(A) A matrix

with the consecutive ones property. (B) The corresponding PQ-tree

, where P-nodes are rounded and Q-nodes are square.

and

are two possible C1P orderings for

, among 13824 possible C1P orderings.

is not a C1P ordering for

: columns 6 and 7 need to be consecutive as they are consecutive children of a same Q-node. (C) An equivalent representation of

which highlights all ancestral genome architectures that correspond to C1P orderings for

: each row corresponds to a chromosomal segment represented by a child of the root, two glued blocks have to be adjacent in any ancestral genome architecture and sets blocks that float in the same box have to be consecutive in any genome architecture but their order is not constrained. Here we see three ancestral chromosomal segments: the first one, which contains markers 1 to 4 is totally ordered; the second one contains markers 5 to 8, with only constraint that markers 6 and 7 are adjacent; the third one contains markers 9 to 14, with 9 and 10 being adjacent, 11 being adjacent to a block that contains 12, 13 and 14 with no order between these three markers. Hence,

is a possible order for this last segment, but not

as 11 is inserted inside the block that contains 12, 13 and 14. All 13824 possible C1P orderings (possible ancestral orderings) are visible on this representation.