There are actually three ways to define a species. The morphological species concept, the biological species concept, and the phylogenetic species concept. Species that can interbreed satisfy the biological species concept but there seems to be more consensus among biologists that constructing a phylogeny is the better way to define species.

This somewhat problematic however because there is rarely enough data about a species to create a complete phylogeny of a species and its common ancestors. Additionally, it is thought that this concept would lead to the naming of many more species than we presently recognize. If you’re interested in this kind of thing I would encourage you to check out the link below!

http://www.askabiologist.org.uk/from_the_lab/species-concept...