Metalinvader665, good point about the Rocky Mountains being impenetrable by the Mississippian Cultures alone. Does anyone have any ideas of how the mountains cultures can be plausibly converted to agriculture?
Let's not get too hasty -- if we get to the point where there are truly powerful states capable of projecting their power that far, anything is possible. Remember it happened IOTL, albeit with more guns and locomotives. If states or other powerful polities start cropping up everywhere though they may have geography to their advantage.
The Rockies aren't even a barrier in the way you're thinking. People can still go around it for trade, travel and other forms of transport.
This was also done IOTL with Pueblo and other Southwestern cultures involved in trade routes that brought corn, beans and other goods to the Eastern Woodlands.
For the actual Rockies themselves, especially the high plains and valleys interspersing them, introduction of the potato or a similar tuber (possibly a native one, but I'm not awake enough to dig through candidates) would definitely be a boon to the region. Chenopods (and other amaranths), as well. These plants are remarkably efficient and versatile and can be used as both a grain crop and a leaf vegetable. There is a plant called kaniwa in Peru (not to be confused with quinoa, a related chenopod) which grows in some of the highest regions of the Altiplano and is remarkably cold hardy. A similar chenopod could be used, perhaps a cold-hardy cultivar of Mississippian goosefoot or Pueblo pigweed (or going even further south, Mexican grain amaranths which are quite superior to the ones grown in the Southwest US).
Isolated inventions of agriculture are rare, though I understand we may be trying to bring about as many as possible. Instead, the practice spreads from its point of inception and cultures use the idea to domesticate more species. In this case we may have fringes of Mississippian and/or Pueblo-derived intensive farming cultures brushing up against the Rockies and the practice slowly trickling up the mountains into small homesteads or farming communities. Outside of the river, they can terrace to add surface area and preserve runoff (be mindful that it's runoff the rivers won't get). At its highest estimate for population parts of the Rockies may resemble some parts of the Alps. Except a little colder, a little drier and actually a little higher for the farmland.
Speaking of the Alps, while farming grain and other vegetables is present in the alpine valleys a major part of alpine agriculture is actually sheep and cows; pastoralist transhumance, in other words. If they have domestic ungulates, much of the agriculture in the Rockies may consist of ranching, herding or seasonal transhumance from the mountains to the lower plains and valleys. If bison are domesticated (would probably take the action of a state, or at least farmers with previous experience of raising ungulates like in the Near East) and herded in the Rockies, I wouldn't be surprised if woolly varieties are bred (since they already have short, but usable wool, it would be faster than if they domesticated actual sheep) that can take the colder winters. Perhaps they could be a yak equivalent; imported llamas would also work well here. In OTL much of the agriculture in western Colorado is indeed ranching for horses and cattle.
Past the Rockies, much of the Colorado Plateau and Great Basin reminds me of western Asia -- especially the areas around Iran. Neither of these places support very large populations even today, but are the birthplace of most Old World herding cultures. Bighorn sheep could be more intensively herded to something at least resembling goatherding, or outside domesticates can be brought in. The initial crop package can consist of a mix of original EAC crops such as little barley (already present in wild/feral form in the Southwest IIRC), sunflower, maybe goosefoot, and drought-tolerant Puebloan corn, squash, tepary beans (IIRC, one of the most drought-tolerant bean varieties out there), and maybe their varieties of amaranth but you should aim to get a Mexican grain amaranth there eventually. They'd definitely do well with Southwest dry farming techniques as well. The ease of growing corn will make a good gateway drug for agriculture, but you should at least introduce beans soon so they don't exhaust the nitrogen too quickly.
You can't go wrong with orchards of mesquite trees either, providing you with plenty of nutritious beans for years and minimal irrigation. Cacti as well; including prickly pear and barrel cactus.
The desert cottontail is also an attractive domestication candidate; unlike European rabbits, they don't burrow and can be given artificial shelter. They are much more social than other cottontails and can be kept in large groups, and of course are adapted to arid plants. They would make a nice microlivestock available as a cheap source of animal protein.
