Search

Key Message: Grain yield and NUE increased over time while nitrogen yield did not drop significantly despite reduced nitrogen input. Selection for grain and nitrogen yield is equivalent to selection for NUE. Breeding and registration of improved varieties with high yield, processing quality, disease resistance and nitrogen use efficiency (NUE) are of utmost importance for sustainable crop production to minimize adverse environmental impact and contribute to food security. Based on long-term variety trials of cereals, winter oilseed rape and grain peas tested across a wide range of environmental conditions in Germany, we quantified long-term breeding progress for NUE and related traits. We estimated the genotypic, environmental and genotype-by-environment interaction variation and correlation between traits and derived heritability coefficients. Nitrogen fertilizer application was considerably reduced between 1995 and 2021 in the range of 5.4% for winter wheat and 28.9% for spring wheat while for spring barley it was increased by 20.9%. Despite the apparent nitrogen reduction for most crops, grain yield (GYLD) and nitrogen accumulation in grain (NYLD) was increased or did not significantly decrease. NUE for GYLD increased significantly for all crops between 12.8% and 35.2% and for NYLD between 8% and 20.7%. We further showed that the genotypic rank of varieties for GYLD and NYLD was about equivalent to the genotypic rank of the corresponding traits of NUE, if all varieties in a trial were treated with the same nitrogen rate. Heritability of nitrogen yield was about the same as that of grain yield, suggesting that nitrogen yield should be considered as an additional criterion for variety testing to increase NUE and reduce negative environmental impact., (© 2024. The Author(s).)

Key Message: Considerable breeding progress in cereal and disease resistances, but not in stem stability was found. Ageing effects decreased yield and increased disease susceptibility indicating that new varieties are constantly needed. Plant breeding and improved crop management generated considerable progress in cereal performance over the last decades. Climate change, as well as the political and social demand for more environmentally friendly production, require ongoing breeding progress. This study quantified long-term trends for breeding progress and ageing effects of yield, yield-related traits, and disease resistance traits from German variety trials for five cereal crops with a broad spectrum of genotypes. The varieties were grown over a wide range of environmental conditions during 1988-2019 under two intensity levels, without (I1) and with (I2) fungicides and growth regulators. Breeding progress regarding yield increase was the highest in winter barley followed by winter rye hybrid and the lowest in winter rye population varieties. Yield gaps between I2 and I1 widened for barleys, while they shrank for the other crops. A notable decrease in stem stability became apparent in I1 in most crops, while for diseases generally a decrasing susceptibility was found, especially for mildew, brown rust, scald, and dwarf leaf rust. The reduction in disease susceptibility in I2 (treated) was considerably higher than in I1. Our results revealed that yield performance and disease resistance of varieties were subject to considerable ageing effects, reducing yield and increasing disease susceptibility. Nevertheless, we quantified notable achievements in breeding progress for most disease resistances. This study indicated an urgent and continues need for new improved varieties, not only to combat ageing effects and generate higher yield potential, but also to offset future reduction in plant protection intensity., (© 2021. The Author(s).)

Key Message: Breeding progress of resistance to fungal wheat diseases and impact of disease severity on yield reduction in long-term variety trials under natural infection were estimated by mixed linear regression models. This study aimed at quantifying breeding progress achieved in resistance breeding towards varieties with higher yield and lower susceptibility for 6 major diseases, as well as estimating decreasing yields and increasing disease susceptibility of varieties due to ageing effects during the period 1983-2019. A further aim was the prediction of disease-related yield reductions during 2005-2019 by mixed linear regression models using disease severity scores as covariates. For yield and all diseases, overall progress of the fully treated intensity (I2) was considerably higher than for the intensity without fungicides and growth regulators (I1). The disease severity level was considerably reduced during the study period for mildew (MLD), tan spot (DTR) and Septoria nodorum blotch (ear) (SNB) and to a lesser extent for brown (leaf) rust (BNR) and Septoria tritici blotch (STB), however, not for yellow/stripe rust (YLR). Ageing effects increased susceptibility of varieties strongly for BNR and MLD, but were comparatively weak for SNB and DTR. Considerable yield reductions under high disease severity were predicted for STB (-6.6%), BNR (-6.5%) and yellow rust (YLR, -5.8%), but lower reductions for the other diseases. The reduction for resistant vs. highly susceptible varieties under high severity conditions was about halved for BNR and YLR, providing evidence of resistance breeding progress. The empirical evidence on the functional relations between disease severity, variety susceptibility and yield reductions based on a large-scale multiple-disease field trial data set in German winter wheat is an important contribution to the ongoing discussion on fungicide use and its environmental impact.

