Food security and land required for food production largely depend on rate of yield gain of major cereal crops. Previous projections of food security are often more optimistic than what historical yield trends would support. Many econometric projections of future food production assume compound rates of yield gain, which are not consistent with historical yield trends. Here we provide a framework to characterize past yield trends and show that linear trajectories adequately describe past yield trends, which means the relative rate of gain decreases over time. Furthermore, there is evidence of yield plateaus or abrupt decreases in rate of yield gain, including rice in eastern Asia and wheat in northwest Europe, which account for 31% of total global rice, wheat and maize production. Estimating future food production capacity would benefit from an analysis of past crop yield trends based on a robust statistical analysis framework that evaluates historical yield trajectories and plateaus.

When information on multiple genotypes evaluated in multiple environments is recorded, a multi-environment single trait model for assessing genotype × environment interaction (G × E) is usually employed. Comprehensive models that simultaneously take into account the correlated traits and trait × genotype × environment interaction (T × G × E) are lacking. In this research, we propose a Bayesian model for analyzing multiple traits and multiple environments for whole-genome prediction (WGP) model. For this model, we used Half-italict priors on each standard deviation term and uniform priors on each correlation of the covariance matrix. These priors were not informative and led to posterior inferences that were insensitive to the choice of hyper-parameters. We also developed a computationally efficient Markov Chain Monte Carlo (MCMC) under the above priors, which allowed us to obtain all required full conditional distributions of the parameters leading to an exact Gibbs sampling for the posterior distribution. We used two real data sets to implement and evaluate the proposed Bayesian method and found that when the correlation between traits was high (>0.5), the proposed model (with unstructured variance–covariance) improved prediction accuracy compared to the model with diagonal and standard variance–covariance structures. The R-software package Bayesian Multi-Trait and Multi-Environment (BMTME) offers optimized C++ routines to efficiently perform the analyses.

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Genetic analyses of complex traits in wheat (Triticum aestivum L.) are facilitated by the availability of unique genetic tools such as chromosome substitution lines and recombinant inbred chromosome lines (RICLs) which allow the effects of genes on single chromosomes to be studied individually. Chromosome 3A of ‘Wichita’ is known to contain alleles at quantitative trait loci (QTLs) that influence variation in grain yield and agronomic performance traits relative to alleles of ‘Cheyenne’. To determine the number, location, and environmental interactions of genes related to agronomic performance on chromosome 3A, QTL and QTL × environment analyses of 98 RICLs‐3A were conducted in seven locations across Nebraska from 1999 through 2001. QTLs were detected for seven of eight agronomic traits measured and generally localized to three regions of chromosome 3A. QTL × environment interactions were detected for some QTLs and these interactions were caused by changes in magnitude and crossover interactions. Major QTLs for kernels per square meter and grain yield were associated within a 5‐centimorgan (cM) interval and appeared to represent a single QTL with pleiotropic effects. This particular QTL displayed environmental interactions caused by changes in magnitude, wherein the positive effect of the Wichita QTL allele was larger in higher yielding environments.