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Wheat (Triticum aestivumL.) is a major staple food crop grown worldwide on >220 million ha. Climate change is regarded to have severe effect on wheat yields, and unpredictable drought stress is one of the most important factors. Breeding can significantly contribute to the mitigation of climate change effects on production by developing drought‐tolerant wheat germplasm. The objective of our study was to determine the annual genetic gain for grain yield (GY) of the internationally distributed Semi‐Arid Wheat Yield Trials, grown during 2002–2003 to 2013–2014 and developed by the Bread Wheat Breeding program at the CIMMYT. We analyzed data from 740 locations across 66 countries, which were classified in low‐yielding (LYE) and medium‐yielding (MYE) environments according to a cluster analysis. The rate of GY increase (GYC) was estimated relative to four drought‐tolerant wheat lines used as constant checks. Our results estimate that the rate of GYC in LYE was 1.8% (38.13 kg ha−1yr−1), whereas in MYE, it was 1.41% (57.71 kg ha−1yr−1). The increase in GYC across environments was 1.6% (48.06 kg ha−1yr−1). The pedigrees of the highest yielding lines through the coefficient of parentage analysis indicated the utilization of three primary sources—‘Pastor’, ‘Baviacora 92’, and synthetic hexaploid derivatives—to develop drought‐tolerant, high and stably performing wheat lines. We conclude that CIMMYT's wheat breeding program continues to deliver adapted germplasm for suboptimal conditions of diverse wheat growing regions worldwide.

In recent years, several statistical models have been developed for predicting genetic values for complex traits using information on dense molecular markers, pedigrees, or both. These models include, among others, the Bayesian regularized neural networks (BRNN) that have been widely used in prediction problems in other fields of application and, more recently, for genome-enabled prediction. The R package described here (brnn) implements BRNN models and extends these to include both additive and dominance effects. The implementation takes advantage of multicore architectures via a parallel computing approach using openMP (Open Multiprocessing) for the computations. This note briefly describes the classes of models that can be fitted using the brnn package, and it also illustrates its use through several real examples.

The Global Wheat Program of the International Maize and Wheat Improvement Center (CIMMYT) develops and distributes improved germplasm targeted toward various wheat growing regions of developing world. The objective of our study was to quantify the genetic yield gains in CIMMYT's spring bread wheat (Triticum aestivumL.) in the Elite Spring Wheat Yield Trial (ESWYT) distributed over the past 15 yr (1995–2009) as determined by the performance of entries across 919 environments in 69 countries. To determine the annual genetic gains, differences in mean yields of the five highest yielding entries from mean trial yield and mean yield of the widely grown international check ‘Attila’ were regressed over 15 yr of ESWYT testing. Across locations in all countries, mean yields of the five highest yielding entries showed an annual gain of 27.8 kg ha−1(0.65%) compared to Attila. Annual yield gains in mega‐environment 1 (ME1) (optimally irrigated), ME2 (high rainfall), Egypt, India, and Pakistan were 27.4 (0.55%), 21.4 (0.62%), 111.6 (1.13%), 32.5 (0.83%), and 18.5 kg ha−1(0.5%), respectively. These results demonstrate continuous genetic yield gains in the elite spring bread wheat lines developed and distributed by CIMMYT and the positive outcomes achieved through breeding and the international exchange of elite spring wheat germplasm that have benefited national programs throughout the world.

The genetic yield progress of 26 spring wheat (Triticum aestivumL.) advanced lines released by the International Maize and Wheat Improvement Centre (CIMMYT) in the period from 1977 to 2008 was evaluated in the selection environment in Mexico as well as at a set of target environments in Asia and Africa. In Mexico, grain yield progress was significantly linear and about 0.7% yr−1and yield was associated with fewer days to heading, cooler canopy temperature at grain filling, and increased stay‐green and thousand kernel weight. These results suggested that changes in the former traits at least partially explain the yield progress. When genetic yield progress was measured in subsets of sites in Asia and Africa grouped into high, intermediate, and low yielding, the genetic yield progress was 0.9, 0.7, and 0.5% yr−1, respectively. We conclude that there is no evidence that genetic gains to increase yield have slowed down in wheat lines released by CIMMYT.

In the high-rainfall zone of Australia (HRZ, >600mm), most pasture systems are dominated by perennial grasses with low levels of inter-dispersed legume. Numerous authors have shown that a legume content of 20–50% is required to maximise livestock production. Consequently, the legume content of these systems needs to be increased if livestock production is to be improved. Perennial legume options such as lucerne (Medicago sativa) and white clover (Trifolium repens) are limited in their application in this zone due to the sensitivity of lucerne to acid soils (pH(CaCl2) <4.8) and waterlogging and the inability of white clover to survive most of the annual summer droughts. To address this problem, a breeding program was undertaken to develop varieties of Lotus corniculatus (birdsfoot trefoil) suitable for the HRZ of southern Australia. In the first cycle, 365 populations were screened in nurseries to select the best 62 plants from the best populations at Yalanbee and Medina in Western Australia. These selections were then grown as half-sib families in spaced-plant nurseries at Waroona and Yalanbee; in the second cycle, 61 individuals, selected from the the two sites, were hand-crossed to produce 3160 plants from 202 pair-crosses. These were gown in a spaced-plant nursery at the University of Western Australia Field Station in Shenton Park. In the third cycle, three polycross populations (YF, T, and F) were produced from selections within the 3160 second-cycle plants, and two additional plants which survived for 4 years on a non-wetting sand at Yalanbee, including a significant drought year in 2006. These varieties are expected to extend the adaptation of L. corniculatus to drier areas and/or lower latitudes.

