There are many variations in hair growth patterns. These don't amount to diseases or abnormalities for the most part. People with bare spots like the ones you describe can't grow acceptable-looking beards. Medications don't help, as far as I know. I doubt that Rogaine would be of use. I also doubt it's alopecia areata, and even if it is, treatment options are poor. If the bare areas are new, then perhaps it is alopecia, and it may regrow spontaneously. If it's always been this way since puberty, then there really isn't anything you can do that I know of. Please consult a dermatologist in person for a more definitive evaluation.
Best.
Dr. Rockoff