One very good example of such a non-violent species which may surprise you.
Humans originally were hunter-gatherers. They had a low population, which maintained itself for the first hundred ninety thousand years by limiting their birthrate (probably through natural family planning or some similar mechanism) to one birth every four years or so. This was due to their nomadic lifestyle and limited transport capability. Four-year-olds can keep up with the tribe on its migrations, whereas smaller children will need to be carried--in a tribe without domesticated animals, all burdens must be carried on human back. A single infant could be carried, but more would burden the mother too much to afford to have her carry any of the tribe's possessions.
Studies of modern-day hunter-gatherer tribes indicate that the average human in such cases would work about twenty hours a week (less than one hour per meal) and spend the rest of the time relaxing. Singing, dancing, joking, caring for children and old people, worshipping whatever deities they believed in, and fiddling with art and new technologies filled in the non-sleep (and breeding) hours.
According to Jared Diamond's treatment (the name escapes me), this did not change until the invention of beer. Beer was a resource-intensive, manpower-intensive consumer product. Very little could be made at one time because it cut so far into the already full social economy of the tribe's off-hours. However, one tribal leader (call him Nimrod) decided to have the tribe plant barley for his beer. Now the tribe had to stay in one location to watch the barley. They soon hunted out all available local game, so rather than have them starve, the leader fed them on excess barley. This was successful because one acre under the plow produces up to ten times the calories of the same acre under forage.
Soon the people had to build permanent shelters to house the population. With no worries about traveling with small children, the women could breed more often, and the excess population was used as field workers to expand the acreage in barley. Excess populations are restive, so the leader made some of the fighting men his guards and enforcers, promising them a larger share of the grain for their services.
Leaders with guards are kings. The shaman was co-opted by having all his material needs provided by the king, with no need to hunt or farm. In exchange, he was to pray to the grain god (which now became the chief god) for fertility and high yields in both farm and womb. Walls were erected to protect the fields from animals and floods, and later from other farming tribes. Forests were cut down to clear more fields, and animals fled the destruction of their habitat, increasing the dependence on grain-based calories.
Generations passed. The priest now employed lesser priests and acolytes to spread the word that loyalty to the king would butter up the grain god and ensure a good harvest, as would paying tithes to the king and making sacrifices (of grain, natch) to the god. There grew up children who had never known any other place than the farm village, and the outside world began to grow scary. Since the children (and their parents) were raised with increasingly fewer forest skills, wandering off from the safety of the village became far less survivable, and far more dangerous. The Other gradually became a hideous threat.
As more and more emphasis was placed on the harvest, the slow and sick became devalued and despised, much less the willful shirker ("If a man worketh not, neither let him eat"). As single-crop farming wore out the land, necessitating war to gain less-infertile territory, yields dropped, and those who could no longer contribute became more and more often euthanized. With a less-diverse, nutrient-poor diet, disease grew rampant (not helped by the use of human faeces as fertilizer) and infant mortality soared. And all these problems were (of course) caused by foreigners, witches (insiders with outsider loyalty--today called radicals or domestic terrorists), and insufficient submission to the god(s). And so it continued, nasty brutish and short, up till the present day.
All because of beer.