Stability of baking quality in bread wheat using several statistical parameters

Stability of quality in bread wheat was investigated for the first time with the alveograph test, a rheological test providing four technological traits. Assessment of stability was reliable because a large set of varieties (ten) were grown over a wide range of environments (14). Varieties and environments were representative of French agricultural practices. A procedure to evaluate stability of quality is proposed. Stability was measured by ecovalence, which was then modelled to determine response to environments for each genotype. A joint regression model was compared to a biadditive model with two multiplicative terms. The regression model explained a very much smaller part of ecovalence than the biadditive model. The latter made it possible to pool cultivars for genotypexenvironment interactions and to characterize varieties for their responsiveness to environments. Two check varieties for stability and instability were identified.     

Relationships between genotype x environment interactions and rank orders for a set of genotypes tested in different environments

Multilocation trials in plant breeding lead to cross-classified data sets with rows=genotypes and columns=environments, where the breeder is particularly interested in the rank orders of the genotypes in the different environments. Non-identical rank orders are the result of genotype x environment interactions. Not every interaction, however, causes rank changes among the genotypes (rank-interaction). From a breeder's point of view, interaction is tolerable only as long as it does not affect the rank orders. Therefore, the question arises of under which circumstances does interaction become rank-interaction. This paper contributes to our understanding of this topic. In our study we emphasized the detection of relationships between the similarity of the rank orders (measured by Kendall's coefficient of concordance W) and the functions of the diverse variance components (genotypes, environments, interaction, error). On the basis of extensive data sets on different agricultural crops (faba bean, fodder beet, sugar beet, oats, winter rape) obtained from registration trials (1985–1989) carried out in the Federal Republic of Germany, we obtained the following as main result: W ₂ ^g /( ₂ ^g + ₂ ^v ) where ₂ ^g =genotypic variance and ₂ ^v = ₂ ^ge + ₂ ^o /L with ₂ ^ge =interaction variance, ₂ ^o =error variance and L=number of replications.     

Implication of correlations among some common stability statistics — a Monte Carlo simulations

Stability analysis of multilocation trials is often based on a mixed two-way model. Two stability measures in frequent use are the environmental variance (S_i²)and the ecovalence (W_i). Under the two-way model the rank orders of the expected values of these two statistics are identical for a given set of genotypes. By contrast, empirical rank correlations among these measures are consistently low. This suggests that the two-way mixed model may not be appropriate for describing real data. To check this hypothesis, a Monte Carlo simulation was conducted. It revealed that the low empirical rank correlation amongS_i²and W_i is most likely due to sampling errors. It is concluded that the observed low rank correlation does not invalidate the two-way model. The paper also discusses tests for homogeneity of S_i²as well as implications of the two-way model for the classification of stability statistics.     

Classifying genotypic data from plant breeding trials: a preliminary investigation using repeated checks

Summary Several subjective choices must be made when classifying genotypes based on data from plant breeding trials. One choice involves the method used to weight the contribution each environment makes to the classification. A second involves the use of either genotype-means for each environment or genotypevalues for each block, i.e., considering each block to be a different environment. Another involves whether environments (or blocks) in which genotypes are nonsignificantly different should be included or excluded from such classifications. An alternative to the use of raw or standardized data, is proposed in which each environment is weighted by a discrimination index (DI) that is based on the concept of repeatability. In this study the effect of three weighting methods (raw, standardized and DI), the choice of using environments or blocks, and the choice of including or excluding environments or blocks in which genotypic effects were not significant, were considered in factorial combination to give 12 options. A data set comprised of five check cultivars each repeated six times in each of three blocks at six environments was used. The effect of these options on the ability of a hierarchical clustering technique to correctly classify the repeats into five groups, each consisting of all the six repeats of a particular check cultivar, was investigated. It was found that the DI weighting method generally led to better recovery of the known structure. Using block data rather than environmental data also improved structure recovery for each of the three weighting methods. The exclusive use of environments in which genotypic effects were significant decreased structure recovery while the contrary generally occurred for blocks. The best structure recovery was obtained from the DI weighting applied to blocks (whether genotypes were significant or not).     

