Occupancy frequencies in additive profiles. Here we show an alignment of profiles X and Y giving Z. A column C of indels (shaded background) has been inserted at position x in order to align X to Y. To compute the number of gap-extensions in column x of Z, three cases must be considered: (1) a gap-extension in the corresponding column of Y, (2) a gap-open in the preceding column of X, and (3) a gap-extension in the preceding column of X. By enumerating all such cases, it is straightforward to compute the occupancy frequencies in Z from the occupancy frequencies of X and Y, plus the alignment path.