Expanding the BonnMu sequence-indexed repository of transposon induced maize (Zea mays L.) mutations in dent and flint germplasm.

The BonnMu resource is a transposon tagged mutant collection designed for functional genomics studies in maize. To expand this resource, we crossed an active Mutator (Mu) stock with dent (B73, Co125) and flint (DK105, EP1, and F7) germplasm, resulting in the generation of 8064 mutagenized BonnMu F2-families. Sequencing of these Mu-tagged families revealed 425 924 presumptive heritable Mu insertions affecting 36 612 (83%) of the 44 303 high-confidence gene models of maize (B73v5). On average, we observed 12 Mu insertions per gene (425 924 total insertions/36 612 affected genes) and 53 insertions per BonnMu F2-family (425 924 total insertions/8064 families). Mu insertions and photos of seedling phenotypes from segregating BonnMu F2-families can be accessed through the Maize Genetics and Genomics Database (MaizeGDB). Downstream examination via the automated Mutant-seq Workflow Utility (MuWU) identified 94% of the presumptive germinal insertion sites in genic regions and only a small fraction of 6% inserting in non-coding intergenic sequences of the genome. Consistently, Mu insertions aligned with gene-dense chromosomal arms. In total, 42% of all BonnMu insertions were located in the 5' untranslated region of genes, corresponding to accessible chromatin. Furthermore, for 38% of the insertions (163 843 of 425 924 total insertions) Mu1, Mu8 and MuDR were confirmed to be the causal Mu elements. Our publicly accessible European BonnMu resource has archived insertions covering two major germplasm groups, thus facilitating both forward and reverse genetics studies.

Genomic prediction using machine learning: a comparison of the performance of regularized regression, ensemble, instance-based and deep learning methods on synthetic and empirical data.

BACKGROUND: The accurate prediction of genomic breeding values is central to genomic selection in both plant and animal breeding studies. Genomic prediction involves the use of thousands of molecular markers spanning the entire genome and therefore requires methods able to efficiently handle high dimensional data. Not surprisingly, machine learning methods are becoming widely advocated for and used in genomic prediction studies. These methods encompass different groups of supervised and unsupervised learning methods. Although several studies have compared the predictive performances of individual methods, studies comparing the predictive performance of different groups of methods are rare. However, such studies are crucial for identifying (i) groups of methods with superior genomic predictive performance and assessing (ii) the merits and demerits of such groups of methods relative to each other and to the established classical methods. Here, we comparatively evaluate the genomic predictive performance and informally assess the computational cost of several groups of supervised machine learning methods, specifically, regularized regression methods, deep, ensemble and instance-based learning algorithms, using one simulated animal breeding dataset and three empirical maize breeding datasets obtained from a commercial breeding program. RESULTS: Our results show that the relative predictive performance and computational expense of the groups of machine learning methods depend upon both the data and target traits and that for classical regularized methods, increasing model complexity can incur huge computational costs but does not necessarily always improve predictive accuracy. Thus, despite their greater complexity and computational burden, neither the adaptive nor the group regularized methods clearly improved upon the results of their simple regularized counterparts. This rules out selection of one procedure among machine learning methods for routine use in genomic prediction. The results also show that, because of their competitive predictive performance, computational efficiency, simplicity and therefore relatively few tuning parameters, the classical linear mixed model and regularized regression methods are likely to remain strong contenders for genomic prediction. CONCLUSIONS: The dependence of predictive performance and computational burden on target datasets and traits call for increasing investments in enhancing the computational efficiency of machine learning algorithms and computing resources.

High-throughput field phenotyping reveals that selection in breeding has affected the phenology and temperature response of wheat in the stem elongation phase.

Crop growth and phenology are driven by seasonal changes in environmental variables, with temperature as one important factor. However, knowledge about genotype-specific temperature response and its influence on phenology is limited. Such information is fundamental to improve crop models and adapt selection strategies. We measured the increase in height of 352 European winter wheat varieties in 4 years to quantify phenology, and fitted an asymptotic temperature response model. The model used hourly fluctuations in temperature to parameterize the base temperature (Tmin), the temperature optimum (rmax), and the steepness (lrc) of growth responses. Our results show that higher Tmin and lrc relate to an earlier start and end of stem elongation. A higher rmax relates to an increased final height. Both final height and rmax decreased for varieties originating from the continental east of Europe towards the maritime west. A genome-wide association study (GWAS) indicated a quantitative inheritance and a large degree of independence among loci. Nevertheless, genomic prediction accuracies (GBLUPs) for Tmin and lrc were low (r≤0.32) compared with other traits (r≥0.59). As well as known, major genes related to vernalization, photoperiod, or dwarfing, the GWAS indicated additional, as yet unknown loci that dominate the temperature response.