Application of a stability statistic to international maize yield trials

Summary Genotype x environment (GE) interaction encountered in experiments complicates genotype selection and varietal recommendation. The integration of yield and stability of genotypes into a single parameter may make selection and recommendation easier. Kang developed a rank-sum method that allows selection for both yield and the stability variance statistics ( _i ² or s _i ² ) of Shukla. The objective of this research was to compare the rank-sum selection method to selection based on yield alone in five international maize (Zea mays L.) yield trials. Ranks were assigned for yield (the highest mean yield received a rank of 1) and for _i ² and s _i ² (the lowest value received a rank of 1). The yield and _i ² ranks and/or the yield and s _i ² ranks for each genotype were summed. Each trial contained two reference entries (REs). Yield rank or rank-sum of each genotype was compared to yield rank or rank-sum of the best RE (BRE). GE interaction was significant for all trials. Heterogeneity in the GE interaction due to the linear effect of a covariate (differences in fertility and/or cultural practices) was significant in Trials 1, 2, and 5. Overall, in all trials, 29 genotypes were selected on the basis of yield alone. On the basis of _i ² and yield rank-sum, 32 genotypes were identified, with 11 being lower yielding than the 29 yield-based selections. On the basis of s _i ² and yield rank-sum, 31 genotypes were selected, with 11 being lower yielding than the yield-bases selections. Obviously, yield is sacrificed when the rank-sum method is used in the selection process. However, selection based on yield alone may not be adequate when GE interaction is significant because of testing in diverse environments.     

A method of estimating varietal stability for data of long-term trials

Summary A method is proposed to analyze the stability of cultivars in long-term varietal trials. The method involves the following steps: (i) regress a standard variety on environmental means; (ii) regress varieties under test on the standard variety; (iii) transform, through a procedure of reparameterization, the regression computed for each variety under test on the standard variety into the regression of the variety on environmental means. Although this method is proposed to analyze data sets from complex designs, it may also possess some advantages over conventional procedures for simpler designs.     

Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials

The additive main effects multiplicative interaction model is frequently used in the analysis of multilocation trials. In the analysis of such data it is of interest to decide how many of the multiplicative interaction terms are significant. Several tests for this task are available, all of which assume that errors are normally distributed with a common variance. This paper investigates the robustness of several tests (Gollob, F _GH1, F_GH2, F_R)to departures from these assumptions. It is concluded that, because of its better robustness, the F _Rtest is preferable. If the other tests are to be used, preliminary tests for the validity of assumptions should be performed.     

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     

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     

Best Linear Unbiased Prediction (BLUP) for regional yield trials: a comparison to additive main effects and multiplicative interaction (AMMI) analysis

Multilocation trials are often used to analyse the adaptability of genotypes in different environments and to find for each environment the genotype that is best adapted; i.e. that is highest yielding in that environment. For this purpose, it is of interest to obtain a reliable estimate of the mean yield of a cultivar in a given environment. This article compares two different statistical estimation procedures for this task: the Additive Main Effects and Multiplicative Interaction (AMMI) analysis and Best Linear Unbiased Prediction (BLUP). A modification of a cross validation procedure commonly used with AMMI is suggested for trials that are laid out as a randomized complete block design. The use of these procedure is exemplified using five faba bean datasets from German registration trails. BLUP was found to outperform AMMI in four of five faba bean datasets.     

籼粳交稻米蒸煮品质性状的遗传效应分析

以2个粳型光温敏核不育系和4个籼稻品种为材料,配制籼粳交组合,用包括基因型×环境互作效应的胚乳性状遗传模型对3个蒸煮品质性状(直链淀粉含量、胶稠度、碱消值)进行了遗传研究,结果表明:直接加性和母体加性效应对三个性状的遗传变异起主要作用.基因型×环境互作主要表现为显性×环境以及细胞质×环境互作.直链淀粉含量的普通遗传率都不显著,只有较高的互作母体遗传率;胶稠度具有显著的普通直接遗传率和互作细胞质遗传率;碱消值的普通直接遗传率和普通母体遗传率都极显著.根据遗传效应预测值对供试亲本的利用价值作了评价。     

Assessment of a method for cultivar selection based on regional trial data

Summary In this study a method for analyzing regional trial data is investigated for its effectiveness in cultivar selection. The method is a synthesis of three procedures: (1) regression analysis for genotype × environment (GE) interaction, and subsequent cluster analysis for grouping cultivars for similarity of response; (2) superiority measure analysis of cultivar performance based on the distance mean square between the test cultivar and the maximum response; (3) type 4 stability analysis for three-way classification data (cultivar × location × year), to measure a cultivar's stability. Each of these three procedures is aimed at different aspects of the selection problem: the first obtains an overview of the types of cultivar response; the second measures a cultivar's general adaptability within the region; the third assesses a cultivar's ability to withstand unpredictable variation, namely that caused by year effects. Four sets of published data, each originally analyzed by a univariate or a multivariate approach, were used as examples. The results suggest that the present method provides direct and useful information for selection purposes. The superiority measure, which is the core of the method, can be used even if the data do not fit the linear model for GE interaction. Plotting the data with a fixed standard represented by the maximum response provides a simple visual tool for identifying environments where a cultivar performs well.Contribution No. C-035 from Research Program Service, Research Branch, Agriculture Canada, Ottawa, Ontario, K1A 0C6     

