Sometimes, but not necessarily. Despite the powerful cultural messages around the subject. From Susan Milius at ScienceNews:
Many creatures that routinely kill their own kind would be terrifying, if they were larger than a jelly bean. Certain male fig wasps unable to leave the fruit they hatch in have become textbook examples, says Mark Briffa, who studies animal combat. Stranded for life in one fig, these males grow “big mouthparts like a pair of scissors,” he says, and “decapitate as many other males as they possibly can.” The last he-wasp crawling has no competition to mate with all the females in his own private fruit palace.
In contrast, big mammals that inspire sports-team mascots mostly use antlers, horns and other outsize male weaponry for posing, feinting and strength testing. Duels to the death are rare.
“In the vast majority of cases, what we think of as fights are solved without any injuries at all,” says Briffa, of Plymouth University in England.
Of course, big mammals are longer-lived than most insects and may accumulate enough life experience and remembered examples to sense when withdrawing would be safer.
What about conflicts among animals that do not have a brain?
Sea anemones don’t have a brain or centralized nervous system, yet costs and benefits of fighting somehow still matter. The animals clearly pick their fights, escalating some blobby sting matches and creeping away from others.
Just how anemones choose, or how any animal chooses when to fight and when to back down, turns out to be a rich vein for research. Theorists have proposed versions of two basic approaches. One, called mutual assessment, “is sussing out when you’re weaker and giving up as soon as you know — that’s the smart way,” Briffa says. Yet the evidence Briffa has so far, he says with perhaps a touch of wistfulness, suggests anemones use “the dumb way of giving up.”
Animals resort to this “dumb” option, called self-assessment, when they can’t compare their opponent’s odds of winning with their own. Maybe they fight in shadowy, murky places. Maybe they don’t have the neural capacity for that kind of comparison. For whatever reason, they’re stuck with “keep going until you can’t keep going anymore,” he says. Never mind if the fight is hopeless from the beginning.More.
We used to just say, “Their instincts tell them these things,” but that statement flat out fails Behe’s test (how, exactly?). It’s good that researchers are now approaching animal mind in a more disciplined way.
It’s not clear to what extent sexual selection contributes to evolution. Darwinians assume that the animal that defeats the competition is “fitter” but that doesn’t necessarily follow. He may or may not have better genetic information to pass on. The victorious elk might be more susceptible than his rivals to a wave of disease that later fells the offspring that inherited the defect from him.
See also: What Darwin’s sexual selection gets you: Antlers in heaven
Can sex explain evolution?
and
Does intelligence depend on a specific type of brain?