The effectiveness of targeting and predicting maize (Zea mays.L) hybrid performance is difficult when the magnitude of genotype x environment (GE) interaction and yield prediction cannot be interpreted and is only based on genotypes (G) and GE means. The traditional analysis of variance (ANOVA) is not sufficient in predicting and giving information into the patterns of genotypes and environments that give rise to GE interaction. The objectives of this study were to show the usefulness of G plus GE interaction (GGE) using the properties of GGE biplot based on the site regression (SREG) model analysis of a biplot in predicting yield performance and stability of early to intermediate maturing hybrids (EIHYB) grown in southern Africa. The SREG analysis model was based on regional trial data of EIHYB from three seasons (2005 - 2007) across 30 environments under four different management practices: well fertilized/rain fed conditions, managed nitrogen stress, managed drought stress, and managed low pH stress. GGE biplots were constructed using the first two principal components (PC1 and PC2) derived from singular value decomposition of environment-centered multi-environmental trials. The PC1 scores of the hybrids and the environments were plotted against their respective PC2 scores to effectively show mean performance and stability for grain yield across years and environments; discriminativeness vs. representativeness of test locations across the years and which-won-where. The SREG model showed that maize hybrids were under major environmental and GE interactions. In spite of large variation from year to year maize hybrids responded positively to better environmental conditions relative to grain yield performance and key environmental patterns could be established.

CIMMYT is the source of improved maize (Zea maysL.) breeding material for a significant portion of the nontemperate maize growing world. Landraces which did not serve as sources for improved maize germplasm may contain untapped allelic variation useful for future breeding progress. Information regarding levels of diversity in different germplasm would help to identify sources for broadening improved breeding pools and in seeking genes and alleles that have not been tapped in modern maize breeding. The objectives of this study were to examine the diversity in maize landraces, modern open pollinated varieties (OPVs), and inbred lines adapted to nontemperate growing areas to find unique sources of allelic diversity that may be used in maize improvement. Twenty‐five simple sequence repeat markers were used to characterize 497 individuals from 24 landraces of maize from Mexico, 672 individuals from 23 CIMMYT improved breeding populations, and 261 CIMMYT inbred lines. Number of alleles, gene diversity per locus, unique alleles per locus, and population structure all differ between germplasm groups. The unique alleles found in each germplasm group represent a great reservoir of untapped genetic resources for maize improvement, and implications for hybrid breeding are discussed.

Spot blotch is an important disease of wheat (Triticum aestivumL.) in South Asia. Division of test sites for this disease into homogenous subregions is expected to contribute to more efficient evaluation and better differentiation of cultivars. Data from a collaborative regional program of South Asia conducted by CIMMYT were analyzed to group testing sites into relatively homogenous subregions for spot blotch area under the disease progress curve (AUDPC). Five‐year data of eight locations from Eastern Gangetic Plains Nursery (EGPSN) and five locations of the Eastern Gangetic Plains Yield Trial (EGPYT) conducted in three countries (India, Nepal, and Bangladesh) of South Asia were used. A hierarchical cluster analysis was used to group locations on the basis of genotype × location interaction effects for spot blotch AUDPC. Cluster analysis divided South Asia into two broad regions and four subregions. This classification was not entirely consistent with the geographic distribution of locations, but clusters mostly followed general geographic‐climatic locations. The locations Varanasi (India) and Bhairahawa (Nepal) were identified as the most suitable sites for evaluation of spot blotch, followed by Rampur (Nepal). The major determinant for the clustering was mean temperature. The results suggest that the major wheat region of South Asia can be divided into subregions, which may reduce the cost of resistance evaluation and aid in developing wheat with resistance to this disease.

A good understanding of the target environment and the extent of genotype × environment (G × E) interaction is essential for all cereal breeding programs. Differential adaptation of bread wheat (Triticum aestivumL.) to various heat‐stressed environments around the world was analyzed by cumulative cluster analysis of locations and genotypes in 9 yr of CIMMYT's High Temperature Wheat Yield Trial (HTWYT). The grouping pattern of yield‐testing environments could largely be explained by the temperature at different growth stages and relative humidity at booting. A clear distinction was observed between sites with heat stress and more temperate locations, and the heat‐stressed environments could be grouped into sites experiencing high temperature throughout the season and sites with more specific terminal heat stress. In addition, dry and humid heat‐stressed locations tended to differentiate. The ability of individual locations to predict yield in different heat‐stressed environments was studied by the shifted multiplicative model (SHMM) site clustering method, and identified locations like Tandojam (Pakistan), which associated well with both heat‐stressed and temperate environments. The good ability of the January planting date in Ciudad Obregon (Mexico) to predict yield performance in many heat‐stressed environments was also confirmed. Genotypes grouped according to their relative performance in different locations, and specific adaptation to the various types of heat‐stressed environments was apparent. However, a subset of genotypes was identified that showed stable, and high yield across all types of environments, both heat‐stressed and temperate.

A shrinkage estimation method, herein named the CCC method, for multiplicative models has been shown to improve predictions of cell means in multienvironment cultivar trials; however, better estimations of shrinkage factors are needed. Objectives of this study were (i) to develop shrinkage factors for AMMI (Additive Main effect and Multiplicative Interaction) multiplicative terms based on the eigenvalue partition (EVP) method and (ii) to compare AMMI models fitted by EVP and CCC shrinkage methods, unshrunken AMMI models chosen by cross validation, and best linear unbiased prediction (BLUP) based on a fixed main effects and random genotype × environment interaction (GEI) model. The prediction methods were applied to three multienvironment cultivar trials, and also to simulated data. The four alternative prediction methods were compared by cross validation with the root mean squared predictive difference (RMSPD). According to the RMSPD cross validation criterion, the EVP shrinkage estimation method produced the most accurate predictions in almost all cases. When error variance was of a small to moderately large magnitude, results for EVP and CCC methods were in close agreement, CCC being slightly worse; EVP became better as error variance became very large, probably because of the unreliability of Gollob́s degrees of freedom as a measure of error variance absorption by the principal components (PC) when data are extremely noisy. Shrunken EVP models were generally more predictively accurate than truncated least squares‐fitted AMMI models and BLUPs, which was also true for CCC except when error variance was large. The EVP shrinkage method appears to be promising for obtaining improved predictions of cultivar performance in multienvironment cultivar trials.

