Fig. 2

Simulation scheme for the Recursive scenario (Fig. 1). a Real input data comprises p genotypes (\({\mathbf{G}}\) matrix) and k taxa abundances (\({\mathbf{B}}\) matrix). SNPs in grey are neutral, those in red act directly on the phenotype y, and those in yellow/orange influence some OTU abundances (marked in magenta color in \({\mathbf{B}}\) matrix); abundances in blue are not genetically controlled. b Given simulated effects, a genotypic value for abundance is obtained via Eq. (2). To obtain the required heritability, abundances in magenta are reordered; to simplify visualization, high abundances (represented by a darker color) are associated with genotype ‘1’. A single SNP is shown as causative for both OTU but there is no limit in practice. c The phenotype is simulated by adding the genome and the microbiome contributions plus a residual. d The general causal diagram