Key Message: Weighted outperformed unweighted genomic prediction using an unbalanced dataset representative of a commercial breeding program. Moreover, the use of the two cycles preceding predictions as training set achieved optimal prediction ability. Predicting the performance of untested single-cross hybrids through genomic prediction (GP) is highly desirable to increase genetic gain. Here, we evaluate the predictive ability (PA) of novel genomic strategies to predict single-cross maize hybrids using an unbalanced historical dataset of a tropical breeding program. Field data comprised 949 single-cross hybrids evaluated from 2006 to 2013, representing eight breeding cycles. Hybrid genotypes were inferred based on their parents' genotypes (inbred lines) using single-nucleotide polymorphism markers obtained via genotyping-by-sequencing. GP analyses were fitted using genomic best linear unbiased prediction via a stage-wise approach, considering two distinct cross-validation schemes. Results highlight the importance of taking into account the uncertainty regarding the adjusted means at each step of a stage-wise analysis, due to the highly unbalanced data structure and the expected heterogeneity of variances across years and locations of a commercial breeding program. Further, an increase in the size of the training set was not always advantageous even in the same breeding program. The use of the two cycles preceding predictions achieved optimal PA of untested single-cross hybrids in a forward prediction scenario, which could be used to replace the first step of field screening. Finally, in addition to the practical and theoretical results applied to maize hybrid breeding programs, the stage-wise analysis performed in this study may be applied to any crop historical unbalanced data.

Key Message: Simultaneous improvement of protein content and grain yield by index selection is possible but its efficiency largely depends on the weighting of the single traits. The genetic architecture of these indices is similar to that of the primary traits. Grain yield and protein content are of major importance in durum wheat breeding, but their negative correlation has hampered their simultaneous improvement. To account for this in wheat breeding, the grain protein deviation (GPD) and the protein yield were proposed as targets for selection. The aim of this work was to investigate the potential of different indices to simultaneously improve grain yield and protein content in durum wheat and to evaluate their genetic architecture towards genomics-assisted breeding. To this end, we investigated two different durum wheat panels comprising 159 and 189 genotypes, which were tested in multiple field locations across Europe and genotyped by a genotyping-by-sequencing approach. The phenotypic analyses revealed significant genetic variances for all traits and heritabilities of the phenotypic indices that were in a similar range as those of grain yield and protein content. The GPD showed a high and positive correlation with protein content, whereas protein yield was highly and positively correlated with grain yield. Thus, selecting for a high GPD would mainly increase the protein content whereas a selection based on protein yield would mainly improve grain yield, but a combination of both indices allows to balance this selection. The genome-wide association mapping revealed a complex genetic architecture for all traits with most QTL having small effects and being detected only in one germplasm set, thus limiting the potential of marker-assisted selection for trait improvement. By contrast, genome-wide prediction appeared promising but its performance strongly depends on the relatedness between training and prediction sets.

