Genomic selection in multi-environment plant breeding trials using a factor analytic linear mixed model.

Genomic selection (GS) is a statistical and breeding methodology designed to improve genetic gain. It has proven to be successful in animal breeding; however, key points of difference have not been fully considered in the transfer of GS from animal to plant breeding. In plant breeding, individuals (varieties) are typically evaluated across a number of locations in multiple years (environments) in formally designed comparative experiments, called multi-environment trials (METs). The design structure of individual trials can be complex and needs to be modelled appropriately. Another key feature of MET data sets is the presence of variety by environment interaction (VEI), that is the differential response of varieties to a change in environment. In this paper, a single-step factor analytic linear mixed model is developed for plant breeding MET data sets that incorporates molecular marker data, appropriately accommodates non-genetic sources of variation within trials and models VEI. A recently developed set of selection tools, which are natural derivatives of factor analytic models, are used to facilitate GS for a motivating data set from an Australian plant breeding company. The power and versatility of these tools is demonstrated for the variety by environment and marker by environment effects.

QTL for yield and associated traits in the Seri/Babax population grown across several environments in Mexico, in the West Asia, North Africa, and South Asia regions.

Heat and drought adaptive quantitative trait loci (QTL) in a spring bread wheat population resulting from the Seri/Babax cross designed to minimize confounding agronomic traits have been identified previously in trials conducted in Mexico. The same population was grown across a wide range of environments where heat and drought stress are naturally experienced including environments in Mexico, West Asia, North Africa (WANA), and South Asia regions. A molecular genetic linkage map including 475 marker loci associated to 29 linkage groups was used for QTL analysis of yield, days to heading (DH) and to maturity (DM), grain number (GM2), thousand kernel weight (TKW), plant height (PH), canopy temperature at the vegetative and grain filling stages (CTvg and CTgf), and early ground cover. A QTL for yield on chromosome 4A was confirmed across several environments, in subsets of lines with uniform allelic expression of a major phenology QTL, but not independently from PH. With terminal stress, TKW QTL was linked or pleiotropic to DH and DM. The link between phenology and TKW suggested that early maturity would favor the post-anthesis grain growth periods resulting in increased grain size and yields under terminal stress. GM2 and TKW were partially associated with markers at different positions suggesting different genetic regulation and room for improvement of both traits. Prediction accuracy of yield was improved by 5 % when using marker scores of component traits (GM2 and DH) together with yield in multiple regression. This procedure may provide accumulation of more favorable alleles during selection.

An assessment of wheat yield sensitivity and breeding gains in hot environments.

Genetic improvements in heat tolerance of wheat provide a potential adaptation response to long-term warming trends, and may also boost yields in wheat-growing areas already subject to heat stress. Yet there have been few assessments of recent progress in breeding wheat for hot environments. Here, data from 25 years of wheat trials in 76 countries from the International Maize and Wheat Improvement Center (CIMMYT) are used to empirically model the response of wheat to environmental variation and assess the genetic gains over time in different environments and for different breeding strategies. Wheat yields exhibited the most sensitivity to warming during the grain-filling stage, typically the hottest part of the season. Sites with high vapour pressure deficit (VPD) exhibited a less negative response to temperatures during this period, probably associated with increased transpirational cooling. Genetic improvements were assessed by using the empirical model to correct observed yield growth for changes in environmental conditions and management over time. These 'climate-corrected' yield trends showed that most of the genetic gains in the high-yield-potential Elite Spring Wheat Yield Trial (ESWYT) were made at cooler temperatures, close to the physiological optimum, with no evidence for genetic gains at the hottest temperatures. In contrast, the Semi-Arid Wheat Yield Trial (SAWYT), a lower-yielding nursery targeted at maintaining yields under stressed conditions, showed the strongest genetic gains at the hottest temperatures. These results imply that targeted breeding efforts help us to ensure progress in building heat tolerance, and that intensified (and possibly new) approaches are needed to improve the yield potential of wheat in hot environments in order to maintain global food security in a warmer climate.

Heat and drought adaptive QTL in a wheat population designed to minimize confounding agronomic effects.

A restricted range in height and phenology of the elite Seri/Babax recombinant inbred line (RIL) population makes it ideal for physiological and genetic studies. Previous research has shown differential expression for yield under water deficit associated with canopy temperature (CT). In the current study, 167 RILs plus parents were phenotyped under drought (DRT), hot irrigated (HOT), and temperate irrigated (IRR) environments to identify the genomic regions associated with stress-adaptive traits. In total, 104 QTL were identified across a combination of 115 traits × 3 environments × 2 years, of which 14, 16, and 10 QTL were associated exclusively with DRT, HOT, and IRR, respectively. Six genomic regions were related to a large number of traits, namely 1B-a, 2B-a, 3B-b, 4A-a, 4A-b, and 5A-a. A yield QTL located on 4A-a explained 27 and 17% of variation under drought and heat stress, respectively. At the same location, a QTL explained 28% of the variation in CT under heat, while 14% of CT variation under drought was explained by a QTL on 3B-b. The T1BL.1RS (rye) translocation donated by the Seri parent was associated with decreased yield in this population. There was no co-location of consistent yield and phenology or height-related QTL, highlighting the utility of using a population with a restricted range in anthesis to facilitate QTL studies. Common QTL for drought and heat stress traits were identified on 1B-a, 2B-a, 3B-b, 4A-a, 4B-b, and 7A-a confirming their generic value across stresses. Yield QTL were shown to be associated with components of other traits, supporting the prospects for dissecting crop performance into its physiological and genetic components in order to facilitate a more strategic approach to breeding.

