According animalism, Pete the person continues to exist just in case Pete the human animal continues to exist. The animal Pete is presumably to be identified with a particular Homo sapiens. Thus suffering a stroke which shuts down all your biological functions will kill you, but suffering a stroke which merely leaves you without higher cognitive functions will not.
Skip this paragraph if you’ve studied philosophy. Animalism is contrasted with a variety of views, including psychological continuity theory, according to which Pete the person continues to exist if Pete’s mental states continue to exist*. This allows, unlike animalism, for the possibility of brain transplants, human/machine conversion and surviving teleportation. A relatively new and increasingly popular theory is conventionalism, according to which whether or not x from an earlier time is the same person as y from a later time depends on certain practices and conventions.
The majority of cells in your body are not Homo sapiens cells. They belong to other species, mostly microbial. What is more, many of these microbial cells are not dead weight, but play critical roles in the functioning of your body. The most famous of these is assistance in digestion, but there are many others besides. Some of these functions are vital; among other things they assist greatly in the digestion of carbohydrates and help in the creation of immunity.
The question arises, is biological communitarianism a more plausible viewpoint than animalism? Biological Communitarianism is the view that identifies you with the multi-species biological community which makes up your body. Thus survival is defined as the continuation of the biological community. I suspect biological communitarianism it is more plausible than animalism. Granted the relevant biological community is in some sense structured around its Homo sapiens component, but it is hard to see why this should be the decisive factor.
The two theories diverge at certain points. For example, imagine that on twin earth there is a species which functions in a very similar way to Homo Sapiens, but has a very different underlying genetics. Call it XYZomo Sapiens. Further let us imagine that this species is in some weird way invasive. If one is transported to twin earth, one will become infected with this species. With great precision it will kill off everything from your neurons to your skin cells, only to slot in a cell which does all of the same things that your old Homo Sapiens cell did. For example, it will kill off a single neuron, only to immediately replace it with a new neuron, which quickly rebuilds the connections of the old cell. Note that the community as a whole continues to function. According to animalism, you die and are replaced by a XYZomo Sapiens that is in some respects similar. According to biological communitarianism, you live, and XYZomo Sapiens takes over the role in the community that was once played by Homo sapiens**.
Philosophers who hate unlikely thought experiments will not be fans of the preceding paragraph. But note that unlike most thought experiments it’s not trying to establish that one candidate view is stronger than the other, but merely that the views at least come apart in some metaphysically and perhaps even nomologically possible situation. As such it does not involve any intuition mongering based on far flung possibilities.
As neither a biological communitarian, nor an animalist***, I think that biological communitarianism might provide us with an interesting platform which to criticise both, if only very mildly. Part of the allure of animalism was its sharp, clean boundaries. But the biological need not be much clearer cut than either the psychological or the conventional. Biological communitarianism gains in biological plausibility but has softer edges than animalism because it is more difficult to point to where the community ends.
*More correctly, if there are appropriate relations of causation and similarity between the mental states of some earlier person X and some later person Y.
** As the reader may perhaps anticipate, this thought experiment was inspired by a terrifying nightmare I once had.
*** My own view is conventionalist psychologism. Our conventions set whether or not persons survive over time, and it just so happens that our actual conventions are based on psychological continuity.