Software and datasets

Model and software selection

Population structure is one of the most important causes of spurious association. Population structure matrix [4] or principal components [29] were incorporated as covariates to reduce spurious associations using general linear models (GLM) as implemented in PLINK [14], TASSEL [15], and GenABEL [30]. These software packages are intensively used due to computationally efficient GLM and popularity (Table 1). Multiple functions, such as file format conversion and linkage disequilibrium analysis, also contribute to their popularity [14,15].

Table 1. GWAS models and software implementations*

*Sorted by publication year and citations by year as of March 12, 2023. GWAS models include general linear model (GLM), mixed linear model (MLM) [5], compressed MLM (CMLM) [12], enriched CMLM (ECMLM) [38], settlement of MLM under progressively exclusive relationship (SUPER) [39], multiple loci mixed model (MLMM) [36], fixed and random model circulating probability unification (FarmCPU) [37], and Bayesian-information and linkage-disequilibrium iteratively nested keyway (BLINK) [26].

#equivalent to the approach of genomic best linear unbiased prediction (gBLUP) in genomic selection [40–42].

Besides population structure, another addition was introduced to control the unequal relatedness (kinship) among individuals within subpopulations using mixed linear models (MLM) [5]. Individuals’ total genetic effects are fitted as random effects with variance and covariance structure defined by the kinship derived from all genetic markers. Multiple algorithms were developed to improve the computing efficiency of MLM, including EMMA [31], P3D [12] (or EMMAx [32]), FaST-LMM [34], BOLT-LMM [13], and GEMMA [35]. These algorithms have the same statistical power as the regular MLM originally solved by the expectation and maximization algorithm [15]. MLM was also enhanced to improve statistical power by accounting for the confounding factor between testing markers and random individual total genetic effects, which causes false negatives. The models with improved statistical power include compressed MLM (CMLM) [12], enriched CMLM (ECMLM) [38], and FaST-LMM-Select [34] or SUPER [39]. FaST-LMM-Select and SUPER are equivalent. Some of the improved MLM models were implemented in software packages with multiple functions, including TASSEL [15] and GAPIT [16,27,28].

To further subtract the confounding between testing markers and the random individual genetic effects to improve statistical power, associated markers were introduced as covariates in the multiple loci mixed model (MLMM) [36]. The random individual genetic effect and testing markers were placed in a random effect model and in a fixed effect model separately (FarmCPU) [37]. Finally, the random individual genetic effects were completely removed in the BLINK model using GLM only [26]. BLINK uses two GLMs iteratively; one selects the associated markers as covariates with maximization of Bayesian information content, and the other tests markers one at a time with the selected associated markers as covariates. By doing so, BLINK not only retains GLM computing efficiency but also gains statistical power, higher than the other multiple loci models, including FarmCPU (Graphical overview). Some of the multiple loci models were implemented in software packages with multiple functions, including GAPIT [16,27,28] and RMVP [17].

Some of the models and software packages were compared for computation efficiency and statistical power against false discovery rates or type I errors (Graphical overview). GAPIT implemented the most models, from GLM, MLM, to SUPER for the single locus models and from MLMM, FarmCPU, to BLINK for the multiple loci models. The computing speed and statistical power can be examined by less than a handful of lines of R code (Box 1). The first three lines import the GAPIT source code, genotype data, and the genetic map from the GAPIT demo data (http://zzlab.net/GAPIT/data). The data contain 281 maize inbred lines and 3,093 single nucleotide polymorphisms (SNPs). The middle three lines set random seed and simulate phenotypes out of 40 SNPs sampled from the first five chromosomes as quantitative trait nucleotides (QTN) with heritability of 70%. The remaining chromosomes serve as a reference so that false positives can be easily identified. The last line calls GAPIT to conduct GWAS with seven models, including FarmCPU and BLINK. The execution takes approximately five minutes on a standard laptop. Some models consume more time than others. Users can assess the computing times of specific models by examining the result files, e.g., Manhattan plots, in the R working directory.

Box 1. R code to import GAPIT and genotype data, simulate phenotypes, and conduct GWAS

GAPIT also combines all the Manhattan plots together for comparison (Figure S1). GLM identifies two QTNs based on the 5% type I error after Bonferroni multiple correction. MLM identifies one, CMLM identifies two, SUPER and MLMM identify seven, FarmCPU identifies eight, and BLINK identifies eleven. Users can replace the demo genotypes and genetic maps with their own, change the number of PCs, specify models, and conduct multiple replicates with different random seeds to achieve a more robust evaluation of the statistical power over different models on specific data sets.

Real case data

Rice 3000 genome project data (http://ricediversity.org/data/index.cfm) were used for real case analysis. This dataset includes 700K SNPs and 847 accessions published with the GWAS results of rice grain length [43]. The genotype data in PLINK format can be downloaded from http://ricediversity.org/data/sets_hydra/HDRA-G6-4-RDP1-RDP2-NIAS-2.tar.gz. The map file can be downloaded from http://ricediversity.org/data/sets_hydra/HDRA-G6-4-SNP-MAP.tar.gz. The phenotype data file can be downloaded from http://ricediversity.org/data/sets_hydra/phenoAvLen_G6_4_RDP12_ALL.tar.gz. The map version of genotype data is Rice Genome Project version 7. The genome position of known genes was searched from the phytozome database (https://phytozome-next.jgi.doe.gov/).

Procedure