This paper poses a problem for traditional phylogenetics: The identity of organisms that reproduce through fission can be understood in several different ways. This prompts questions about how to differentiate parent organisms from their offspring, making vertical gene transfer unclear. Differentiating between parents and offspring stems from what I call the identity problem. How the problem is resolved has implications for phylogenetic groupings. If the identity of a particular asexual organism persists through fission, the vertical lineage on a phylogenetic tree (...) will split differently than if the identity of an organism does not survive the fission process. (shrink)