Enforcing consistency of multiple alignments. When aligning more than two sequences, care must be taken that new local alignments are compatible with existing alignments. (a) If the two alignments in shaded blocks are already made, the underlined sequence fragments cannot be aligned. (b) The sequence fragments when one local alignment has already been made, and the next (dotted lines) is about to be made. (c) The sequence fragments after the second local alignment has been made. At each stage, each sequence fragment has limits on what other fragments it can be aligned with in every other sequence. For example, in (b), the fragment 0.2 in seq 2 can only be aligned with fragments > 0.1 in seq 1, but the fragment 0. in seq 3 can be aligned with any part of seq 1. After the local alignment is made in (c), the frag 0.1 in seq 3 inherits the more stringent limit from its paired frag in seq 2: it can only be aligned with seq 1 > 0.1, and this limit is moreover "propagated" right to seq 3 frag 0.2. Likewise, the "right-hand" limits (none in this case) are propagated to seq 3 frag 0.0 which means, in this case, that seq 3 frag 0.0 can be aligned to any fragment in seq 1.