https://en.wikipedia.org/wiki/Laboratory_experiments_of_speciation

Such sub-speciation definitely happens - that's how we got the variety of animals with different traits within a species (for example all the subspecies of bears or dogs there are).

An accumulation of small changes that happen in a short time leads to large changes over a long time.

That's an assertion. Is there empirical evidence for that? Has anyone observed it? It's one thing to change color and thickness of the coat or the length of the beak, but it doesn't follow big complex changes which require simultaneous mutation of multiple interdependent systems of the organism are possible through the process of adaptation.

By whether or not the populations can interbreed. If they can interbreed they are the same species. If they can not interbreed they are separate species.

Horses and donkeys interbreed. Are they the same species? There are many examples of hybridization.