In this scenario, the alpha male doesn't just lead and defend a harem, he will fight any adult male he encounters to the death. This starts a feedback loop where only the strongest, most aggressive males produce successful offspring and the young males need to flee the group before they reach adolescence and start producing the hormones that set off the alpha male.
Who doesn't need to flee? Male offspring that produce very little or no male hormones. These trigger neither fighting nor mating responses in the alpha male and can live their lives safely in the group, gathering food, guarding the group and generally performing the more risky tasks. Unfortunately, they don't produce viable sperm or have mating drive.
In this case, sterile individuals take the place of males, but there can't be too many or the male genes will not spread. The ratio of male : female : sterile might be 1 : 2 : 1.
This scenario plays out in a (post-apocalyptic) world with many irradiated areas. a relatively small number of individuals are born with very high tolerance for radiation and the ability to detect it. Unfortunately, this comes at the cost of their fertility.
They protect their siblings/family/group from radiation by testing food and water. Some even eat/drink and regurgitate food before the rest of the group eat/drink it. Only 1 or 2 per group are needed to make it successful, so the ratio could be 1 in 10 of either gender. Perhaps it's determined by radiation exposure in the womb that turns on certain genes, leading to a variable rate.
It's just a phase
This scenario may not count as individuals may be fertile before or after their sterile worker phase. Individuals that experience stress while growing up due to food shortages or other factors caused by overpopulation do not develop sexually and instead become focused on work/production. Only a prolonged period of abundance will trigger development into fertile state.
This would be helpful in a species that is not very mobile or isolated due to geography (islands maybe?). The populations that don't have this feature will overpopulate their environment and collectively die off, while the ones with the sterile phase will stabilize until the situation improves, old individuals have died off or a new location is discovered to migrate to.