Prediction accuracies for growth and wood attributes of interior spruce in space using genotyping-by-sequencing

Background

Genomic selection (GS) in forestry can substantially reduce the length of breeding cycle and increase gain per unit time through early selection and greater selection intensity, particularly for traits of low heritability and late expression. Affordable next-generation sequencing technologies made it possible to genotype large numbers of trees at a reasonable cost.

Results

Genotyping-by-sequencing was used to genotype 1,126 Interior spruce trees representing 25 open-pollinated families planted over three sites in British Columbia, Canada. Four imputation algorithms were compared (mean value (MI), singular value decomposition (SVD), expectation maximization (EM), and a newly derived, family-based k-nearest neighbor (kNN-Fam)). Trees were phenotyped for several yield and wood attributes. Single- and multi-site GS prediction models were developed using the Ridge Regression Best Linear Unbiased Predictor (RR-BLUP) and the Generalized Ridge Regression (GRR) to test different assumption about trait architecture. Finally, using PCA, multi-trait GS prediction models were developed. The EM and kNN-Fam imputation methods were superior for 30 and 60% missing data, respectively. The RR-BLUP GS prediction model produced better accuracies than the GRR indicating that the genetic architecture for these traits is complex. GS prediction accuracies for multi-site were high and better than those of single-sites while multi-site predictability produced the lowest accuracies reflecting type-b genetic correlations and deemed unreliable. The incorporation of genomic information in quantitative genetics analyses produced more realistic heritability estimates as half-sib pedigree tended to inflate the additive genetic variance and subsequently both heritability and gain estimates. Principle component scores as representatives of multi-trait GS prediction models produced surprising results where negatively correlated traits could be concurrently selected for using PCA2 and PCA3.

Conclusions

The application of GS to open-pollinated family testing, the simplest form of tree improvement evaluation methods, was proven to be effective. Prediction accuracies obtained for all traits greatly support the integration of GS in tree breeding. While the within-site GS prediction accuracies were high, the results clearly indicate that single-site GS models ability to predict other sites are unreliable supporting the utilization of multi-site approach. Principle component scores provided an opportunity for the concurrent selection of traits with different phenotypic optima.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1597-y) contains supplementary material, which is available to authorized users.     

Wide- versus specific-adaptation strategy for lucerne breeding in northern Italy

This study is aimed at comparing wide- versus specific-adaptation strategies for lucerne in northern Italy on the basis of actual dry matter yield gains over 12 harvests from phenotypic selection, assessing the value of specific genetic bases and selecting environments for the contrasting subregion A (no drought stress/sandy-loam soil) and subregion C (summer drought stress/silty-clay soil). A second aim is to investigate the adaptive responses of five sets of 18 half-sib progenies. The following selected populations were evaluated along with five cultivars: GW–SW, GA–SA, GA–SC, GC–SC and GC–SA (where GW, GA and GC are the genetic bases for wide adaptation, subregions A and C; SW, SA and SC are the selection environments for wide adaptation, subregions A and C). The selection and test environments were four artificial environments created by the factorial combination of two drought stress levels by two soil types. Two environments represented the subregions A and C whereas the combination of the other two environments represented the intermediate subregion B. Genotype × environment interaction (P ≤ 0.001) due to both environmental factors and implying cross-over interaction between the contrasting subregions occurred for the populations and the five selections. Specific genetic bases (GA and GC) implied gains in their target subregions of 5.2% for subregion A and 2.9% for subregion C compared with the widely adapted one (GW). The gain of SA (‘no stress/sandy-loam soil’) over SC (‘stress/silty-clay soil’) decreased from subregion A (10.6%) through subregion C (1.7%) but exhibited an advantage per se across environments of 5.4%. The best specific selections (GA–SA for subregions A and B; GC–SA for subregion C) implied higher yields of 9.8% in subregion A and 6.5% in subregion C, and over twofold greater selection efficiency across the region, relative to GW–SW. Half-sib progeny × artificial environment interaction (P ≤ 0.05) occurred in three sets of progenies whose parents belonged to cultivars with different or similar adaptation.