The objective of this study is to describe the present organisational structure of Boran cattle breeding and develop a model breeding programme using a deterministic approach under the current structure of the Boran Cattle Breeders Society. A breeding unit of 13,000 cows supplying bulls to a commercial population of 39,000 cows was assumed. Selection criteria used were growth and reproduction traits while breeding objective traits targeted were growth, carcass, reproduction, survival, milk yield and feed intake traits. Higher selection intensity was possible for breeding sires resulting in higher genetic gains compared to dams even though selection accuracies were generally low. Annual genetic gains were positive except for dressing percentage, cow survival rate, and age at first calving. However, a reduction of age at first calving by 9.5 days obtained a return of Ksh 49.76. The overall monetary genetic gain obtained was Ksh 84.89 with a profit per cow per year of Ksh 377.98. The basic breeding programme could be expanded to accommodate a larger population of Boran cattle. The implications of the results are also discussed.

Broadening the genetic base of heterotic pools is a key to ensure continued genetic gains in hybrid breeding and extend hybrid cultivation to new areas. In the present study, two Central European heterotic pools (Carsten and Petkus) and five Eastern European open-pollinated varieties (OPVs, Pop-1 to Pop-5) were studied with the objectives to (1) investigate the genetic diversity in OPVs and the heterotic pools using molecular and field data, (2) evaluate the molecular diversity among OPVs, (3) examine the combining ability for grain yield of the OPVs when crossed with testers in field trials, and (4) develop a strategy for targeted introgression of OPV germplasm into the heterotic pools. In total, 610 S(0) plants, 347 from OPVs and 263 from heterotic pools, were developed. Clones of the S(0) plants of OPVs were crossed with two testers belonging to each heterotic pool, while clones of heterotic pools were crossed with only the opposite tester. Testcrosses were evaluated for grain yield in multi-location trials. In addition, 589 S(0) plants were fingerprinted with 30 SSR markers. The data revealed that the Carsten pool has a narrow genetic base and should be the primary target for broadening the established heterotic pattern. Mean and genetic variance suggested that Pop-2 and Pop-4 are good candidates for introgression in Petkus pool and Pop-5 in Carsten pool. Nevertheless, introgression of Pop-5 in Carsten could reduce the genetic diversity between heterotic pools. Therefore, we suggest that either selected plants of Pop-5 should be introgressed or more Eastern European germplasm should be fingerprinted and field evaluated to identify promising germplasm for broadening the established heterotic pattern.

Introgression libraries facilitate the identification of favorable exotic alleles or genomic regions, which can be exploited for improving elite breeding material. We evaluated the first two introgression libraries in rye (Secale cereale L.) on the phenotypic and molecular level. Our objectives were to detect candidate introgression lines (pre-ILs) with a better testcross performance than the recurrent parent and identify donor chromosome segments (DCS) responsible for the improved performance. We introduced DCS from the self-incompatible heterozygous exotic Iranian primitive rye accession Altevogt 14160 (donor) into the genetic background of the elite inbred line L2053-N (recurrent parent) by marker-assisted backcrossing and developed 40 BC(2)S(3) lines in each introgression library. Testcross performance for three agronomic and six quality traits was evaluated in replicated field trials across two testers at five locations over 2 years. The phenotypic effect of the DCS was analyzed for all traits. The pre-ILs had on average a testcross performance comparable to that of the recurrent parent. Significant (P < 0.05) differences between individual pre-ILs and the recurrent parent were detected for all traits except for heading date. For more than 60% of the significant (P < 0.05) differences, the pre-ILs were superior to the recurrent parent. For some pre-ILs, specific DCS were identified containing presumably quantitative trait loci responsible for the superior hybrid performance. Consequently, our study revealed that the development and employment of introgression libraries offers the opportunity for a targeted increase of genetic diversity of elite rye material for hybrid performance of agronomically important traits.

