In the philosophy of biology it has been claimed many times that a popular position regarding the question of what species are, among biologists, is cladism. For my current purposes, the defining trait of cladism is captured in the following quote:
According to cladism, a species becomes extinct whenever it sends forth a new side species. (LaPorte 2004, 54)
So, for example, if Homo floresiensis is truly a species, and it derives, via a speciation event, from Homo sapiens, then, after the speciation, there is no Homo sapiens: there is Homo floresiensis and a new species, very similar to sapiens. In general, whenever there is speciation the mother species disappears.
I am under the impression that this description of the situation is not the one most mainstream biologists would endorse. I take it that a more common description would be one under which, if a number of Homo sapiens get isolated in an island and go on to form a new species, Homo sapiens exists both before and after this speciation event. I would like to know whether cladism, described as above, is really a popular position, or whether I am right about what most biologists would say about the relation between floresiensis and sapiens.
It might also be that biologists declare themselves cladists when explicitly theorizing about the nature of species, but fall back to a less extreme form of cladism in the actual practice. Evidence in favour of or against this possibility (coming from biology, not the philosophy of biology) would also be appreciated.
As Noah has pointed below, what I have called extreme cladism might be very far from cladism, as usually interpreted. This is precisely the kind of claim I would like to see substantiated.
LaPorte, Joseph. 2004. Natural Kinds and Conceptual Change. Cambridge University Press.