Hierarchical modelling of variance components makes analysis of resolvable incomplete block designs more efficient.

The standard approach to variance component estimation in linear mixed models for alpha designs is the residual maximum likelihood (REML) method. One drawback of the REML method in the context of incomplete block designs is that the block variance may be estimated as zero, which can compromise the recovery of inter-block information and hence reduce the accuracy of treatment effects estimation. Due to the development of statistical and computational methods, there is an increasing interest in adopting hierarchical approaches to analysis. In order to increase the precision of the analysis of individual trials laid out as alpha designs, we here make a proposal to create an objectively informed prior distribution for variance components for replicates, blocks and plots, based on the results of previous (historical) trials. We propose different modelling approaches for the prior distributions and evaluate the effectiveness of the hierarchical approach compared to the REML method, which is classically used for analysing individual trials in two-stage approaches for multi-environment trials.

Accuracy of prediction from multi-environment trials for new locations using pedigree information and environmental covariates: the case of sorghum (Sorghum bicolor (L.) Moench) breeding.

KEY MESSAGES: We investigate a method of extracting and fitting synthetic environmental covariates and pedigree information in multilocation trial data analysis to predict genotype performances in untested locations. Plant breeding trials are usually conducted across multiple testing locations to predict genotype performances in the targeted population of environments. The predictive accuracy can be increased by the use of adequate statistical models. We compared linear mixed models with and without synthetic covariates (SCs) and pedigree information under the identity, the diagonal and the factor-analytic variance-covariance structures of the genotype-by-location interactions. A comparison was made to evaluate the accuracy of different models in predicting genotype performances in untested locations using the mean squared error of predicted differences (MSEPD) and the Spearman rank correlation between predicted and adjusted means. A multi-environmental trial (MET) dataset evaluated for yield performance in the dry lowland sorghum (Sorghum bicolor (L.) Moench) breeding program of Ethiopia was used. For validating our models, we followed a leave-one-location-out cross-validation strategy. A total of 65 environmental covariates (ECs) obtained from the sorghum test locations were considered. The SCs were extracted from the ECs using multivariate partial least squares analysis and subsequently fitted in the linear mixed model. Then, the model was extended accounting for pedigree information. According to the MSEPD, models accounting for SC improve predictive accuracy of genotype performances in the three of the variance-covariance structures compared to others without SC. The rank correlation was also higher for the model with the SC. When the SC was fitted, the rank correlation was 0.58 for the factor analytic, 0.51 for the diagonal and 0.46 for the identity variance-covariance structures. Our approach indicates improvement in predictive accuracy with SC in the context of genotype-by-location interactions of a sorghum breeding in Ethiopia.

Average semivariance yields accurate estimates of the fraction of marker-associated genetic variance and heritability in complex trait analyses.

The development of genome-informed methods for identifying quantitative trait loci (QTL) and studying the genetic basis of quantitative variation in natural and experimental populations has been driven by advances in high-throughput genotyping. For many complex traits, the underlying genetic variation is caused by the segregation of one or more 'large-effect' loci, in addition to an unknown number of loci with effects below the threshold of statistical detection. The large-effect loci segregating in populations are often necessary but not sufficient for predicting quantitative phenotypes. They are, nevertheless, important enough to warrant deeper study and direct modelling in genomic prediction problems. We explored the accuracy of statistical methods for estimating the fraction of marker-associated genetic variance (p) and heritability ([Formula: see text]) for large-effect loci underlying complex phenotypes. We found that commonly used statistical methods overestimate p and [Formula: see text]. The source of the upward bias was traced to inequalities between the expected values of variance components in the numerators and denominators of these parameters. Algebraic solutions for bias-correcting estimates of p and [Formula: see text] were found that only depend on the degrees of freedom and are constant for a given study design. We discovered that average semivariance methods, which have heretofore not been used in complex trait analyses, yielded unbiased estimates of p and [Formula: see text], in addition to best linear unbiased predictors of the additive and dominance effects of the underlying loci. The cryptic bias problem described here is unrelated to selection bias, although both cause the overestimation of p and [Formula: see text]. The solutions we described are predicted to more accurately describe the contributions of large-effect loci to the genetic variation underlying complex traits of medical, biological, and agricultural importance.

