Genetic differentiation is correlated with spatial separation
To assess the biogeographic patterns of nodule populations, we calculated the hierarchical F ST of samples at different population levels. The top level was management, where we compared organic fields (DKO) versus field trial sites, whereas plot and field were the lowest levels for the field trials and DKO samples, respectively (Figure 1 and Figure S1 ).S ignificance was tested by permutation. For example, when comparing organic (DKO) versus conventional (field trial) management, samples were moved from one management to the other to check if this generally resulted in a lower F ST. For each management type, we then tested for the effect of country for the field trials or groupings for the DKO samples. We observed no differentiation between the conventionally managed sites (DK+F+UK) and the organic DKO population. The reason is that there is no overlap in Rhizobiumpopulations between the UK and DK+F trial sites. Therefore the difference between the three trial sites is as high as the difference between trial sites and organic fields. To test the effect of groupings and field/plots on the differentiation, we then analysed field trial sites (DK, F, and UK) and the organic fields (DKO) separately.
For the field trial subset, country (DK, F, and UK), had a significant effect (Table 2 ). The block design and clover genotype (Figure S1 ) did not have any effect onF ST with the exception of nodA , where there was a small but highly significant effect. Permuting the plots within the individual field trial sites showed that the plots are also significantly associated with Rhizobium population differentiation. Furthermore, we added the block design and clover genotype level to the test (Figure S1 ) and found that both block and clover genotype had a small but significant effect onnodA differentiation when samples were permuted within the same country (Table 2 ).
In the DKO subset, the grouping (DKO1, DKO2, DKO3, DKO4, DKO5, DKO6), based on geographic proximity (Figure 1 ), had a significant effect on differentiation for the core genes, recA andrpoB , but not for the accessory genes, nodA andnodD (Table 2 ). Field had a significant effect for all four genes within the DKO subset. We concluded that the grouping level was a valid way to cluster the samples for the cores genes, and used the DKO subset to calculate pairwise F ST between the six DKO clusters (Figure 1 and Figure 4 ). The fields differ in geographic placement, while the clover genotypes and the field management were similar between sites, allowing us to explore the geographic differences in nodule population within a homogeneous set of managements (Table S1 ).
Pairwise F ST between the DKO clusters displays a significant correlation between F ST and geographic distance. The overall F ST is highest for the two core genes, and the correlation is highest and most significant for rpoB (Figure 4 ). The level of genetic differentiation between populations increased with distance, with the effect being most pronounced for chromosomal core genes, indicating that the core gene population composition is related to geographic origin. Since the samples are not independent, we performed a Mantel test with 5000 replicates to test if the correlation betweenF ST and geographical distance is significantly different from randomised datasets. Three genes, rpoB ,recA , and nodA , have a significant correlation between genetic differentiation and geographical distance (rpoB : R2=0.737, p-value=0.002, slope=6.310e-07; recA : R2=0.617, p-value=0.019, slope=4.156e-07; nodA : R2=0.632, p-value=0.047, slope=1.748e-07), butF ST and geographical distance are not significantly correlated for nodD (nodD : R2=0.420, p-value=0.115, slope=7.058e-08).