Leveraging data from the Genomes-to-Fields Initiative to investigate genotype-by-environment interactions in maize in North America

Overcoming the "feast or famine" effect: improved interaction testing in genome-wide association studies

In genetic association analysis of complex traits, detection of interaction (either GxG or GxE) can help to elucidate the genetic architecture and biological mechanisms underlying the trait. Detection of interaction in a genome-wide interaction study (GWIS) can be methodologically challenging for various reasons, including a high burden of multiple comparisons when testing for epistasis between all possible pairs of a set of genomewide variants, as well as heteroscedasticity effects occurring in the presence of GxG or GxE interaction. In this paper, we address the problem of an even more striking phenomenon that we call the "feast or famine" effect that occurs when testing interaction in a genomewide context. We show that in any given GxE GWIS, the type 1 error of standard interaction tests performed genomewide can vary widely from the nominal level, where the actual type 1 error in any given GWIS varies as a predictable function of the observed trait and environmental values. Using standard methods, some GWISs will have systematically underinflated p-values ("feast"), and others will have systematically overinflated p-values ("famine"), which can lead to false detection of interaction, reduced power, inconsistent results across studies, and failure to replicate true signal. This startling phenomenon is specific to detection of interaction in a GWIS, and it may partly explain why such detection has often proved challenging and difficult to replicate. We show that the feast or famine effect occurs across a wide range of GxE analysis methods, including but not limited to (1) testing interaction in a linear or linear mixed model (LMM) using standard approaches such as t-tests/Wald tests, likelihood ratio tests, or score tests; (2) doing a combined interaction-association test in a linear model or LMM using standard approaches; (3) testing interaction with multiple environments or multiple SNPs, where these are modeled as random effects in a LMM using standard approaches; (4) performing tests of interaction in a GWIS where significance is assessed using permutation of the trait residuals. We show theoretically that the key cause of this phenomenon is which variables are conditioned on in the analysis. Using this insight, we have developed (i) a diagnostic ratio to detect which GWASs are subject to a strong "feast or famine" effect and (ii) the TINGA method to adjust the interaction test statistics to make their p-values approximately uniform under the null hypothesis. In simulations we show that TINGA both controls type 1 error and improves power. TINGA allows for covariates and population structure through use of a linear mixed model and accounts for heteroscedasticity. We apply TINGA to detection of epistasis in a study of flowering time in Arabidopsis thaliana.

Global genotype by environment prediction competition reveals that diverse modeling strategies can deliver satisfactory maize yield estimates

Predicting phenotypes from a combination of genetic and environmental factors is a grand challenge of modern biology. Slight improvements in this area have the potential to save lives, improve food and fuel security, permit better care of the planet, and create other positive outcomes. In 2022 and 2023, the first open-to-the-public Genomes to Fields initiative Genotype by Environment prediction competition was held using a large dataset including genomic variation, phenotype and weather measurements, and field management notes gathered by the project over 9 years. The competition attracted registrants from around the world with representation from academic, government, industry, and nonprofit institutions as well as unaffiliated. These participants came from diverse disciplines, including plant science, animal science, breeding, statistics, computational biology, and others. Some participants had no formal genetics or plant-related training, and some were just beginning their graduate education. The teams applied varied methods and strategies, providing a wealth of modeling knowledge based on a common dataset. The winner's strategy involved 2 models combining machine learning and traditional breeding tools: 1 model emphasized environment using features extracted by random forest, ridge regression, and least squares, and 1 focused on genetics. Other high-performing teams' methods included quantitative genetics, machine learning/deep learning, mechanistic models, and model ensembles. The dataset factors used, such as genetics, weather, and management data, were also diverse, demonstrating that no single model or strategy is far superior to all others within the context of this competition.

MegaLMM improves genomic predictions in new environments using environmental covariates

Multienvironment trials (METs) are crucial for identifying varieties that perform well across a target population of environments. However, METs are typically too small to sufficiently represent all relevant environment-types, and face challenges from changing environment-types due to climate change. Statistical methods that enable prediction of variety performance for new environments beyond the METs are needed. We recently developed MegaLMM, a statistical model that can leverage hundreds of trials to significantly improve genetic value prediction accuracy within METs. Here, we extend MegaLMM to enable genomic prediction in new environments by learning regressions of latent factor loadings on Environmental Covariates (ECs) across trials. We evaluated the extended MegaLMM using the maize Genome-To-Fields dataset, consisting of 4,402 varieties cultivated in 195 trials with 87.1% of phenotypic values missing, and demonstrated its high accuracy in genomic prediction under various breeding scenarios. Furthermore, we showcased MegaLMM's superiority over univariate GBLUP in predicting trait performance of experimental genotypes in new environments. Finally, we explored the use of higher-dimensional quantitative ECs and discussed when and how detailed environmental data can be leveraged for genomic prediction from METs. We propose that MegaLMM can be applied to plant breeding of diverse crops and different fields of genetics where large-scale linear mixed models are utilized.