What if we get the civilizations east and west of the Rockies to both start expanding into the Rocky Mountains? Instead of trying to attack the nomadic peoples there directly we could have the empires begin to develop what farmable land can be found and start to terrace small amounts of the area. Communities around these farming communities could also start hunting the surrounding wildlife to supplement their diet and to sell. Maybe once huntable wildlife starts to run low outside the mountains hunters may start relocating from across the continent to the mountain communities and start depleting the wildlife there. Once the governments on the North American continent start to realize that certain species are on the verge of extinction might we see them starting to restrict hunting in certain regions?
Would we see a situation where the before mentioned domino effect spreads into the Rocky Mountains, with the remaining communities there vassalized or made an ally with one of the Empires. We could have blocks forming allied to the east and west North American empires. Maybe the mountains are developed despite there being vast tracts of land available for agriculture because the North American power blocks see the mountains as a useful defensive barrier that they wish to gain control of? They might both be afraid of each other after seeing their rapid expansion.
This would work, and you don't even need to aggressively destroy a hunter-gatherer's livelihood. Simple expansion and increased influence in these areas will make for more attempts at agriculture, especially through more direct trade and marriages allowing for flow of information.
Also, restricting hunting on areas as large as the Rockies is something that only very advanced states can do...and even then, it's still difficult to enforce. Switching to agriculture in this extent would only occur if the animals are nearly hunted to extinction, which would take a large population density, especially for the Plains.
Remember the mountains (and plateaus west of them, and pretty much anywhere else on Earth) have a finite carrying capacity, and the biggest limitation here is fresh water. Aquifers can be easily drained or contaminated, rivers can be diverted to the point of drying up and ponds generally don't make for good drinking water. If population density goes out of control it can destroy carrying capacity, at least momentarily.
Thesaurus Rex, how high might we be able to get the population of New Zealand by the year 1600?
Human history is a delicate interplay of nature, culture, and individual choice. Here, however, nature has more of an upper hand in deciding the fate of the Polynesians. New Zealand before people was essentially an Eden; abundant wild food, no land predators, and consequently game that's easy to hunt. In turn the proto-Maori concentrated less on elements of Polynesian agriculture and opted to eat the horse-sized ducks running around.
After the moas went extinct, you see increased competition for food but even in many of these areas it's still easy to get wild food. It's going to be difficult to get them to transition to wholly intensive systems of agriculture. You could perhaps have a region of NZ just barely touching the carrying capacity of the current methods of subsistence, coinciding with a politically powerful hapu whose chief calls for agricultural and political reforms that try to push agriculture beyond subsistence farming, creating increased social stratification and complexity.
They'd definitely need to keep chickens past the moa extinction. If this isn't possible, they can domesticate wekas. They aren't as prolific as chickens, but having fowl like that around the towns will definitely help. Waterfowl such as paradise shelducks and Pacific black ducks might have potential. The Maori's kunekune pig has a unique ability among pigs in being able to live almost entirely off of grazing; rather than keeping them by the subsistence farms, the tending of large herds of kunekune could be a professional activity like shepherding.
They're definitely gonna need to go beyond digging sticks. Some kind of hand plough or hoe will be more effective for large fields. Necessity will create the best tool for the job. But the way they did it IOTL is going to be very strenuous just by using digging sticks. What will really help them is more crops and domesticates like wheat, rice, sheep and water buffalo. Your global trade routes might do that.
The most realistic estimate for precolonial NZ's population seems to be about 100,000. I'm no agricultural scientist so it would be hard for me to crunch the numbers on just how many people can be fed by traditional Maori agriculture etc. But taking colonial NZ's population in mind (using them as a template for advanced agricultural techniques and management), Europeans went from 2,000 people in 1840 to 770,000 by 1901. Taking account of things like more advanced agricultural techniques in the 1800s, I imagine a souped-up Maori might reach a conservative estimate of 250-350,000 people by 1600, provided wars don't contribute to a significant amount of deaths.
This might be off topic but given the technology at the 1700's could we ever see the population growth tapering off in a more modest version of that we're seeing today? Due to the lower quality of living and tech at the time it would be a very small tapering off if at all. It may be ASB but if there was a government at the time that was committed to improving sanitation and quality healthcare (by that time's standard) for it's populace, providing education to all of it's citizens, giving the people control over the government and giving all citizens the opportunity to move up in wealth and social status would that be enough for a very small tapering off?
This is exactly how you
increase population growth, not decrease.