Molecular detection of genomic regions associated with grain yield and yield-related components in an elite bread wheat cross evaluated under irrigated and rainfed conditions.

Grain yield and grain weight of wheat are often decreased by water-limitation in the north-eastern cropping belt of Australia. Based on knowledge that CIMMYT lines are well-adapted in this region, a recombinant inbred line (RIL) population between two elite CIMMYT bread wheats (Seri M82 and Babax) was evaluated under water-limited environments. Fourteen productivity traits were evaluated in 192 progeny in up to eight trials. For three aggregations of the environments (all, high yield or low yield), multiple quantitative trait loci (QTL) were detected, each explaining <15% of variation. Co-location of multiple trait QTL was greatest on linkage groups 1B-a, 1D-b, 4A-a, 4D-a, 6A-a, 6B-a, 7A-a and an unassigned linkage group. Two putative QTL (LOD > 3) from Seri (6D-b and UA-d) increased grain yield and co-located with a suggestive (2 < LOD < 3) and a putative QTL for increased stem carbohydrate content (WSC), respectively; the latter QTL also co-located with a putative anthesis QTL for earlier flowering. Both QTL were detected only in high yield (>4t ha(-1)) environments. A third increased grain yield QTL (7A-a) from Babax co-located with QTL for increased grain number. Six putative QTL increased grain weight and co-located with QTL for harvest index, grains per spike and spike number. Three putative QTL for increased grains per spike co-located with strong QTL for earlier flowering, increased grain weight and fewer spikes. A group of progeny that exceeded the mean grain yield and grain weight of commercial checks had an increased frequency of QTL for high WSC, large grain size, increased harvest index and greater height, but fewer stems, when compared to low yielding (20% less), low grain weight progeny. These findings were consistent with agronomic analyses of the germplasm and demonstrate that there should be opportunities to independently manipulate grain number and grain size which is typically difficult due to strong negative correlations.

Multi-environment QTL mixed models for drought stress adaptation in wheat.

Many quantitative trait loci (QTL) detection methods ignore QTL-by-environment interaction (QEI) and are limited in accommodation of error and environment-specific variance. This paper outlines a mixed model approach using a recombinant inbred spring wheat population grown in six drought stress trials. Genotype estimates for yield, anthesis date and height were calculated using the best design and spatial effects model for each trial. Parsimonious factor analytic models best captured the variance-covariance structure, including genetic correlations, among environments. The 1RS.1BL rye chromosome translocation (from one parent) which decreased progeny yield by 13.8 g m(-2) was explicitly included in the QTL model. Simple interval mapping (SIM) was used in a genome-wide scan for significant QTL, where QTL effects were fitted as fixed environment-specific effects. All significant environment-specific QTL were subsequently included in a multi-QTL model and evaluated for main and QEI effects with non-significant QEI effects being dropped. QTL effects (either consistent or environment-specific) included eight yield, four anthesis, and six height QTL. One yield QTL co-located (or was linked) to an anthesis QTL, while another co-located with a height QTL. In the final multi-QTL model, only one QTL for yield (6 g m(-2)) was consistent across environments (no QEI), while the remaining QTL had significant QEI effects (average size per environment of 5.1 g m(-2)). Compared to single trial analyses, the described framework allowed explicit modelling and detection of QEI effects and incorporation of additional classification information about genotypes.

Global adaptation patterns of Australian and CIMMYT spring bread wheat.

The International Adaptation Trial (IAT) is a special purpose nursery designed to investigate the genotype-by-environment interactions and worldwide adaptation for grain yield of Australian and CIMMYT spring bread wheat (Triticum aestivum L.) and durum wheat (T. turgidum L. var. durum). The IAT contains lines representing Australian and CIMMYT wheat breeding programs and was distributed to 91 countries between 2000 and 2004. Yield data of 41 reference lines from 106 trials were analysed. A multiplicative mixed model accounted for trial variance heterogeneity and inter-trial correlations characteristic of multi-environment trials. A factor analytic model explained 48% of the genetic variance for the reference lines. Pedigree information was then incorporated to partition the genetic line effects into additive and non-additive components. This model explained 67 and 56% of the additive by environment and non-additive by environment genetic variances, respectively. Australian and CIMMYT germplasm showed good adaptation to their respective target production environments. In general, Australian lines performed well in south and west Australia, South America, southern Africa, Iran and high latitude European and Canadian locations. CIMMYT lines performed well at CIMMYT's key yield testing location in Mexico (CIANO), north-eastern Australia, the Indo-Gangetic plains, West Asia North Africa and locations in Europe and Canada. Maturity explained some of the global adaptation patterns. In general, southern Australian germplasm were later maturing than CIMMYT material. While CIANO continues to provide adapted lines to northern Australia, selecting for yield among later maturing CIMMYT material in CIANO may identify lines adapted to southern and western Australian environments.

Levene tests of homogeneity of variance for general block and treatment designs.

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plots.