Because I get so many questions about this step in one of my published papers. (Well more accurately, my PI gets questions about this step and he sometimes forwards them on to me for an answer). The paper referred to in this guide is this one.
There are two completely different steps to reconstructing maize subgenomes: 1) putting together ancestral chromosome pairs 2) grouping one copy of each ancestral chromosome together into subgenome 1 and the other copy of each ancestral subgenome 2.
Ancestral chromosome pair reconstruction:
This step hinges on a single assertion backed up by a number of papers: inversions and other forms of within chromosome rearrangements significantly outnumber translocations (movement of sequence from one chromosome to another). This observation has been backed up by a number of previous studies.
Give that fact (within chromosome rearrangements are more common than between chromosome rearrangments), when two different pieces of the same maize chromosome are orthologous to different parts of the same sorghum chromosome, we can say that those parts of the maize chromosome originated from the same copy of that sorghum chromosome in the twenty chromosome (two equivalent to each single chromosome of sorghum) tetraploid ancestor of maize.
A good example of this is the comparison between maize chromosome 1 and sorghum chromosome 1 in Figure 1 of the paper you are inquiring about. There are actually two separate segments of maize chromosome 1 which are orthologous to different parts of sorghum chromosome 1. In theory each segment could have come from a different copy sorghum chromosome 1 in the tetraploid maize ancestor and were combined on one maize chromosome through translacations, but the most parsimonious explanation is that both segments came from a single maize chromosome.
Once we reassemble that first copy of sorghum chromosome 1 (the two pieces on maize chromosome 1), we know that any remaining pieces of the maize genome orthologous to sorghum chromosome 1 must have come from the second copy of that chromosome in the tetraploid ancestor of maize. In this case there is one piece on maize chromosome 5 and one piece on maize chromosome 9, but since we have already reconstructed one whole copy of the chromosome, the only source for these two segments is the second chromosome copy.
Repeat this logic 9 more times and you have reconstructed ten pairs of ancestral maize chromosomes, just like we did in the paper. (And as cited in our PNAS paper, we weren’t the first to come up with this idea. Before the maize genome was even complete or the sorghum genome was published, another group was able to derive approximately the same ten chromosome pairs by comparing a genetic map of maize to the rice genome: http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.0030123 )
Assigning ancestral chromosomes to subgenomes
In this step we examined the number of maize-sorghum orthologs shared between each maize ancestral chromosome and the orthologous sorghum chromosome. This is figure 2 from our 2011 PNAS paper. As you can see in that figure, for each pair of maize ancestral chromosomes, one copy retains a lower percentage of genes found in sorghum along its entire length and the other copy retains a higher percentage of genes found in sorghum along its entire length. (Too avoid being thrown off by new/transposed genes in sorghum we excluded sorghum genes without orthologs in rice, but you can get the same results without that filtering step, the main difference is that the % retained is lower.)
The maize ancestral chromosome copy which retained a higher percentage of genes also found in sorghum was assigned to maize subgenome 1 and the maize ancestral chromosome copy which retained a smaller percentage of genes also found in sorghum was assigned to maize subgenome 2.
Then we went back and colored maize subgenome 1 blue in figures 1 & 2 and maize subgenome 2 red in those same two figures. Which I think is one of the things that confuses people. The red and blue color coding in Figure 1 shows a distinction we didn’t actually make until after the analysis shown in Figure 2.
Schnable, James C., Nathan M. Springer, and Michael Freeling. “Differentiation of the Maize Subgenomes by Genome Dominance and Both Ancient and Ongoing Gene Loss.” Proceedings of the National Academy of Sciences 108, no. 10 (March 8, 2011): 4069 –4074.