Many studies have shown the practical advantages of applying the additive main effects and multiplicative interaction (AMMI) model to multienvironment trials; however, a theory about the contributions of error and genotype × environment interaction (GEI) variance components to interaction principal components (PCs) in AMMI models is needed. The objectives of this work were to (i) develop an eigenvalue partition (EVP) method for separating variation attributable to each AMMI interaction PC into interaction variance and error variance components: (ii) develop root mean square predictive difference (RMSPD) on the basis of the EVP theory (RMSPEVP), for selecting the best truncated AMMI model; (iii) apply the RMSPDEVPcriterion to three multienvironment cultivar trials and to simulation data generated for selecting the best truncated AMMI model; and (iv) validate the EVP method by comparing results of the RMSPDEVPcriterion with those obtained with the criterion conventionally used to choose a truncated AMMI model by cross validation (RMSPDCV). A data resampling method was devised to estimate the contribution of error variance to the eigenvalues. The coefficients of the structural GEI variance component were always larger than those of the error variance component for the earlier PC axes. As the error associated with the cell means decreased and the number of replications increased, the portion of the cumulative GEI explained by the earlier AMMI PC axes generally increased, whereas the portion of the error sum of squares (SS) explained by the earlier AMMI PC axes decreased. The RMSPDEVPand RMSPDCVmethods selected similar truncated AMMI models. The RMSPDEVPcriterion is useful for selecting the best truncated AMMI models with the advantage that it can be applied to all trial replications.

Understanding the way different environments differentiate cultivars for yield allows the plant breeder to optimize choice of parents, germplasm screening, yield testing, and resource use within the target region. To determine the associations among yield testing environments, wheat (Triticum aestivumL.) yield data from 963 replicated trials sown across a 20‐yr period were analyzed by means of pattern analysis and the shifted multiplicative model (SHMM) to group sites within and across years. Pattern analysis identified four primary clusters of sites and four representative locations within these clusters were identified by squared Euclidean distances. Group‐1 represented primarily Mediterranean and West Asian locations and South American sites. Group‐2 was comprised of generally warmer sites in southern and eastern Asia. Group‐3 comprised higher rainfall locations in South America and eastern Africa and Group‐4 represented cooler sites in South America and West Asia. The respective key locations for each of the four groups were Sakha, Egypt; Quezaltenango, Guatemala; Londrina, Brazil; and Pirsabak, Pakistan. The four key sites were then used to examine site clusters within each year by SHMM. The sites at Pirsabak and Sakha associated best across all global wheat‐growing regions where a combined total of 700 of 1117 (62%) possible clusters with other global wheat locations were realized. This compared with 52% for Quezaltenango and 38% for Londrina. Factors with a primary influence on site clustering were cropping season moisture availability and temperature. Genotype performance at Pirsabak and Sakha can be used to enhance genetic progress in a range of related wheat growing environments thereby improving the effectiveness of global wheat breeding.

Diverse and varied crop genetic resources are necessary (though not sufficient) for adequate food production in a rapidly changing world. Since the scientific community first raised public concern several decades ago, modern cultivars have been viewed as the cause of declining diversity in the world's crop genetic resources. This paper tests the hypothesis of increasing genetic uniformity in modern spring bread wheat (Triticum aestivumL.) cultivars from 1965, a year which marks the release of some of the first modern semidwarf cultivars carrying Rht1and Rht2genes in the developing world. Results from previously published studies are summarized. Preliminary molecular analyses, and new analyses of cultivar numbers, areas, ages, and genealogies are presented. An estimated 77% of the spring bread wheat area in the developing world today is sown to CIMMYT‐related wheats, but this does not imply that they are genetically uniform. The hypothesis of increasing genetic uniformity is tested by assessing changes in the diversity of leading progenitors over three decades, in terms of several dimensions of diversity. Latent dimensions include genetic distance and genealogies. Apparent dimensions include performance with respect to yield potential, maintenance and stability across management (input use), and growing environments. The data are not consistent with the view that the genetic diversity of modern semidwarf wheat grown in the developing world has decreased over time. Moreover, since national programs in developing countries cross CIMMYT lines with their own materials before releasing them, the genetic diversity in their cultivars is at least as great as that present among CIMMYT lines.

Two maize (Zea maysL) lines, susceptible and resistant to first‐generation southwestern corn borer (SWCB), Diatraea grandiosellaDyar, were hybridized then backcrossed to the susceptible parent to form a population that was selected over three backcross generations by either marker‐assisted or conventional selection for resistance to first generation SWCB leaf feeding. Quantitative trait loci (QTL) mapping was done by BC1F1genotyping and BC1F2infestation with SWCB. Three putative QTL were identified on chromosomes 7, 9, and 10 accounting for 28% of the phenotypic variance. Marker‐assisted selection (MAS) proceeded by selecting plants heterozygous at the QTL regions and homozygous for the recurrent parent genotype outside the QTL regions in the BC1F1and BC2F1generations. BC2F2individuals were selected for the homozygous donor genotype in the QTL regions. Conventional selection initiated from the most resistant 30 BC1F2lines. Conventional trials of BC2F2and BC2F3families were infested with SWCB and based on leaf damage ratings selected selfed progeny of the former generation formed the subsequent trial entries. A comparative trial of BC2F3lines, selected by the two methods, was evaluated under SWCB infestation at three locations. Leaf damage ratings were taken at all locations and larvae weight was taken at one location. No significant differences for leaf damage ratings or larvae weight were found between lines selected by the two methods. Both methods produced lines significantly improved over the susceptible parent for SWCB leaf feeding damage indicating that the methods were equivalent as conducted in this experiment.