Fusarium head blight is one of the most important wheat diseases causing grain yield and quality losses as well as mycotoxin contamination all over the world. Since Fusarium cannot be reliably controlled with fungicides, breeding has become a favorable tool to decrease the infection severity. In most cases, selection for Fusarium resistance is done by artificial infection in the field. However, there is a risk in preferring late heading genotypes, because heading of wheat is negatively correlated to head blight severity. Because an indirect selection for late maturity is not intended, we considered a statistical approach to avoid this problem. In this paper, we propose a mixed model to analyze extensive Fusarium head blight rating in resistance breeding experiments of wheat. The objective of the analysis was to select for Fusarium resistance, while at the same time ensuring that late heading genotypes, which show less head blight over the shorter vegetation period, are not preferred. Thus, selection was to be done such that genetic variability for heading date was retained. Therefore, the statistical model contained a covariate to adjust for differences in the heading date. The use of covariate adjustment is an easily handled alternative to a bivariate analysis. Covariate adjustment will in practice often work almost equally well as bivariate analysis. Any statistical software with powerful mixed model analysis tools can be used for this type of analysis. We propose an ad hoc method to obtain heritability estimates and a form of LSD (least significance difference) as a measure of accuracy on the basis of the proposed model and under special consideration of the experimental design. The ad hoc LSD was used as a rough measure to judge rankings of genotypic means (BLUPs). Friedman's super smoother was used to compare smoothed rank estimates for adjusted and unadjusted genotypes against increasing smoothed heading dates. Traits were transformed to meet the model assumptions, especially homogeneity of errors and normality, and back-transformation of means and standard errors was conducted by using the delta method.

According to quantitative genetic theory, linkage disequilibrium (LD) can hamper the short- and long-term selection response in recurrent selection (RS) programs. We analyzed LD in two European flint maize populations, KW1265 x D146 (A x B) and D145 x KW1292 (C x D), under modified recurrent full-sib selection. Our objectives were to investigate (1) the decay of initial parental LD present in F(2) populations by three generations of intermating, (2) the generation of new LD in four (A x B) and seven (C x D) selection cycles, and (3) the relationship between LD changes and estimates of the additive genetic variance. We analyzed the F(2) and the intermated populations as well as all selection cycles with 104 (A x B) and 101 (C x D) simple sequence repeat (SSR) markers with a uniform coverage of the entire maize genome. The LD coefficient D and the composite LD measure Delta were estimated and significance tests for LD were performed. LD was reduced by intermating as expected from theory. A directional generation of negative LD between favorable alleles could not be observed during the selection cycles. However, considerable undirectional changes in D were observed, which we attributed to genetic sampling due to the finite population size used for recombination. Consequently, a long-term reduction of the additive genetic variance due to negative LD was not observed. Our experimental results support the hypothesis that in practical RS programs with maize, LD generated by selection is not a limiting factor for obtaining a high selection response.

Selection and random genetic drift are the two main forces affecting the selection response of recurrent selection (RS) programs by changes in allele frequencies. Therefore, detailed knowledge on allele frequency changes attributable to these forces is of fundamental importance for assessing RS programs. The objectives of our study were to (1) estimate the number, position, and genetic effect of quantitative trait loci (QTL) for selection index and its components in the base populations, (2) determine changes in allele frequencies of QTL regions due to the effects of random genetic drift and selection, and (3) predict allele frequency changes by using QTL results and compare these predictions with observed values. We performed QTL analyses, based on restriction fragment length polymorphisms (RFLPs) and simple sequence repeats (SSRs), in 274 F(2:3) lines of cross KW1265 x D146 (A x B) and 133 F(3:4) lines of cross D145 x KW1292 (C x D) originating from two European flint maize populations. Four (A x B) and seven (C x D) cycles of RS were analyzed with SSRs for significant allele frequency changes due to selection. Several QTL regions for selection index were detected with simple and composite interval mapping. In some of them, flanking markers showed a significant allele frequency change after the first and the final selection cycles. The correlation between observed and predicted allele frequencies was significant only in A x B. We attribute these observations mainly to (1) the high dependence of the power of QTL detection on the population size and (2) the occurrence of undetectable QTL in repulsion phase. Assessment of allele frequency changes in RS programs can be used to detect marker alleles linked to QTL regions under selection pressure.

