Supporting Information Legends Figure S1. Structure of rice chromosomes. Centromeres are indicated as indentations between the two chromosome arms. Corresponding colours indicate homologous chromosomal segments that originated from the WGD. Of the ancient duplicated chromosome pairs, only Os11 and Os12 still have a very similar size and position of the centromere. Note that chromosomes 3, 7 and 10 are derived from 2 ancestral chromosomes. The same is the case for chromosomes 2, 4 and 6. Figure S2. Divergence time estimates for the WGD and individual grass species. For each estimate, individual estimates for gene pairs (ohnologs in a. and orthologs in b.-d.) were calculated and the distribution of the estimates was plotted. As a measure for how narrow the divergence time distribution curve is, we calculated the interquartile range (IQR), i.e. the range where the middle 50% of the divergence time estimates for individual genes lie. Values within the IQR are colored black, those outside are gray. Results of divergence time estimates are also summarized in Table 1. Figure S3. Sequence alignment of the terminal region of O. sativa chromosomes 11 and 12. The segment shown covers the region of the putative recombination breakpoint. Note that sequence conservation drops visibly in the region of the first intron of gene Os11g01200 which we interpret as the point where recombination between the homeologous chromosomes occurred. Figure S4. Comparison of the region of the second recombination breakpoint between O. sativa chromosomes 11 and 12. Sequences that could be aligned are connected by shaded areas. Genes are indicated by black boxes. Blue labels indicate genes in forward orientation, while red labels indicate genes in reverse orientation. The recombination breakpoint (red arrow) is characterized by a distinct drop in sequence conservation. To the left of the breakpoint (i.e. distal), gene content is very similar, while to the right (i.e. proximal), gene content differs strongly and only few sequence segments can be aligned. The recombination breakpoint is located in the promoter region of genes Os11g04760 and Os12g04540. Figure S5. Comparisons of the terminal 3 Mbp of chromosomes 11 and 12 in O. sativa and O. barthii. Sequence alignments were done in segments of 10 kb in the terminal 3 Mbp of both chromosomes. a. Alignment of chromosome 11 and 12 segments from O. sativa shows overall good sequence colinearity within the terminal ~2.5 Mbp. b. In contrast, alignment of chromosome 11 of O. sativa with chromosome 12 from O. barthii identifies two inversions approximately at position 1.2-1.5 Mbp. c. The same is found in a comparison of chromosome 12 from O. sativa and O. barthii and in (d) a comparison of chromosomes 11 and 12 from O. barthii. This indicates that the inversion events occurred in the O. barthii lineage. e. Boxplots of distributions of sequence identities in chromsomes 11 and 12 between O. sativa and O. barthii done in segments of 10 kb. Both comparisons resulted in a mean sequence identity of 98.7%. Figure S6. Topologies of phylogenetic trees of ohnologs and orthologs in grasses. The left side shows the evolutionary pathways of genes which were duplicated by the ancient whole genome duplication (WGD) and subsequent sequence exchange. The left side shows outcomes for duplications in one or both species. The right side shows the corresponding phylogenetic trees. The different combinations of duplication events result in tree types 1 through 3 (T1 through T3, see main text and Supplementary Figures 5 and 6). Figure S7. Phylogenetic trees of ohnolog/ortholog tetrades from A11/A12 group chromosomes from Brachypodium and rice. For each tetrad, closest homologs from Arabidopsis were used as outgroups. In cases where the four grass genes yielded different Arabidopsis homologs, all those homologous were included. The numbers at the forks indicate the number of times the group consisting of the species which are to the right of that fork occurred among the trees, out of 100.00 trees. Figure S8. Examples of molecular dating of gene pairs originating from an ancestral whole-genome duplication (WGD). To test whether inter-homeolog sequence exchange is a general mechanism, we identified duplicated chromosomal segments that originate from the ancestral WGD from six species. The x-axis indicates the gene number along the chromosome (proxy for the physical position). The yaxis indicated the divergence time of the gene pairs. Each data point represents a running average over 20 genes. The structure of the compared chromosomes is drawn underneath the plot. Approximate positions of centromeres are indicated as black ovals. Divergence time estimates of WGD gene pairs are more or less even along the chromosomes, oscillating around the estimated time of the underlying WGD approximately 50 million MYA. a. WGD gene pairs from rice chromosome 2 (Os02) vs. Os06/Os04. b. WGD gene pairs from sorghum chromosome 2 (Sb02) vs. Sb10/Sb06. Figure S9. Identification of groups of gene pairs that arose from the WGD. Genes of one chromosome are plotted against those of its homeolog, using the gene number as a proxy for the physical position. Blastn hits with E-values <10E-10 are indicated as dots. Our software divides then plot into squares of user-defined size. The number of gene pair hits per square is then scored (indicated by the colour code). This allowed convenient identification of large duplicated segments. Table S1. Gene onthology mapping of A11/A12 genes. Table S2. Gene ontology identifiers of A11/A12 genes conserved in rice, sorghum and Brachypodium.