On one hand is the scientific perspective: inherently reductionist, it simplifies our needs to (a) what the scientific community thinks they are, and (b) what we can understand. The grade-school USDA food pyramid recommends so many servings of fruit, so many of vegetables and carbohydrates. This approach underlies pharmacology, where an active ingredient is identified, its effect measured and it is applied to the situation. This kind of approach has successfully served commercial dogfood for many canine generations.
Of course it hasn't always had a fair trial. It has been subverted by human tendencies to fats and high glycemic starches. More importantly, its been driven by economics: subsidized corn products, financial pressure to produce ever cheaper foodstuffs, societal "fast food" expectations.
The other side of the spectrum is inherently teleological. For religious people this is straightforward; for everyone else, imaginary purpose must be ascribed to aspects of nature. Bear with me, supposed purpose is, at least the easiest way to understand ecosystems. It is merely the purpose of a mouse to survive and reproduce. Given the chance it will pursue those. But...it is the purpose of mice to: disperse seeds fecally, graze/stimulate small plants, break down high value feed wastes into manures, and provide feed for larger carnivores. Of course any such list we create could never be comprehensive.
Within framework, pigs for example are rooting omnivores. Their natural purposes might be to: aerate soils around trees, predate on grubs, disperse bush berries, prevent tree disease by consuming large amounts of fallen seasonal fruit, and provide feed for (brave) cougars. This teleology is inherently reflexive i.e. the relationship between pigs and and berries is, in nature, bidirectional and mutually beneficial (though this may not be obvious e.g. wolf predation, prevents overpopulation starvation and culls sick caribou).
So what should I feed my pigs: grubs, berries and tubers? That can get difficult. My purposes are of course different: instead of just reproduction I also want: Tender meat, Tasty meat, Quick Growth (up to slaughter size), and affordable feed.
So we turn to science. Science says: corn is cheap, easy to grow, pigs need carbs to put on quick weight and mellow out strong flavors.
But we smack into two rules:
We don't know everything. Our lack of knowledge about the way things happen in nature is complemented by our lack of knowledge in recreating nature as we want (the scientific approach). We can't see the secondary effects of our artificial situations. That's the advantage of doing it natures way: Nature has it all figured out. But Nature will play by nature's rules for nature's purpose, not for ours.
Second, we all play by natures rules. Nature always bats last. You can't get something for nothing. Feed an animal nothing but corn, and the animal stops growing. It needs protein. Feed it corn and soybeans and it gets sick. Add artificial minerals and vitamins, and it soon needs antibiotics. Every gain is a loss somewhere else, and the effects are not obvious. For raising animals, it often shows up in the meat, either as nutrient deficiency (Vitamin A deficient fat on corn diets) or as toxic presence (heavy metal growth stimulants), or superabundance (corn fed pigs have too much cholesterol; but we do need some in our meat).
Sorry for switching between animals and humans. But I believe it is very similar. The "hunter-gatherer diet" is a great example of a diet "as nature intended." Of course naturally speaking humans have very odd selective pressures; many of us have moved to many climates we're fare poorly without artificial props; we live in artificially large communities; and thus have confuzzled what nature "intends" for us to consume. Feeding livestock faces the exact set of natural dissonances with natures intended harmony
So for me, I do the best I can with myself, trying to mimic nature's methods: for feeding, housing, grouping. Tentatively, we intentionally deviate from (our understanding of) natures prescription. Realistically we heavily deviate, due to economic and practical limitations. This is definitely a "lifetime of learning" topic. Expect on the topic to be less theoretical and more pragmatic.
See below: Turkeys are a good example of a species native to this climate and forage type. Although domestication has rendered them less hardy and slightly dependent on grains, they are some the easiest meat to grow, as they are right at home eating greens, bugs, and surviving North American Winters. I believe that natural diets for them implies natural diet for us when we eat them. Enjoy!