Leaf microbiome experiments
Brachi B, Filiault D, Whitehurst H, Darme P, Le Gars P, Le Mentec M, Morton TC, Kerdaffrec E, Rabanal F, Anastasio A, Box MS, Duncan S, Huang F, Leff R, Novikova P, Perisin M, Tsuchimatsu T, Woolley R, Dean C, Nordborg M, Holm S and Bergelson J  performed a GWAS for the leaf microbiome in A. thaliana. The study included a panel of 198 A. thaliana accessions planted with 2 replicates in the spring of 2012 and 2013 at four sites located in Ullstorp (lat: 56.067, long: 13.945; SU in short), Ratchkegården (lat: 55.906, long: 14.260; SR in short), Ramsta (lat:62.85, long 18.193; NM in short), and Ådal (lat: 62.862, long 18.331; NA in short). The bacterial and fungal abundance of each leaf sample was measured by16s/ITS rRNA gene sequencing. Accessions were genotyped by a high-throughput sequencing technique, obtaining 186,161 SNPs after quality control. For a detailed description of experimental design, sampling strategy, microbial sequencing, and SNP genotyping, refer to Brachi B, Filiault D, Whitehurst H, Darme P, Le Gars P, Le Mentec M, Morton TC, Kerdaffrec E, Rabanal F, Anastasio A, Box MS, Duncan S, Huang F, Leff R, Novikova P, Perisin M, Tsuchimatsu T, Woolley R, Dean C, Nordborg M, Holm S and Bergelson J .
In this study, we choose 200 bacterial OTUs and 200 fungal OTUs at the top-abundance from each site for microbial network inference. These numbers of OUTs account for the top 95.89% of bacterial relative abundance and top 95.50% of fungal relative abundance, respectively, (Supplemental Table 1). OTU1-200 are listed as bacteria and OTU200-400 as fungi. Brachi B, Filiault D, Whitehurst H, Darme P, Le Gars P, Le Mentec M, Morton TC, Kerdaffrec E, Rabanal F, Anastasio A, Box MS, Duncan S, Huang F, Leff R, Novikova P, Perisin M, Tsuchimatsu T, Woolley R, Dean C, Nordborg M, Holm S and Bergelson J  measured fecundity for each plant, whose genetic architecture is disssected using both SNPs and microbes.
Quantitative microbial networks
Using Wu’s descriptors, we reconstruct and visualized 400-node interaction networks based on mutualism, antagonism, aggression, and altruism, for eight year-site experiments. OTU abundance is chosen as the trait that determines the strategies of microbial interactions. We calculate the relative OTU abundance of primary, secondary leaders, tertiary leaders and followers in the mutualism network, the relative OTU abundance of two antagonists in the antagonism network, the relative OTU abundance of hawks and doves in the aggression network, and the relative OTU abundance of altruist and egoists in the altruism network . Different members were shown by the metric of colors.
Hub taxa are identified from each type of microbial network using the R igraph package. We calculate the degree of each node in a network. To reduce the bias, we statistically identify the hub taxa with the highest degree and closeness centrality [13, 37]. Meanwhile, six network indices, including connectivity (Con), closeness (C(u)), betweenness(B(u)), eccentricity (E(u)), eigencentrality (G(u)), and Pagerank (P(u)) are calculated, as described previously .
Mapping QTL networks underlying microbial networks
We apply a likelihood approach for detecting significant SNPs that are associated with each of the six network properties for eight year-site experiments . We further use bnlearn R package to reconstruct Bayesian genetic networks among the significant SNPs detected. SNP-SNP interactions are visualized by the plot function. Hub QTLs, playing a key role in genetic networks, are identified.
We implement path analysis to test whether a significant SNP affects plant fecundity directly or through an indirect pathway of microbial interactions. Let g denotes the genotype, y denotes the network property, and z denotes the fecundity. We calculated the Pearson correlation between y (continuous) and z (continuous) across individuals, denoted as ryz. Let rgy and rgz denote the correlations between g and y and between g and z, respectively. We calculate the path coefficients Pz←g from the equation
rgz =Pz←g + Pz←yrgy, with Pz←y = ryz,
where Pz←g is the direct path from g to z and Pz←yrgy is the indirect path through microbial networks.