Plant breeders frequently evaluate large numbers of entries in field trials for selection. Generally, the tested entries are related by pedigree. The simplest case is a nested treatment structure, where entries fall into groups or families such that entries within groups are more closely related than between groups. We found that some plant breeders prefer to plant close relatives next to each other in the field. This contrasts with common experimental designs such as the alpha-design, where entries are fully randomized. A third design option is to randomize in such a way that entries of the same group are separated as much as possible. The present paper compares these design options by simulation. Another important consideration is the type of model used for analysis. Most of the common experimental designs were optimized assuming that the model used for analysis has fixed treatment effects. With many entries that are related by pedigree, analysis based on a model with random treatment effects becomes a competitive alternative. In simulations, we therefore study the properties of best linear unbiased predictions (BLUP) of genetic effects based on a nested treatment structure under these design options for a range of genetic parameters. It is concluded that BLUP provides efficient estimates of genetic effects and that resolvable incomplete block designs such as the alpha-design with restricted or unrestricted randomization can be recommended.

Altering root system architecture is considered a method of improving crop water and soil nutrient capture. The analysis of quantitative trait loci (QTLs) for root traits has revealed inconsistency in the same population evaluated in different environments. It must be clarified if this is due to genotype x environment interaction or considerations of statistics if the value of QTLs for marker-assisted breeding is to be estimated. A modified split-plot design was used where a main plot corresponded to a separate experiment. The main plot factor had four treatments (environments), which were completely randomized among eight trials, so that each treatment was replicated twice. The sub-plot factor consisted of 168 recombinant inbreed lines of the Bala x Azucena rice mapping population, randomly allocated to the seven soil-filled boxes. The aim of the trial was to quantify QTL x environment interaction. The treatments were chosen to alter partitioning to roots; consisting of a control treatment (high-soil nitrogen, high light and high-water content) and further treatments where light, soil nitrogen or soil water was reduced singly. After 4 weeks growth, maximum root length (MRL), maximum root thickness, root mass below 50 cm, total plant dry mass (%), root mass and shoot length were measured. The treatments affected plant growth as predicted; low nitrogen and drought increased relative root partitioning, low-light decreased it. The parental varieties Bala and Azucena differed significantly for all traits. Broad-sense heritability of most traits was high (57-86%). Variation due to treatment was the most important influence on the variance, while genotype was next. Genotype x environment interaction was detected for all traits except MRL, although the proportion of variation due to this interaction was generally small. It is concluded that genotype x environment interaction is present but less important than genotypic variation. A companion paper presents QTL x environment analysis of data.

Modifying plant root systems is considered a means of crop improvement targeted to low-resource environments, particularly low nutrient and drought-prone agriculture. The identification of quantitative trait loci (QTLs) for root traits has stimulated marker-assisted breeding to this end, but different QTLs have been detected in different populations of the same species, and importantly, in the same population when grown in different experimental environments. The presence of QTL x environment interaction is implicated, and this must be characterised if the utility of the target QTLs is to be realised. Previous attempts to do this suffer from a lack of control over replicate environments and inadequate statistical rigour. The Bala x Azucena mapping population was grown in two replicate experiments of four treatment environments, a control, a low light, a low soil nitrogen and a low soil water treatment. After a 4 weeks growth, maximum root length, maximum root thickness, root mass below 50 cm, total plant dry mass, % root mass and shoot length were measured. A summary of the overall results is presented in an accompanying paper. Here, QTL analysis by composite interval mapping is presented. A total of 145 QTLs were detected, mapping to 37 discrete loci on all chromosomes. Superficial evidence of QTL x E (great difference in LOD score) was tested by single-marker analysis which confirmed QTL x E for five loci representing only five individual trait-loci interactions. Some loci appeared to be stable across environments. Some QTLs were clearly more or less active under low light, low nitrogen or drought. A few notable loci on chromosomes 1, 2, 3, 5, 7 and 9 are briefly discussed. Also discussed are some remaining statistical shortcomings that will be addressed in another companion paper.

