Gene tree parsimony for incomplete gene trees: addressing true biological loss

However, the standard calculation for the number of losses can be incorrect when incompleteness is due to true biological loss! Consider the simple example gt = ((a, b), c) and ST = ((a, (b, d)), c). Under the standard formula, Lstd(gt, ST) = 0, since ST(gt) = gt. Under the assumption that incompleteness is due to true biological loss, the genome for d does not have the gene. Because d is sister to b and all the other taxa have the gene, the gene must have been present in the parent of d, and lost on the branch leading to d. Therefore, the standard formula for the number of losses can be incorrect when gene trees are incomplete due to gene birth and death (i.e., true biological loss)