Near-isogenic Rhtlines of ten modern bread wheat (TriticumaestivumL.) and six durum wheat (T. turgidumL.) cultivars weredeveloped and evaluated in replicated trials under three soil moisturetreatments for two years in northwestern Mexico. The three soil moisturetreatments were created by providing one, two or six irrigations during eachcrop season. Grain yield and other traits were measured for each line ineach trial. Mean grain yields of short and tall T. aestivumor T.turgidumisolines were similar in the lowest yielding environment whenmean grain yields (0% grain moisture) of T. aestivumand T.turgidumwere 2,232 and 1,870 kg ha-1, respectively. Mean grainyield of dwarf T. aestivumwas significantly higher than that of tallgenotypes in another five trials with moderate to high yields. Theperformance of dwarf and tall T. turgidumisolines was unpredictablein moderate yielding trials, and the dwarf isolines yielded significantly morein trials that received six irrigations. Given that the tall isolines producedsignificantly more straw than their shorter counterparts, cultivation of tallwheats may be beneficial in semiarid environments where farmers' yields areclose to 2.5 t ha-1or lower, and straw has value.

Large areas of wheat (Triticum aestivum L. Fion et Paol.) are grown under above-optimal temperatures causing significant yield reductions. Adaptation of wheat to such areas through genetic improvement is a way of increasing production in those regions. To identify new and novel sources of heat tolerance, 2,255 Mexican wheat landraces, grown for seed regeneration under semi-controlled conditions in the screenhouse, were evaluated for leaf chlorophyll content (LCC). The landraces were collected from areas with seasonal high temperatures. Based on these initial results, two subgroups of 127 landraces each were selected, one with high LCC values and one with low LCC values. During 1997 the selected subgroups were grown in the screenhouse and in field trials in Cd. Obregon, Mexico. The landraces were evaluated for traits associated with heat tolerance: LCC, canopy temperature depression, and thousand-kernel weight (KWT). The objectives of the study were to identify new sources of heat tolerance and to assess the feasibility of combining basic seed regeneration with characterization for needed traits like heat tolerance. A highly significant correlation was found between LCC in the screenhouse and in field trials, indicating the promise of using a screenhouse for cost effective evaluation of heat tolerance traits. This strategy could be used to identify regions or groups of germplasm that merit more intense screening. Highly significant correlations were also found between LCC and KWT. Three landrace cultivars with superior and consistent LCC values were identified. These accessions are potentially useful sources for improving heat tolerance in cultivated wheat.

Abstract: An understanding of the genetic and environmental basis of genotype×environment interaction (GEI) is of fundamental importance in plant breeding. In mapping quantitative trait loci (QTLs), suitable genetic populations are grown in different environments causing QTLs×environment interaction (QEI). The main objective of the present study is to show how Partial Least Squares (PLS) regression and Factorial Regression (FR) models using genetic markers and environmental covariables can be used for studying QEI related to GEI. Biomass data were analyzed from a multi-environment trial consisting of 161 lines from a F3:4 maize segregating population originally created with the purpose of mapping QTLs loci and investigating adaptation differences between highland and lowland tropical maize. PLS and FR methods detected 30 genetic markers (out of 86) that explained a sizeable proportion of the interaction of maize lines over four contrasting environments involving two low-altitude sites, one intermediate-altitude site, and one high-altitude site for biomass production. Based on a previous study, most of the 30 markers were associated with QTLs for biomass and exhibited significant QEI. It was found that marker loci in lines with positive GEI for the highland environments contained more highland alleles, whereas marker loci in lines with positive GEI for intermediate and lowland environments contained more lowland alleles. In addition, PLS and FR models identified maximum temperature as the most-important environmental covariable for GEI. Using a stepwise variable selection procedure, a FR model was constructed for GEI and QEI that exclusively included cross products between genetic markers and environmental covariables. Higher maximum temperature in low- and intermediate-altitude sites affected the expression of some QTLs, while minimum temperature affected the expression of other QTLs.

The methodology used by the International Maize and Wheat Improvement Center (CIMMYT) to develop and improve its maize (Zea maysL.) germplasm involves evaluation of families or experimental varieties in extensive international testing trials. The genotype‐environmental interaction is produced by differential genotypic responses to varied environmental conditions. Its effect is to limit the accuracy of yield estimates and complicate the identification of specific genotypes for specific environments. The objective of this study was to use the Additive Main effects and Multiplicative Interaction (AMMI) method, with additive effects for genotypes and environments and multiplicative terms for genotype‐environment interaction, for analyzing data from two international maize cultivar trials. Results from the first trial were: (i) predictive assessment selected AMMI with one principal component axis, (ii) AMMI increased the precision of yield estimates equivalent to increasing the number of replications by a factor of 4.30, (iii) AMMI provided much insight into genotype‐environment interactions, and (iv) AMMI selected a different highest‐yielding genotype than did treatment means in 72% of the environments. Results for the second trial were that predictive assessment selects the AMMI with none of the principal component axes, which increased precision equivalent to increase the number of replications by a factor of 2.59.