It is often found that heterosis tends to increase with genetic distance of the parents, though the correlation is not usually very close. It is therefore important to test the null hypothesis that the correlation is zero. The present work shows that standard procedures tend to yield too liberal tests, owing to the lack of independence among genetic distances and among heterosis estimates. A valid alternative is to use a permutation test, which was first suggested by Mantel [(1967) Cancer Res 27: 209--220). This test is well-known among plant breeders and geneticists, who often use it to test the correlation among two distance matrices. Its use is not restricted to the comparison of distance matrices. This is demonstrated in the present work, using two published datasets on marker-based genetic distances of maize inbreds or populations and heterosis of their crosses. It is shown that the test is also applicable in the presence of missing data.

Experiments using cDNA microarrays for the identification of genes with certain expression patterns require a thoughtfully planned design. This study was conducted to determine an optimal design for a microarray experiment to estimate differential gene expression between hybrids and their parental inbred lines in maize (i.e. dominance). It has two features: the contrasts of interest contain more than two genotypes and the procedure may be customised to other microarray experiments where different effects may influence hybridisation signals. A mixed model was used to include all important effects. Impacts during growth of the plant material were taken into consideration as well as those occurring during hybridisation. The results of a preliminary experiment were used to determine which effects were to be included in the model, and data from another microarray experiment were used to estimate variance components. In order to select good designs, an optimality criterion adapted to the problem of differential gene expression between hybrids and their parental inbred lines was defined. Two approaches were used to determine an optimal design: the first one simplifies the problem by dividing it into several subproblems, whereas the second is more sophisticated and uses a simulated annealing (SA) algorithm. We found that the first approach constitutes a useful means for designing microarray experiments to study this problem. Using the more sophisticated SA approach the design can be further improved.

Quantitative trait locus (QTL) studies in plants frequently employ phenotypic data on a population of lines (doubled haploid lines, recombinant inbred lines, etc.) tested in multiple environments. An important feature of such data is the genetic correlation among observations on the same genotype in different environments. Detection of QTL-by-environment interaction requires tests which take this correlation into account. In this article, a comparison was made of the properties of several such tests by means of simulation. The results indicate that a split-plot analysis of variance (ANOVA), being an approximate method, tends to be too liberal under departures from the Huynh-Feldt condition. A standard two-way ANOVA, which ignores genetic correlation, yields inappropriate tests and should be avoided. In contrast, mixed model approaches as well as univariate and multivariate repeated-measures ANOVA yield valid results. This supports the use of a flexible mixed model framework in more complex settings, which are difficult to tackle by repeated-measures ANOVA. .

Tests for linkage are usually performed using the lod score method. A critical question in linkage analyses is the choice of sample size. The appropriate sample size depends on the desired type-I error and power of the test. This paper investigates the exact type-I error and power of the lod score method in a segregating F(2) population with co-dominant markers and a qualitative monogenic dominant-recessive trait. For illustration, a disease-resistance trait is considered, where the susceptible allele is recessive. A procedure is suggested for finding the appropriate sample size. It is shown that recessive plants have about twice the information content of dominant plants, so the former should be preferred for linkage detection. In some cases the exact alpha-values for a given nominal alpha may be rather small due to the discrete nature of the sampling distribution in small samples. We show that a gain in power is possible by using exact methods.

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, FGH2, FR)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.

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 i (2) )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 i (2) and 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 i (2) as well as implications of the two-way model for the classification of stability statistics.

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.

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 ≅ σ 2 (g) /(σ 2 (g) + σ 2 (v) ) where σ 2 (g) =genotypic variance and σ 2 (v) = σ 2 (ge) + σ 2 (o) /L with σ 2 (ge) =interaction variance, σ 2 (o) =error variance and L=number of replications.