Schematic depiction of the MORIA merger tree format. Unlike conventional formats, a MORIA tree is represented by two-dimensional arrays spanning the number of halos and the number of snapshots. White fields represent times when the given halo did not exist. Time flows from right to left, with gray arrows indicating the descendant of each halo. When a halo ends, it either has a descendant at the final snapshot or merges into another halo. The ordering of the tree is determined by those mergers (see Section 4.5 for details).