The strongest survives

I spent sometime in watching a documentary which tells stories about a group of lions living on the great plain of Africa. They are feed well when the rain season comes and suffer starving(starvation for) most of the time, when there is a drought. As the top predatory animal there, most threats to Lions comes from bad weather and their rivals-- other lions who want to conquer more lands(territory) and have more(mate with) females. It's full of responsibility to be the king of a group of lions. The king has to be strong enough to protect his kids cubs and female lions (lionesses) from a the provocation of other lions. If the king lose in a fight, it is because he was either killed or exiled with bloody wounds. In order to mate with female lions in the group, the winner usually kills the former king's kids cubs nursed by their mother. It's very brutal but it's the way for the winners to control the whole group(and ensure their DNA is passed on. Females won't begin their new reproductive cycles until after the cubs are killed or grow up). Then the new leader has to  sire his own kids (cubs) and land to protect. The same situation happened in a group of monkeys in from India,which I know (learned about) from a another documentory. When I open a historical(an encyclopedia) book, I am(was) shocked that I to find out that the same thing not only happened in animal's (with lions, but also with other species in the animal) world. I wonder if it is a rule of from Darwin's evolutionism theory.