Which is the correct formulation?
I wouldn't call either one incorrect or less correct than the other. However, you two are probably not the only ones who could either find the first form not very readable (or not "stylish") or misinterpret the second one. I would thus avoid both forms, and I would try to modify the sentence to improve readability and avoid possible misinterpretations.
For example, if the referenced paper was the first to propose that division, you can avoid the issue altogether by writing:
Following/According to (Marler & Mitani, 1988), we can also divide calls into stereotyped (discrete) and graded (continuous)
Or you can avoid the parentheses by writing (I don't know the topic, I'm just interpreting):
We can also divide calls into stereotyped or graded (Marler & Mitani, 1988): stereotyped calls are discrete in character, whereas graded ones are continuous"