Factor-Analytic Variance-Covariance Structures for Prediction Into a Target Population of Environments.

Finlay-Wilkinson regression is a popular method for modeling genotype-environment interaction in plant breeding and crop variety testing. When environment is a random factor, this model may be cast as a factor-analytic variance-covariance structure, implying a regression on random latent environmental variables. This paper reviews such models with a focus on their use in the analysis of multi-environment trials for the purpose of making predictions in a target population of environments. We investigate the implication of random versus fixed effects assumptions, starting from basic analysis-of-variance models, then moving on to factor-analytic models and considering the transition to models involving observable environmental covariates, which promise to provide more accurate and targeted predictions than models with latent environmental variables.

Sustaining rice productivity through weather-resilient agricultural practices.

BACKGROUND: Enhancing productivity and profitability and reducing climatic risk are the major challenges for sustaining rice production. Extreme weather can have significant and varied effects on crops, influencing agricultural productivity, crop yields and food security. RESULTS: In this study, a comparative evaluation of two crop management systems was performed involving farmers adopting a weather forecast-based advisory service (WFBAS) and usual farmers' practice (FP). WFBAS crop management followed the generated weather forecast-based advice whereas the control farmers (FP) did not receive any weather forecast-based advice, rather following their usual rice cultivation practices. The results of the experiments revealed that WFBAS farmers had a significant yield advantage over FP farmers. With the WFBAS technology, the farmers used inputs judiciously, utilized the benefit of favorable weather and minimized the risk resulting from extreme weather events. As a result, besides the yield enhancement, WFBAS provided a scope to protect the environment with the minimum residual effect of fertilizer and pesticides. It also reduced the pressure on groundwater by ensuring efficient water management. Finally, the farmers benefited from higher income through yield enhancement, reduction of the costs of production and reduction of risk. CONCLUSION: A successful and extensive implementation of WFBAS in the rice production system would assist Bangladesh in achieving Sustainable Development Goal 2.4, which focuses on rice productivity and profitability of farmers as well as long-term food security of the country. © 2023 The Authors. Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Single-parent expression complementation contributes to phenotypic heterosis in maize hybrids.

The dominance model of heterosis explains the superior performance of F1-hybrids via the complementation of deleterious alleles by beneficial alleles in many genes. Genes active in one parent but inactive in the second lead to single-parent expression (SPE) complementation in maize (Zea mays L.) hybrids. In this study, SPE complementation resulted in approximately 700 additionally active genes in different tissues of genetically diverse maize hybrids on average. We established that the number of SPE genes is significantly associated with mid-parent heterosis (MPH) for all surveyed phenotypic traits. In addition, we highlighted that maternally (SPE_B) and paternally (SPE_X) active SPE genes enriched in gene co-expression modules are highly correlated within each SPE type but separated between these two SPE types. While SPE_B-enriched co-expression modules are positively correlated with phenotypic traits, SPE_X-enriched modules displayed a negative correlation. Gene ontology term enrichment analyses indicated that SPE_B patterns are associated with growth and development, whereas SPE_X patterns are enriched in defense and stress response. In summary, these results link the degree of phenotypic MPH to the prevalence of gene expression complementation observed by SPE, supporting the notion that hybrids benefit from SPE complementation via its role in coordinating maize development in fluctuating environments.

Effects of systematic data reduction on trend estimation from German registration trials.

KEY MESSAGE: VCU trials can provide unbiased estimates of post-breeding trends given that all data is used. Dropping data of genotypes tested for up to two years may result in biased post-breeding trend estimates. Increasing yield trends are seen on-farm in Germany. The increase is based on genetic trend in registered genotypes and changes in agronomic practices and climate. To estimate both genetic and non-genetic trends, historical wheat data from variety trials evaluating a varieties' value for cultivation und use (VCU) were analyzed. VCU datasets include information on varieties as well as on genotypes that were submitted by breeders and tested in trials but could not make it to registration. Therefore, the population of registered varieties (post-registration population) is a subset of the population of genotypes tested in VCU trials (post-breeding population). To assess post-registration genetic trend, historical VCU trial datasets are often reduced, e.g. to registered varieties only. This kind of drop-out mechanism is statistically informative which affects variance component estimates and which can affect trend estimates. To investigate the effect of this informative drop-out on trend estimates, a simulation study was conducted mimicking the structure of German winter wheat VCU trials. Zero post-breeding trends were simulated. Results showed unbiased estimates of post-breeding trends when using all data. When restricting data to genotypes tested for at least three years, a positive genetic trend of 0.11 dt ha-1 year-1 and a negative non-genetic trend (- 0.11 dt ha-1 year-1) were observed. Bias increased with increasing genotype-by-year variance and disappeared with random selection. We simulated single-trait selection, whereas decisions in VCU trials consider multiple traits, so selection intensity per trait is considerably lower. Hence, our results provide an upper bound for the bias expected in practice.

