Dominant bucks don't do all the breeding. DNA parentage studies find that breeding is spread through all ages of bucks far more evenly than was originally assumed. Now age/dominance does help with breeding success. Although 3 1/2+ year-old bucks make up the smallest percentage of the male population, they father the majority of the offspring, and although yearling bucks are the largest segment of the male population, they are responsible for the smallest percentage of offspring. But even in a very balanced herd, with old bucks present, bucks of all ages will successfully breed, even some yearlings.
Dominance only matters when more than one buck encounters the same estrus doe. The dominant buck gets her and the lesser buck(s) back down. However, a doe is going to be in estrus for 24-48 hours, and she may allow copulation 4-6 times during that time-frame. And every one of those copulations may be with a different buck, especially if a young or subordinate buck is the first to encounter her, followed by bucks higher on the social ladder sequentially encountering her. Now of all those breedings, who becomes the father? It could be any of the bucks.
And one thing to remember, "breeding" is different than "conception." Several bucks may breed with a doe while she is in heat, but only one becomes the father of each fawn. And interestingly, DNA studies find that 27% of "twin" fawn pairs were fathered by different bucks.