Alpha Male in Mammals for the most part has a territory he defends and perhaps a harem of Females that he tries to keep herded in that territory, and the Beta Males are usually younger Males that try to take the territory and the harem away from the Alpha male, usually in violent struggles, but sometimes merely by shows of force with little violence.
There are also Gamma Males which have given up on ever being the Alpha mail and essentially roam around outside of any Alpha Male’s territory.
There are also basically two types of females, those in the harem of the Alpha male and those like the Gamma males that roam on their own.
Point is some studies I read long ago shows the population is bimodal, with the Alpha-Beta-harem mode and the occasional pairings of Gama and escaped or outcast females.
What is rarely mentioned is that these two modes are Matriarchal and Patriarchal, the Matriarchal mode is where the female in the harem stays with the father and is visited by the outside male, and here brother raises the kids in human society.
It is not an ideal world where at some time women ruled the men as many have fantasized.
The Patriarchal mode is where there are exchanges of females between families in humans and the wife goes to live with the husbands family. In this case there is a contract between the wife and the husband because they are free agents in the other mode of the population.
The Alpha-Beta-Harem mode comes into play when fertility is a sparse resource. When fertility is not such a scarce resource then it is possible to have an economy trading women which is good for genetic variety. Genetic variety in the case of Matriarchy is when husbands are brought in on a temporary basis and visit their wives at the fathers home.
These are two different kinship systems that are based on the bimodal population of mammals in general.
Anyway this is what I remember from a series of articles I read in Science a long time ago. Maybe there is more up to date information available on this Mammalian basis for the distinction between Alpha, Beta, Gamma, and Pharmacon (Doubly outcast) males within primitive social structures.