Models to estimate genetic gain of soybean seed yield from annual multi-environment field trials.

KEY MESSAGE: Simulations demonstrated that estimates of realized genetic gain from linear mixed models using regional trials are biased to some degree. Thus, we recommend multiple selected models to obtain a range of reasonable estimates. Genetic improvements of discrete characteristics are obvious and easy to demonstrate, while quantitative traits require reliable and accurate methods to disentangle the confounding genetic and non-genetic components. Stochastic simulations of soybean [Glycine max (L.) Merr.] breeding programs were performed to evaluate linear mixed models to estimate the realized genetic gain (RGG) from annual multi-environment trials (MET). True breeding values were simulated under an infinitesimal model to represent the genetic contributions to soybean seed yield under various MET conditions. Estimators were evaluated using objective criteria of bias and linearity. Covariance modeling and direct versus indirect estimation-based models resulted in a substantial range of estimated values, all of which were biased to some degree. Although no models produced unbiased estimates, the three best-performing models resulted in an average bias of [Formula: see text] kg/ha[Formula: see text]/yr[Formula: see text] ([Formula: see text] bu/ac[Formula: see text]/yr[Formula: see text]). Rather than relying on a single model to estimate RGG, we recommend the application of several models with minimal and directional bias. Further, based on the parameters used in the simulations, we do not think it is appropriate to use any single model to compare breeding programs or quantify the efficiency of proposed new breeding strategies. Lastly, for public soybean programs breeding for maturity groups II and III in North America, the estimated RGG values ranged from 18.16 to 39.68 kg/ha[Formula: see text]/yr[Formula: see text] (0.27-0.59 bu/ac[Formula: see text]/yr[Formula: see text]) from 1989 to 2019. These results provide strong evidence that public breeders have significantly improved soybean germplasm for seed yield in the primary production areas of North America.

50 years of rice breeding in Bangladesh: genetic yield trends.

To assess the efficiency of genetic improvement programs, it is essential to assess the genetic trend in long-term data. The present study estimates the genetic trends for grain yield of rice varieties released between 1970 and 2020 by the Bangladesh Rice Research Institute. The yield of the varieties was assessed from 2001-2002 to 2020-2021 in multi-locations trials. In such a series of trials, yield may increase over time due to (i) genetic improvement (genetic trend) and (ii) improved management or favorable climate change (agronomic/non-genetic trend). In both the winter and monsoon seasons, we observed positive genetic and non-genetic trends. The annual genetic trend for grain yield in both winter and monsoon rice varieties was 0.01 t ha-1, while the non-genetic trend for both seasons was 0.02 t ha-1, corresponding to yearly genetic gains of 0.28% and 0.18% in winter and monsoon seasons, respectively. The overall percentage yield change from 1970 until 2020 for winter rice was 40.96%, of which 13.91% was genetic trend and 27.05% was non-genetic. For the monsoon season, the overall percentage change from 1973 until 2020 was 38.39%, of which genetic and non-genetic increases were 8.36% and 30.03%, respectively. Overall, the contribution of non-genetic trend is larger than genetic trend both for winter and monsoon seasons. These results suggest that limited progress has been made in improving yield in Bangladeshi rice breeding programs over the last 50 years. Breeding programs need to be modernized to deliver sufficient genetic gains in the future to sustain Bangladeshi food security.

Generating designs for comparative experiments with two blocking factors.

Often, comparative experiments involve a single treatment factor and two blocking factors, for example, augmented row-column, two-phase, and incomplete row-column experiments. These experiments are widely used in agriculture. Finding good designs for these experiments is a major challenge when the number of treatments is large and the blocking structure is complex. In this paper, we first propose a new search algorithm that is combined with efficient update formulae, so that optimal designs with two blocking factors can be found within a reasonable time. Second, we compare augmented row-column designs generated with our new method to those obtained from CycDesigN, DiGGer, and the OPTEX procedure of SAS in terms of computing times as well as the quality of solutions. Third, we illustrate our proposed approach with four applications. We show an example where our efficient update formulae work while existing update formulae cannot be applied, and we use our search framework to generate augmented row-column, two-phase, and incomplete row-column designs. We end the paper with a conclusion along with suggestions for potential applications.

