I'm designing an alien species and I want the males to have deer-like antlers. Now I also need this species to have a genetic predisposition (as in it is not just a cultural affectation) to be primarily monogamous (as their progeny require a lot of attention/effort much like human larvae).
Of course since antlers in the real world are used by stags to attract mates and "defend" (mostly symbolically as they aren't actually that useful to harm opposition) their harems from other males the two traits I want are at first glance incompatible.
There are potential solutions to this problem however. The first, probably most obvious answer is to find a utility other than that of male compitition for my creatures' antlers that is somehow exclusive to males. I really can't think of any possible usefulness that would only apply to males though.
The second resolution that I have considered would be that monogamy is a relatively recent evolutionary development in the species that I want to create and thus that the antlers are vestigial. This would of course mean however that larger antlers would gradually be selected against, quickly leading to stags without any antlers at all (there are conditions which can cause a stag to be born unable to ever grow antlers without even needing successive mutations in the real world). Approximately how long would it take for most males to not have antlers?
My main question is this: Would it be realistic for the majority of the males within a primarily monogamous species to have antlers?