Global Genotype by Environment Prediction Competition Reveals That Diverse Modeling Strategies Can Deliver Satisfactory Maize Yield Estimates

Predicting phenotypes from a combination of genetic and environmental factors is a grand challenge of modern biology. Slight improvements in this area have the potential to save lives, improve food and fuel security, permit better care of the planet, and create other positive outcomes. In 2022 and 2023 the first open-to-the-public Genomes to Fields (G2F) initiative Genotype by Environment (GxE) prediction competition was held using a large dataset including genomic variation, phenotype and weather measurements and field management notes, gathered by the project over nine years. The competition attracted registrants from around the world with representation from academic, government, industry, and non-profit institutions as well as unaffiliated. These participants came from diverse disciplines include plant science, animal science, breeding, statistics, computational biology and others. Some participants had no formal genetics or plant-related training, and some were just beginning their graduate education. The teams applied varied methods and strategies, providing a wealth of modeling knowledge based on a common dataset. The winner's strategy involved two models combining machine learning and traditional breeding tools: one model emphasized environment using features extracted by Random Forest, Ridge Regression and Least-squares, and one focused on genetics. Other high-performing teams' methods included quantitative genetics, classical machine learning/deep learning, mechanistic models, and model ensembles. The dataset factors used, such as genetics; weather; and management data, were also diverse, demonstrating that no single model or strategy is far superior to all others within the context of this competition.

Using machine learning to combine genetic and environmental data for maize grain yield predictions across multi-environment trials

KEY MESSAGE

Incorporating feature-engineered environmental data into machine learning-based genomic prediction models is an efficient approach to indirectly model genotype-by-environment interactions. Complementing phenotypic traits and molecular markers with high-dimensional data such as climate and soil information is becoming a common practice in breeding programs. This study explored new ways to combine non-genetic information in genomic prediction models using machine learning. Using the multi-environment trial data from the Genomes To Fields initiative, different models to predict maize grain yield were adjusted using various inputs: genetic, environmental, or a combination of both, either in an additive (genetic-and-environmental; G+E) or a multiplicative (genotype-by-environment interaction; GEI) manner. When including environmental data, the mean prediction accuracy of machine learning genomic prediction models increased up to 7% over the well-established Factor Analytic Multiplicative Mixed Model among the three cross-validation scenarios evaluated. Moreover, using the G+E model was more advantageous than the GEI model given the superior, or at least comparable, prediction accuracy, the lower usage of computational memory and time, and the flexibility of accounting for interactions by construction. Our results illustrate the flexibility provided by the ML framework, particularly with feature engineering. We show that the feature engineering stage offers a viable option for envirotyping and generates valuable information for machine learning-based genomic prediction models. Furthermore, we verified that the genotype-by-environment interactions may be considered using tree-based approaches without explicitly including interactions in the model. These findings support the growing interest in merging high-dimensional genotypic and environmental data into predictive modeling.

A fast algorithm to factorize high-dimensional tensor product matrices used in genetic models

Many genetic models (including models for epistatic effects as well as genetic-by-environment) involve covariance structures that are Hadamard products of lower rank matrices. Implementing these models requires factorizing large Hadamard product matrices. The available algorithms for factorization do not scale well for big data, making the use of some of these models not feasible with large sample sizes. Here, based on properties of Hadamard products and (related) Kronecker products, we propose an algorithm that produces an approximate decomposition that is orders of magnitude faster than the standard eigenvalue decomposition. In this article, we describe the algorithm, show how it can be used to factorize large Hadamard product matrices, present benchmarks, and illustrate the use of the method by presenting an analysis of data from the northern testing locations of the G × E project from the Genomes to Fields Initiative (n ∼ 60,000). We implemented the proposed algorithm in the open-source "tensorEVD" R package.