Collection and description of the maize (Zea maysL.) germplasm complexes of Mexico began in 1943, and efforts toward the potential utilization of the 25 recognized Mexican races were initiated in 1961. This study was conducted to determine the performance of the 25 Mexican races and 300 interracial crosses evaluated in three environments identified as high (2249 m), intermediate (1800 m), and low (1300 m) elevations. Data were analyzed with the Gardner‐Eberhart model, Analysis II. At the high elevation the races Cónico, Cónico Norteño, and Chalqueño had high mean yields per se and in crosses. Cacahuacintle and Maiz Dulce had equally high yield in crosses but had lower per se yield. At the intermediate elevation, the best yielding races in crosses and per se were Comiteco, Harinoso de Ocho, Celaya, Maiz Dulce, Tabloncillo, and Tuxpeno. At the low elevation, the highest per se yields were exhibited by Harinoso de Ocho, Celaya, Pepitilla, and Tabloncillo. Across all elevations, the best general combiners were Cacahuacintle, Harinoso de Ocho, and Maiz Dulce. Results of this study could be used to (i) introgress the heterotic patterns found among races into new commercial varieties or populations, (ii) search for race collections with better agronomic type that belong to the racial heterotic pattern, (iii) improve gene pools based on racial heterotic patterns and geographical origins, (iv) establish reciprocal recurrent selection between two races that exhibited heterosis when crossed, or (v) develop hybrids based on lines derived from the collections studied in each environment.

Abstract: Bread wheats (Triticum aestivum L.) were evaluated for plant characteristics contributing to grain yield and plant adaptation under various drought patterns. The usefulness of these traits as explicit selection criteria in developing drought tolerant wheat varieties was investigated in three experiments. Cultivars from four germplasm groups, representing the four relevant major and distinct global wheat growing environments, were grown under the respective simulated early, late, continuous and no drought conditions by manipulating irrigation in north western Mexico. Additionally, 560 advanced lines from the CIMMYT breeding program were grown under late drought conditions, and 16 randomly selected advanced genotypes were studied in more detail under late and no drought conditions. In these three studies, the association between yield in drought-stressed environments and yield in non drought-stressed environments was interpreted to reflect genotypic high yield potential, mainly by way of high biomass development. However, yield potential only partly explained the superior performance under drought. For each pattern of drought stress, particular and often different plant traits were identified that further contributed specific adaptation to the distinct drought stress conditions. Knowledge of these traits will be useful for developing CIMMYT germplasm for specific drought-stressed areas. Ultimately, these studies demonstrate that both yield potential and specific adaptation traits are useful criteria in breeding for drought environments, and should be combined to achieve optimum performance and adaptation to drought stress.

Abstract:  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.

Maize (Zea maysL.) geneticists and breeders in the USA are concerned with the narrow base of Corn Belt germplasm. Numerous experiments using exotic germplasm from other countries have been conducted to broaden the germplasm base. Our study was undertaken to evaluate the potential use of an exotic germplasm source for the improvement of an adapted maize population and to determine the optimum proportion of exotic germplasm to be introgressed. Ninety S1families from three populations representing three levels of introgression of exotic maize germplasm into an adapted population were developed and evaluated at two locations. The S1families from the cross (50% adapted germplasm) yielded significantly less than those from adapted (100% adapted germplasm) and backcross (75% adapted germplasm). Both the adapted and the backcross populations were early maturing and yielded similarly. This suggests that major genes for lack of adaptation are acting in the cross population. A significant nonlinearelationship between S1family means and proportion of adapted material in the base population was noted for all traits. The use of an exotic source has increased the genetic variation in the cross population. With an appropriate effective population size, the cross can be used as a base population in a selection program, if useful genes from the exotic source are at low frequencies.

Summary In maize (Zea mays L.) source germplasm having tolerance to inbreeding is needed for the derivation of productive inbred lines. The germplasm with non-temperature adaptation, generally suffer from large inbreeding depression (ID). the objective of the present study was to improve four white subtropical populations for tolerance to ID through S3 recurrent selection. Two cycles of selection were conducted and the effect of selection was evaluated in the first selfed (S1) and random0mated (Synthetic-2=Syn-2) generations. To complete each cycle. 200 to 250 S3 progenies were evaluated and 15 to 20 superior ones selected for recombination in each population. Selection was practiced for high grain yield, vigour and other agronomie traits. The S1 and Syn-2 generations of the original (C0) and improved (C1, C2) populations were evaluated in a split-split plot design, with populations in main plots, generations in subplots and cycles in sub-subplots. In all populations, S1 and Syn-2 generations of C2 were significantly higher yielding than the C0 and the linear gain per cycle varied from 16.3 to 28.8% in S1 generation and 5.5 to 10.7% in Syn-2 generation. Selection reduced the anthesis-silking interval but slightly increased plant height, grain moisture and days to silk. An increase in plant height was expected because of emphasis on vigour during selection. For grain yield. ID decreased from 48.4% in C0 populations to 37.9% in C2, indicating an improved tolerance to inbreeding. Further, the selection accumulated favourable alleles; and Pop. 42 seemed to be the best source populations for deriving high yielding inbred lines. It may be concluded that S3 recurrent selection was effective in improving grain yield and the improved populations would provide better germplasm sources for the derivation of productive inbred lines.