An adjusted coefficient of determination (R2 ) for generalized linear mixed models in one go.

The coefficient of determination (R2 ) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.

Long-term trends in yield variance of temperate managed grassland.

The management of climate-resilient grassland systems is important for stable livestock fodder production. In the face of climate change, maintaining productivity while minimizing yield variance of grassland systems is increasingly challenging. To achieve climate-resilient and stable productivity of grasslands, a better understanding of the climatic drivers of long-term trends in yield variance and its dependence on agronomic inputs is required. Based on the Park Grass Experiment at Rothamsted (UK), we report for the first time the long-term trends in yield variance of grassland (1965-2018) in plots given different fertilizer and lime applications, with contrasting productivity and plant species diversity. We implemented a statistical model that allowed yield variance to be determined independently of yield level. Environmental abiotic covariates were included in a novel criss-cross regression approach to determine climatic drivers of yield variance and its dependence on agronomic management. Our findings highlight that sufficient liming and moderate fertilization can reduce yield variance while maintaining productivity and limiting loss of plant species diversity. Plots receiving the highest rate of nitrogen fertilizer or farmyard manure had the highest yield but were also more responsive to environmental variability and had less plant species diversity. We identified the days of water stress from March to October and temperature from July to August as the two main climatic drivers, explaining approximately one-third of the observed yield variance. These drivers helped explain consistent unimodal trends in yield variance-with a peak in approximately 1995, after which variance declined. Here, for the first time, we provide a novel statistical framework and a unique long-term dataset for understanding the trends in yield variance of managed grassland. The application of the criss-cross regression approach in other long-term agro-ecological trials could help identify climatic drivers of production risk and to derive agronomic strategies for improving the climate resilience of cropping systems. Supplementary Information: The online version contains supplementary material available at 10.1007/s13593-023-00885-w.

Contrasting drivers of belowground nitrogen cycling in a montane grassland exposed to a multifactorial global change experiment with elevated CO2 , warming, and drought.

Depolymerization of high-molecular weight organic nitrogen (N) represents the major bottleneck of soil N cycling and yet is poorly understood compared to the subsequent inorganic N processes. Given the importance of organic N cycling and the rise of global change, we investigated the responses of soil protein depolymerization and microbial amino acid consumption to increased temperature, elevated atmospheric CO2 , and drought. The study was conducted in a global change facility in a managed montane grassland in Austria, where elevated CO2 (eCO2 ) and elevated temperature (eT) were stimulated for 4 years, and were combined with a drought event. Gross protein depolymerization and microbial amino acid consumption rates (alongside with gross organic N mineralization and nitrification) were measured using 15 N isotope pool dilution techniques. Whereas eCO2  showed no individual effect, eT had distinct effects which were modulated by season, with a negative effect of eT on soil organic N process rates in spring, neutral effects in summer, and positive effects in fall. We attribute this to a combination of changes in substrate availability and seasonal temperature changes. Drought led to a doubling of organic N process rates, which returned to rates found under ambient conditions within 3 months after rewetting. Notably, we observed a shift in the control of soil protein depolymerization, from plant substrate controls under continuous environmental change drivers (eT and eCO2 ) to controls via microbial turnover and soil organic N availability under the pulse disturbance (drought). To the best of our knowledge, this is the first study which analyzed the individual versus combined effects of multiple global change factors and of seasonality on soil organic N processes and thereby strongly contributes to our understanding of terrestrial N cycling in a future world.

Protein use efficiency and stability of baking quality in winter wheat based on the relation of loaf volume and grain protein content.

