I can answer this question for English colonial America. I would recommend Virginia DeJohn Anderson’s Creatures of Empire: How Domestic Animals Transformed Early America (2006), which examines the interactions between Indians, English colonists, and animals in the seventeenth-century. She argues that deep divisions existed between colonial and Native handling of livestock became a major source of friction in everyday life on the eastern seaboard.

Native peoples in New England and the Chesapeake did not have familiar animals. Some Native peoples did keep dogs (which had evolved distinctly in North America), but they had only very loose associations with people. Unlike tame or familiar English dogs, they served mostly to catch vermin and provide warnings. Their experiences with animals were as game to be used and respected for food, clothing, and other tools. Algonian peoples also attributed spiritual powers to certain animals. When Native people encountered the large domestic animals brought by the English, they had no framework into which they could fit them. They viewed (and feared) livestock as wild beasts.

English colonists, meanwhile, drew their experiences from backgrounds in husbandry. In England, hunting was a sport restricted to royalty and aristocracy. Colonists envisioned domesticating, rather than hunting, native American species such as turkeys, buffalo, and beavers. In colonial New England, the pattern of town living and the migration of full families allowed the English pattern of husbandry to be reproduced better than in other colonies. They used oxen to clear trees and plow their fields. Sheep, which were needed for winter clothing, grazed on town commons. New England had the female servant labor necessary for dairying. The northern colonies also sold livestock (mostly to plantations in the West Indies) in lieu of a cash crop.

English settlers held their style of agriculture as normative. They believed the Christian idea that man’s role was to subdue and care for all living things (a hierarchical understanding of creation called the Great Chain of Being). They thought that teaching Indians to raise livestock would help to civilize and Christianize them by taming their baser impulses. Cattle in particular required a lot of care, and at least in the English pattern of husbandry, a sedentary society. The link between cattle and civility ran deeply in the early modern English consciousness. In a famous captivity narrative of a New England woman captured by Indians, she feels deeply comforted when she sees “a place where English cattle had been.” (Mary Rowlandson, Narrative of the Captivity and Restoration of Mrs. Mary Rowlandson) Local governments in the colonies tried to promote cattle husbandry among the Indians. For example, one scheme in Virginia offered a group of Indians a cow for every eight wolves’ heads they returned—a plan which both encouraged Indians to conform to English expectations for agriculture and also made the world safer for cattle.

Of course given the shortage of labor in these new societies, English settlers, especially in the Chesapeake, were unable to maintain their English standards of husbandry. They began to practice free range husbandry, letting hogs forage for their own food in the woods and then luring their earmarked pigs back to the plantation for slaughter. Instead of fencing their pastures, as had been the practice in England, colonists began to fence their crops to protect them from wolves, deer, and hogs, as had been the practice of the Native peoples of the region.

Trespassing animals became a major source of tension between the peoples. By the middle of the seventeenth century, English colonists began to enforce their legal code across animals of the New World. Unlike Native ideas about animals, it distinguished between animals marked by earmarks or collars to indicate ownership and those that were wild in nature. Slaughtering livestock was seen as an act of war, and Anderson argues that two of the best-known seventeenth-century conflicts (King Philip’s War and Bacon’s Rebellion) had sources in frictions over livestock.