The concept of variance effective population size [Ne(v)] and other expressions are reviewed and described for specific sampling steps in germplasm collection and regeneration of monoecious species. Special attention is given to procedures for computing the variance of the number of contributed gametes [V(k)] to the next generation. Drift, as it occurs between generations, was considered to contain a component due to the sampling of parents and a subsequent component due to the sampling of gametes. This demonstrates that drift, caused by reduction of seed viability, damages the genetic integrity of accessions stored in germplasm banks. The study shows how mating designs, such as plant-to-plant or chain crossings with additional female gametic control, can partially alleviate this problem. Optimal procedures for increasing Ne(v) when collecting germplasm in the field are also discussed. The effect of different female and male gametic control strategies on Ne(v) is considered under several situations. Practical examples illustrating the use of V(k) and Ne(v) expressions are given.

The main goals of genetic resource management are to acquire, maintain, distribute, characterize, regenerate, preserve, evaluate, and utilize the genetic diversity of crops and their wild relatives. The objectives of this study for ex-situ conservation of maize (Zea mays L.) are to review and describe: (1) practical regeneration methods that are based on population genetic theory; (2) practical problems encountered in choosing core subsets of a maize collection. Whenever possible, regeneration procedures should control the number of pollen parents (male gametes; through controlled hand pollination) and the number of female parent gametes (by harvesting equal numbers of kernels from each seed plant). When the number of pollen and seed parents are controlled during regeneration, the effective population size (Ne) is twice the size of the original population (N). Examples of practical methods for controlling the number of male and female parents are presented. The procedure involves random-paired plant crosses and taking equal numbers of seeds from each maize ear. To form a core subset, accessions of a maize race are subdivided through a stratified sampling procedure. Delineation of a core subset from a Tuxpeño racial collection is described as an example.

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (Di). Thus, Di is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. Di is equal to the mean of the ith genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large Di. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of Di was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of Di's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on Di.

The shifted multiplicative model (SHMM) is used in an exploratory step-down method for identifying subsets of environments in which genotypic effects are “separable” from environmental effects. Subsets of environments are chosen on the basis of a SHMM analysis of the entire data set. SHMM analyses of the subsets may indicate a need for further subdivision and/or suggest that a different subdivision at the previous stage should be tried. The process continues until SHMM analysis indicates that a SHMM with only one multiplicative term and its “point of concurrence” outside (left or right) of the cluster of data points adequately fits the data in all subsets. The method is first illustrated with a simple example using a small data set from the statistical literature. Then results obtained in an international maize (Zea mays L.) yield trial with 20 sites and nine cultivars is presented and discussed.

The maize (Zea mays L.) improvement program of the International Maize and Wheat Improvement Center (CIMMYT) develops broad-based maize populations and, until recently, improved all of them through full-sib family selection with international testing. The purpose of this study was to estimate the genetic and genetic × environment variance components for ten of those populations and to measure expected yield improvement from full-sib selection. Mean yield ranged from 3.35–6.81 t ha-1. For five populations the average yield in the last cycle was higher than in the initial cycles. Several populations showed no improvement or yielded less in the final cycle of selection, either because selection intensity was low or because strong selection pressure was applied simultaneously for several traits. Variation resulting from differences among family means within cycles and from interaction between families and locations within cycles were significant in all populations and cycles. Results indicate that variability among full-sib families was maintained throughout the cycles for all populations. The large sge2/sg2ratio shown by most populations suggests that yield response per cycle could be maximized if the environments in which progenies are tested were subdivided and classified into similar subsets. The proportion of the predicted response realized in improved yield varied for each population.

The yield stability of some CIMMYT tropical maize (Zea mays L.) populations of early and intermediate maturity, measured by the performance of varieties derived from them, was determined. Results of the stability analyses, conducted over international environments from 1980 to 1983, indicated that selections from Mezcla Amarilla exhibited good stability in high yielding sites. Varieties derived from Antigua-Republica Dominicana tended to be more stable in unfavourable environments, whereas selections from Blanco Cristalino-1 and Blanco Dentado-2 were stable in both low and high production sites. The combination of enviromental factors in the specific test locations, namely Poza Rica (Mexico), Tocumen (Panama), Islamabad (Pakistan), and Ferkessedougou (Ivory Coast), allowed selection of varieties that are very stable in other regions of the world. The varieties formed on the basis of multilocational data do not seem to be any more stable than those formed using data from a single location.

A major objective of the CIMMYT Maize Program is to develop open-pollinated varieties of maize (Zea mays L.) that are well adapted to a wide range of environments. To achieve this breeding goal, it is essential that the program use a stability technique that will identify high-yielding, stable genotypes accurately in international trials conducted under different environmental conditions. The objective of this study was to compare a spatial method with a modified conventional regression analysis method to determine the yield stability of 27 CIMMYT maize varieties evaluated at 37 locations. The methods also were compared on the basis of their consistency in assessing the stability of varieties when certain locations were omitted, and when subsets of varieties were analyzed. The varieties found to be stable by the spatial method with all sites included in the analysis were also stable (1) when the lowest and highest yielding sites were excluded from the analyses, and (2) when the varieties were considered, along with others, as a subset of the original group of materials. Stability parameters determined by regression analysis, however, varied for some varieties when (1) extreme sites were excluded, and (2) a subset of entries was considered in isolation. Because the spatial method was more consistent in identifying high-yielding stable varieties, it was considered the more useful of the two methods.

