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Assessment of two statistical approaches for variance genome-wide association studies in plants


Genomic loci that control the variance of agronomically important traits are increasingly important due to the profusion of unpredictable environments arising from climate change. The ability to identify such variance-controlling loci in association studies will be critical for future breeding efforts. Two statistical approaches that have already been used in the variance genome-wide association study (vGWAS) paradigm are the Brown–Forsythe test (BFT) and the double generalized linear model (DGLM). To ensure that these approaches are deployed as effectively as possible, it is critical to study the factors that influence their ability to identify variance-controlling loci. We used genome-wide marker data in maize (Zea mays L.) and Arabidopsis thaliana to simulate traits controlled by epistasis, genotype by environment (GxE) interactions, and variance quantitative trait nucleotides (vQTNs). We then quantified true and false positive detection rates of the BFT and DGLM across all simulated traits. We also conducted a vGWAS using both the BFT and DGLM on plant height in a maize diversity panel. The observed true positive detection rates at the maximum sample size considered (N = 2815) suggest that both of these vGWAS approaches are capable of identifying epistasis and GxE for sufficiently large sample sizes. We also noted that the DGLM decisively outperformed the BFT for simulated traits controlled by vQTNs at sample sizes of N = 500. Although we conclude that there are still certain aspects of vGWAS approaches that need further refinement, this study suggests that the BFT and DGLM are capable of identifying variance-controlling loci in current state-of-the-art plant or agronomic data sets.

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Fig. 1: False positive detection rates for the null setting at a false discovery rate of 0.05.
Fig. 2: True positive detection rates under the “Epistasis” scenario.
Fig. 3: True positive detection rates under the “GxE” scenario.
Fig. 4: True positive detection rates under the “vQTN” scenario.
Fig. 5: Genome-wide association study (GWAS) of plant height in the Goodman maize diversity panel.

Data availability

The genotypic data, simulated trait data, ROC curves, and code to simulate traits are available at


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We would like to thank the Associate Editor and four anonymous referees for their helpful suggestions. The research conducted in this manuscript is supported by the National Science Foundation project accession numbers 1355406 and 1733606, the University of Illinois Urbana-Champaign Department of Crop Science’s J.C. Hackleman and Lawrence E. Schrader and Elfriede Massier Plant Physiology Fellowship Programs.

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Authors and Affiliations



MDM conducted all simulations and analyses, wrote the computer program that will simulate vQTNs, created all figures and tables, and wrote and edited the manuscript. SBF contributed to the design of the simulation settings, made edits to the computer program to make it more computationally efficient, and edited the manuscript. GM contributed to various aspects of the statistical analysis, including how to use the DGLM in a meaningful manner, as well as how to interpret the results of the simulation study. These contributions significantly guided the direction of our study. AEL oversaw the entire analysis, designed the simulation study, designed the procedure for simulating vQTNs, and wrote and edited the manuscript.

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Correspondence to Alexander E. Lipka.

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Associate editor: Yuan-Ming Zhang.

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Murphy, M.D., Fernandes, S.B., Morota, G. et al. Assessment of two statistical approaches for variance genome-wide association studies in plants. Heredity 129, 93–102 (2022).

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