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For estimating OTU heritability, the core microbe counts were quantile-normalized and were then provided to genetics complex trait analysis (GCTA) to estimate phenotypic variance explained by all SNPs with genome-based restricted maximum likelihood (GREML) method (56, 57), with farms as qualitative covariates and the first five GRM PCs and diet components as quantitative covariates, following the GCTA command gcta64 --reml –pheno [phenotype_file] –mpheno [phneotype_index] --grm --autosome-num 29 –covar [farms_covars_file] --qcovar [quant_covariates_file].

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