Thirteen maize (Zea mays L.) populations including five adapted, five adapted x exotic, two composites of adapted and exotic, and one exotic selected for adaptability were crossed in a diallel mating system. The parents and 78 crosses and nine check hybrids were evaluated for grain yield and plant height in five environments. The Gardner-Eberhart model Analysis II indicated that additive and nonadditive gene effects accounted for 60 and 40% of the total variation among populations, respectively, for grain yield and 86% and 14% of the total variation, respectively, for plant height. Components of heterosis were significant in the combined analysis for both traits. Adapted Corn Belt populations tended to have higher performance in crosses and greater values of variety heterosis than 50% adapted populations. ‘Nebraska Elite Composite’, ‘Corn Belt’ x ‘Mexican’, and ‘Corn Belt’ x ‘Brazilian’ showed high mean yields in crosses, however, they were not among those with high estimates of variety heterosis. One exotic population (‘Tuxpeno’ x ‘Antigua Grupo 2’) and three adapted populations [‘307 Composite’, ‘NB(S1)C-3’, and ‘NK(S1)C-3’] might be combined together to form a high-yielding population. It may be possible to synthesize two useful populations for reciprocal recurrent selection by grouping ‘Tuxpeno’ x ‘Antiqua Grupo 2’, ‘NB(S1)C-3’, and ‘NS(FS)LFW-8’ into one population and ‘NK(S1)C-3’, ‘Krug’x‘Tabloncillo’, and ‘307 Composite’ in the other one.

The International Spring Wheat Yield Nursery (ISWYN) has been distributed annually since 1964 and the results provide a base for investigating relationships among locations. Ordination and clustering of locations was conducted using 26 years of grain yield data. Ordination and clusters based on the discrimination of germplasm were compared with ‘mega-environments’, which are groupings of locations defined by CIMMYT on the basis of climatic factors and perceptions of major biotic and abiotic stresses. Discrepancies among mega-environmental groupings, clusters and ordinations may identify locations for which major stresses affecting wheat yield are yet unidentified.

Principal coordinates analysis was used to determine the yield stability of some CIMMYT maize populations (Zea mays L.) measured by the performance of the varieties selected from them. The varieties included in this study were derived from subtropical of early and intermediate maturity maize populations. The analyses included grain yield data from international trials conducted from 1979 to 1983.

In hexaploid wheat (Triticum aestivumL.) disease resistance genes transferred from alien sources are often associated with undesirable traits. Replicated trials using near‐isogenic lines of spring wheat ‘Seri 82’ were conducted for 2 yr under non‐moisture stress and simulated moisture stress conditions to determine the effects of the 7DL.7Ag and 1BL.1RS translocations [from Agropyron elongatum(Host) Beauv. and Secale cerealeL., respectively] on grain yield and related traits. Mean grain yield of the 1B lines was significantly higher (3.2%) than that of the 1BL.1RS translocation lines in non‐moisture stress trials, but not significantly higher in the moisture stress trials. The mean grain yields of the five highest yielding reconstituted Seri 82 genotypes (1BL.1RS) were significantly lower than that of the genotypes without the 1BL.1RS translocation in non‐moisture stress (3.2%) and moisture stress (5.2%) conditions. Incorporation of the 7DL.7Ag translocation caused a significant increase (9%) in biomass at harvest in non‐moisture stress trials. The mean grain yields of the five highest yielding 7DL.7Ag lines were significantly higher (8.2%) than the reconstituted Seri 82 genotypes in non‐moisture stress conditions and more than 16% lower under moisture stress. Lower grain yields of the 7DL.7Ag lines under moisture stress could be due to their excessive pre‐heading biomass production. Several yield‐related traits of the near‐isogenic genotypes varied significantly. Presence of each translocation caused lateness and, when present together, the 1BL.1RS and 7DL.7Ag translocations delayed heading and maturity by 7 and 5 d, respectively. The genetic background of the recipient wheat can affect the utility of a translocation.

Information about combining ability and heterotic patterns among CIMMYT's maize (Zea maysL.) gene pools and populations should assist research programs in their hybrid development activities. A nine‐parent diallel was formed to (i) study the combining ability of CIMMYT's subtropical and temperate intermediate‐maturity maize gene pools and populations and (ii) evaluate the potential of CIMMYT's subtropical and temperate materials as exotic germplasm sources for temperate breeding programs. Parents and crosses were evaluated in 5 environments in Mexico and 11 in the USA. Highly significant, positive general combining ability (GCA) effects for yield were observed with Populations 42, 47, and 34 in Mexico. The Population 42 × Population 47 cross ranked first in yield (7.87 Mg ha−1, with 9.1% high‐parent heterosis). Population 33 x Population 45 was the only cross with a significant, positive specific combining ability (SCA) effect for yield. Average yields in U.S. environments were low (3.49 Mg ha‐I), due partially to adaptation problems and late plantings. Only Pool 41 had a significant, positive GCA effect for yield in the USA. The four highest yielding combinations included Pool 41 with Populations 42, 47, 34, and 45. In Mexican subtropical environments, superior crosses included Population 42 × Population 47 (white grain) and Population 33 × Population 45 (yellow grain). Though the CIMMYT materials did not generally perform well in U.S. environments, Pool 41 and Population 42 showed the best potential as exotic germplasm sources for temperate breeding program

