What you are describing is known as the Biological Species Concept. It's one of at least 28 species concepts that have been proposed in the scientific literatur

What you are describing is known as the Biological Species Concept. It's one of at least 28 species concepts that have been proposed in the scientific literature -- they were surveyed in a review paper whose reference irritatingly escapes me. Anyway, the BSC is not the only game in town (and is particularly useless to those, like me, who are palaeontologists.)