On a more serious note: philosophers who use a process-based ontology/metaphysics would be a little more careful with words: you're defined by your position in given historical processes. Some of these, of course, are initiated by you, hence 'what you do.'
So in the case of a zebra, it's a zebra because it's genesis lies in a historical process: zebras giving birth. If you have two parents who are zebras, then you're a zebra. The first zebras became zebras once they are unable to sexually reproduce with another species, I forget the exact biology term here. For another example, I'm a citizen of the United States because I'm part of a historical process by which people are born in a particular space, both geographical and political, over a certain time period. I don't possess some sort of intrinsic US-ian property.
If you're interested in this kind of thing, Whitehead, Deleuze, and more recently, de Landa (who I adapted the zebra example from) are all materialists who replace identity with process.