Maize (Zea maysL.) breeders working with lowland tropical germplasm have experienced difficulties in developing good inbred lines. One limitation is moderate to drastic inbreeding depression (ID) these germplasms. In the present study, two cycles of S3 recurrent selection were conducted in four white maize populations (Pop. 21, Pop. 25, Pop. 29, Pop. 32) with tropical adaptation to improve them as hybrid‐oriented source germplasm, and the effect of selection was examined in the selfed (S1) and randomly mated (Syn‐2) generations. In each population, 200 to 250 S3 progenies were evaluated and 15 to 20 selected and intermated to form improved versions after cycle 1 (C1) and cycle 2 (C2). Selection was practiced for high grain yield, vigor, and other agronomic traits during inbreeding generations and in the S3‐progeny tests. The S1 and Syn‐2 generations of the C0, C1, and C2 of four populations were evaluated in three environments in Mexico, using split‐split plot design with populations in main plots, generations in subplots, and cycles in sub‐subplots. Selection improved the grain yield of the S1 generation, and the linear gain per cycle (Gc) was 12, 9, 4, and 4% in Pop. 21, Pop. 29, Pop. 32, and Pop. 25, respectively, being significant in Pop. 21 and Pop. 29. The C2 of Pop. 21 had the highest grain yield in both Syn‐2 and S1 generations. Generally, selection did not significantly affect grain moisture, days to silk, and anthesis‐silking interval, but it increased plant height in different populations. Combined over populations, however, grain moisture was significantly increased in addition to grain yield and plant height in both S1 and Syn‐2 generations. The linear Gc for grain yield across populations was 7.41 and 3.20% in the S1 and Syn‐2 generations, respectively. The effect of selection on grain yield and plant height was generally lower in the Syn‐2 than the S1 generation of Pop. 25, Pop. 29, and Pop. 32, but was comparable in two generations of Pop. 21. The ID for grain yield across populations decreased from 39% in CO to 35% in C2. The selection was effective in improving grain yield and reducing ID; and the improved populations would serve as better germplasm sources for the extraction of vigorous inbred lines.

Forty-eight bread wheat (Triticum aestivum L.) released cultivars and elite advanced lines were evaluated for their ability to produce embryogenic callus using three different media. Basal N6 medium supplemented with dicamba (E1), MS medium containing 2,4-D (E3) or MS medium containing 2,4-D plus different amino acids (E5) were used for callus initiation and maintenance. Plant regeneration was achieved on basal MS medium with indole-3-acetic acid (IAA) and 6-benzylamino purine (BAP) and rooting on MS with 1-naphthaleneacetic acid (NAA). Percentage regeneration varied widely with both genotype and initiation medium, with values ranging from 2% to 94%. The number of plantlets produced per embryo ranged from 6 to 42. Thirteen genotypes showed at least 50% regeneration after culture on E5 medium; 3 genotypes after culture on E3 initiation medium and 1 after initiation on E1. After four subcultures, over a 16-week period, 41 genotypes (85%) lost their ability to regenerate plants while the remaining 7 lines (15%) retained plant regeneration potential but at reduced levels. E3 medium was found to be the best for maintaining regeneration potential after four subcultures.

One objective of the regeneration of genetic populations is to maintain at least one copy of each allele present in the original population. Genetic diversity within populations depends on the number and frequency of alleles across all loci. The objectives of this study on outbreeding crops are: (1) to use probability models to determine optimal sample sizes for the regeneration for a number of alleles at independent loci; and (2) to examine theoretical considerations in choosing core subsets of a collection. If we assume that k-1 alleles occur at an identical low frequency of p0 and that the kth allele occurs at a frequency of 1-[(k-1)p0], for loci with two, three, or four alleles, each with a p0 of 0.05, 89–110 additional individuals are required if at least one allele at each of 10 loci is to be retained with a 90% probability; if 100 loci are involved, 134–155 individuals are required. For two, three, or four alleles, when p0 is 0.03 at each of 10 loci, the sample size required to include at least one of the alleles from each class in each locus is 150–186 individuals; if 100 loci are involved, 75 additional individuals are required. Sample sizes of 160–210 plants are required to capture alleles at frequencies of 0.05 or higher in each of 150 loci, with a 90–95% probability. For rare alleles widespread throughout the collection, most alleles with frequencies of 0.03 and 0.05 per locus will be included in a core subset of 25–100 accessions.

The shifted multiplicative model (SHMM) is used with a cluster method to identify subsets of sites in an international maize (Zea mays L.) trial without genotypic rank-change. For cluster analysis, distance between two sites is defined as the residual sum of squares after fitting SHMM with one multiplicative term (SHMM1) if SHMM1 does not show genotypic rank-change. However, if SHMM1 does show genotypic rank-change, the distance between two sites is defined as the smaller of the sums of squares owing to genotypes within each of the two sites. Calculation of distance between two sites is facilitated by using the site regression model with one multiplicative term (SREG1), which can be reparameterized as SHMM1 when only two sites are considered. The dichotomous splitting procedure, used on the dendrogram obtained from cluster analysis, will first perform SHMM analyses on each of the last two cluster groups to join (end of the dendrogram). If SHMM1 does not give an adequate fit, the next step is to move down the branches of the tree until groups of sites (clusters) are found to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign. Five final groups of sites to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign were obtained. The procedure appears to be useful in identifying subsets of sites in which genotypic rank-change interactions are negligible.

Multilocation trials are important for the CIMMYT Bread Wheat Program in producing high-yielding, adapted lines for a wide range of environments. This study investigated procedures for improving predictive success of a yield trial, grouping environments and genotypes into homogeneous subsets, and determining the yield stability of 18 CIMMYT bread wheats evaluated at 25 locations. Additive Main effects and Multiplicative Interaction (AMMI) analysis gave more precise estimates of genotypic yields within locations than means across replicates. This precision facilitated formation by cluster analysis of more cohesive groups of genotypes and locations for biological interpretation of interactions than occurred with unadjusted means. Locations were clustered into two subsets for which genotypes with positive interactions manifested in high, stable yields were identified. The analyses highlighted superior selections with both broad and specific adaptation.

The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (Ne) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.

Cultivated bread wheat (Triticum aestivumL.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschiiCoss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschiiand T. turgidum, and then crossed to T. aestivumto produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vsimproved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHWand SHWDwith respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWDand the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidumand Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii—T. aestivumand T. turgidum—T. aestivumpopulations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels.