The native Indians use to kill animals. Some tribes were wasteful, some went out of their way to ensure they kept the balance. In the latter case, tribes tried to use all of the animal.
- emphasis added
I thought I'd emphasis the above to point out how a modern perspective can slip into our thinking without us realizing it.
There isn't alot of evidence that prior to the 20th century that Native American religions were all that concerned with concepts like 'balance' much less 'balance' as used to mean 'living sustainably in the environment'. For stone age peoples, the notion that man might have the strength to overthrow nature seems laughable. Stone age peoples don't use 'all of the animal' for aesthetic reasons or because they can concieve of humanity exterminating a species. They use all of the animal because hunter-gather peoples are acquainted with hunger and deprivation and if you don't use every resource in your environment you will starve or die of exposure or in some other highly painful way. Stone Age peoples, like any group of successful impoverished humans, are thrifty by necessity.
Stone Age peoples are concerned with mollifying the spirits not because of what they fear to do to nature, but because of what they fear nature will do to them. It's a way of exerting some control in a world that seems and often is entirely beyond their control.
European philosophers have been romanticizing this way of life for millenia. It's quintesentially European to look at some stone age culture and say, "They are better than we are.", while ignoring the fact that the admired culture was basically the same as they were only with less stuff. Roman orators said the same sort of things basically about the Germans. You can find Roman orators proclaiming that German barbarians were universally brave, that they didn't know how to lie, that their women were always modest, and that adultery was unknown. Of course, that is all obviously nonsense, and its pretty clear that what said Roman orators were really doing was projecting all the virtues that they found lacking in their own society on to some distant barbarians that no one in his audience would be closely acquainted with. The idea is boiled down to its essentials basically some old fart (or sometimes young fart) saying, "Back in the good old days, youngin' respected their elders..."
In the 1960's, a number of these white Philosophers invented indigenous environmentalism. The most famous of these is the Chief Seattle hoax, but there were all sorts of things that basically amounted to some white guy hijacking native beliefs for his own purposes. If you actually go do the archaelogy though, you find all sorts of evidence of slow motion environmental degradation from river bank erosion, to crop failures, to desertification in pre-Columbian North America to say nothing of the extent that human hunting habits may have contributed to the extinction of large mega-fauna in North America.
When the North American priestly class asks the spirits of the world to live in peace with them, they aren't thinking about 'environmental balance'. They are thinking that nature is going to capriciously wipe them off the face of the earth. When they utilize every part of a buffalo, they aren't thinking, "I have to maintain a low carbon footprint." They are thinking, "Can I get enough food off this to last the winter?" If it was an aesthetic and moral choice on their part to be 'poor' (like say with the Amish), when white guys showed up and gave them guns, they wouldn't have gleefully helped exterminate the buffalo to sell buffalo hides.