KEY MESSAGE: A novel approach based on the loaf volume-grain protein content relation is suggested to consider the static protein use efficiency and stability as efficient quality-related descriptors for wheat varieties. The most important trait for baking quality of winter wheat is loaf volume (V). It is mostly determined by grain protein content (GPC) and quality. New varieties with a high potential of grain protein use efficiency (ProtUE) are very important for reducing the surplus use of nitrogen fertilizer in areas where nitrogen leaching is large. This is also an important goal of agricultural policies in the European Union. Additionally, ProtUE needs to be very stable across environments in the face of progressing climate change with more volatile growing conditions. We evaluated a new approach to assess ProtUE and stability based on the V-GPC relationship instead of using only single traits. The study comprised 11,775 baking tests from 355 varieties grown 1988-2019 in 668 different environments in Germany. V was predicted by quadratic and linear regression functions for quality groups, indicating a reduction of ProtUE from 1988 to 2019. We introduced a dynamic and a static approach to assess ProtUE and stability as potential criteria in variety registration. We found a considerably lower heritability of the dynamic ProtUE (h2 = 43%) compared to the static ProtUE (h2 = 92%) and a lower dynamic stability (h2 = 32%) than for the static stability (h2 = 51%). None of these measures is in conflict with the selection for high V. In particular, V and static ProtUE are strongly genetically associated (r = 0.81), indicating an advantage of the static over the dynamic approach.

Assessing the between-country genetic correlation in maize yield using German and Polish official variety trials.

KEY MESSAGE: We assess the genetic gain and genetic correlation in maize yield using German and Polish official variety trials. The random coefficient models were fitted to assess the genetic correlation. Official variety testing is performed in many countries by statutory agencies in order to identify the best candidates and make decisions on the addition to the national list. Neighbouring countries can have similarities in agroecological conditions, so it is worthwhile to consider a joint analysis of data from national list trials to assess the similarity in performance of those varieties tested in both countries. Here, maize yield data from official German and Poland variety trials for cultivation and use (VCU) were analysed for the period from 1987 to 2017. Several statistical models that incorporate environmental covariates were fitted. The best fitting model was used to compute estimates of genotype main effects for each country. It is demonstrated that a model with random genotype-by-country effects can be used to borrow strength across countries. The genetic correlation between cultivars from the two countries equalled 0.89. The analysis based on agroecological zones showed high correlation between zones in the two countries. The results also showed that 22 agroecological zones in Germany can be merged into five zones, whereas the six zones in Poland had very high correlation and can be considered as a single zone for maize. The 43 common varieties which were tested in both countries performed equally in both countries. The mean performances of these common varieties in both countries were highly correlated.

Assessing the response to genomic selection by simulation.

KEY MESSAGE: We propose a simulation approach to compute response to genomic selection on a multi-environment framework to provide breeders the number of entries that need to be selected from the population to have a defined probability of selecting the truly best entry from the population and the probability of obtaining the truly best entries when some top-ranked entries are selected. The goal of any plant breeding program is to maximize genetic gain for traits of interest. In classical quantitative genetics, the genetic gain can be obtained from what is known as "Breeder's equation". In the past, only phenotypic data were used to compute the genetic gain. The advent of genomic prediction (GP) has opened the door to the utilization of dense markers for estimating genomic breeding values or GBV. The salient feature of GP is the possibility to carry out genomic selection with the assistance of the kinship matrix, hence improving the prediction accuracy and accelerating the breeding cycle. However, estimates of GBV as such do not provide the full information on the number of entries to be selected as in the classical response to selection. In this paper, we use simulation, based on a fitted mixed model for GP in a multi-environmental framework, to answer two typical questions of a plant breeder: (1) How many entries need to be selected to have a defined probability of selecting the truly best entry from the population; (2) what is the probability of obtaining the truly best entries when some top-ranked entries are selected.

Leveraging probability concepts for cultivar recommendation in multi-environment trials.

KEY MESSAGE: We propose using probability concepts from Bayesian models to leverage a more informed decision-making process toward cultivar recommendation in multi-environment trials. Statistical models that capture the phenotypic plasticity of a genotype across environments are crucial in plant breeding programs to potentially identify parents, generate offspring, and obtain highly productive genotypes for target environments. In this study, our aim is to leverage concepts of Bayesian models and probability methods of stability analysis to untangle genotype-by-environment interaction (GEI). The proposed method employs the posterior distribution obtained with the No-U-Turn sampler algorithm to get Hamiltonian Monte Carlo estimates of adaptation and stability probabilities. We applied the proposed models in two empirical tropical datasets. Our findings provide a basis to enhance our ability to consider the uncertainty of cultivar recommendation for global or specific adaptation. We further demonstrate that probability methods of stability analysis in a Bayesian framework are a powerful tool for unraveling GEI given a defined intensity of selection that results in a more informed decision-making process toward cultivar recommendation in multi-environment trials.