Chimpanzees, our closest related species, have a
dominance hierarchy that mostly predicts who succeeds at mating. In that study, the alpha male had 7 children, by being possessive of females and aggressive towards other males. The lowest ranked beta male had no children.
Mating success can’t be predicted entirely by dominance. Chimps avoid incest, so some lower ranking males get an opportunity with the alpha male’s relatives. Some lower ranking males mate opportunistically, sneaking in sex while the alpha isn’t paying attention. Sometimes two males will have sex with the same female, young males can produce more sperm than the older alpha so they can sometimes win in that case. The lowest ranking males can only get mates by forming consortships — basically, they take a younger and less desirable female, take her away from the tribe and live alone with her.