In the case of the Mouflon sheep, that is correct. In the case of plants and grasshoppers, it often is a new species in literally a single generation. They would not be the original species, and are not reproductively compatible.
Depends, as I just explained.
Looking back in time, however, I’m not sure we can even distinguish these two cases from genetics. The data would end up looking essentially the same.
However, from genetics alone, we would not be able to easily distinguish (it seems) between the grasshopper and Mouflon sheep scenarios.
Only within a time range. However, we are also looking at the “human lineage” (see Dennis’s claim #2), which include all our ancestors even before they are Homo sapiens.
Right now, we are looking at evidence against a single couple origin within the last 500 kya. With further analysis (e.g. using PSMC), I suppose that might increase up to about 700 or 800 kya, but we do not know for sure yet.
However, before that point, say at about 750 kya or 2 mya, I’m not sure we can rule out a single couple bottleneck in our ancestors. Those are interesting dates too. 750 kya is when Homo sapiens, Neanderthals and Denisovans (for which we only have a knuckle) share a common ancestor. This group of species (or subspecies if they are the same species) appear to be the only hominids with hyoid bones, which might be a marker for modern linguistic capability. 2 mya is when Homo erectus arises and becomes cosmopolitan, and here is where we think clothing might arise, as does language/tools beyond other animals, and more.
At either transition, ignoring theology entirely, was their a tight bottleneck? The consensus is, right now, that there was a very tight bottleneck, at least 2 mya. Perhaps not consensus, but definitely a live option when I have talked to anthropologists is a bottleneck 750 kya. How tight would those bottlenecks be? I’m not sure we can know from extant evidence.
@Christy, these are great questions. Thanks for putting them forward. Hopefully this clarifies where it seems the science stands.