In the case of the HSC model, we can find both situations in the same duplicated region, creating a complex pattern of nucleotide variation and LD along the duplicates.
Same as for WHSC1, WHSC2 and LETM1, some of our novel candidates lie in the same duplicated or deleted regions (Supplementary Table 5).
In the other 27 regions corresponding to the eight other blocks, resistance-associated markers aligned with neighbouring intervals of the A. thaliana sequence suggesting that these resistance-associated are not strictly located in the same duplicated region (Additional file 7).
Since in the optimal sequence x i generates y1 in the same duplicate operation that generates y j from x i +1, we have OPT i (x, y1 y j,| y |) = OPT i +1 x, y j,| y |).
In particular, we would like to dissect apart the molecular changes in the protein-coding region that occurred when persistent duplicates were young (an early stage of duplicate gene evolution) from those changes that occurred in the same duplicates after they became old (a later stage of duplicate gene evolution).
Either: Case 1: y1 was the last (or rightmost) character in the substring of x that was copied to produce y1, (see Fig. 4), or Case 2: x i +1 is also copied in the same duplicate operation as x i, possibly along with other characters as well (see Fig. 5).
To compute the latter, recall that since x i and x i +1 are copied in the same duplicate operation, the number of duplicates necessary to generate y1 y j,| y | using x i and x i +1 is equal to the number of duplicates necessary to generate y j,| y | using x i +1, namely d i +1 x, y j,| y |), (see Fig. 5 and Eq. 2).
Another gene, the one corresponding to e_gw.10.14.1 in amphioxus (V2_158 EFEMP/FBLN) might have been duplicated in the same duplication event as gpa and gpb.
(Note that, throughout, all figures consider the case in which C and A retain the same duplicate. For each case there is an equivalent case in which C and B (but not A) retain the same duplicate).
Interestingly, the 3 trypsin inhibitor genes were located in the same clone, and tandemly duplicated sequences were found in OnTI2 and OnTI3.
In fact, some of the same drawings are duplicated within that patent and this most recent one (like the image displayed on the right).
