It's definitely an under-researched subject, probably because the larger part of the scientific community and especially the part with more say in research subjects is male.
This is a start though!
The year I got serious about Paleo I noticed sometimes when I had been strict about my diet (low carb and also low fat at that time) for a few weeks, menstruation would be delayed, and one cheat meal could make me ovulate again.
Eventually I stopped menstruating for 6 months due to chronic calorie restriction and probably overtraining. Libido was ebbing for a month or two before menstruation stopped, and was zip the whole time. I guess there was no use for it...
After that I gained a lot of weight very fast and I began experiencing problems I'd never had with my periods. I'll spare you all the details... All stories I'd heard from my girl friends, but never experienced before. Different symptoms in the time between ovulation and menstruation too. A saliva test showed ALL my sex hormones were elevated, including testosterone.
GLA really helped with the premenstrual stuff. Carbs (even Paleo carbs) in the week before make the first few days of bleeding a nightmare. Also, it gets better with every pound I lose.
My hunch is that diet and bodyfat % makes more of a difference than exercise, but I've never really NOT exercised for more than a couple weeks, so I can't tell for sure.
By the way, over here we have no mercy for the guys. We learned 'em early on. Now we can exchange woman tales and they don't even giggle.