The genome-wide vQTL analysis was conducted using the Levene’s test implemented in the software tool OSCA (http://cnsgenomics.com/software/osca) (61). The Levene’s test used in the study [also known as the median-based Levene’s test or the Brown-Forsythe test (31)] is a modified version of the original Levene’s test (30) developed in 1960 that is essentially a one-way ANOVA test of the variable zij=yijyi, where yij is the phenotype of the jth individual in the ith group and yi is the median of the ith group. The Levene’s test statistic(nk)(k1)i=1kni(zi.z..)2i=1kj=1ni(zijzi.)2approximately follows an F distribution with k − 1 and nk degrees of freedom under the null hypothesis, where n is the total sample size, k is the number of groups (k = 3 in vQTL analysis), ni is the sample size of the ith group, i.e., n=i=1kni,zij=yijyi˜,zi.=1nij=1nizij, and z..=1Ni=1kj=1kzij.

The experiment-wise significance level was set to 2.0 × 10−9, which is the genome-wide significance level (i.e., 1 × 10−8) (38, 39) divided by the effective number of independent traits (i.e., 5.00 for our 13 traits). The effective number of independent traits was estimated on the basis of the phenotypic correlation matrix (note S4) (66). To determine the number of near-independent vQTLs, we performed an LD clumping analysis for each trait using PLINK2 (--clump option with parameters --clump-p1 2.0e-9 --clump-p2 2.0e-9 --clump-r2 0.01 and --clump-kb 5000) (63). To visualize the results, we generated the Manhattan and regional association plots using the ggplot2 package in R.

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