The Mississippians were distinguished in their diet by the amount of corn/maize they ate. Maize was introduced to the area sometime around 800 AD, and the Mississippian tribes began practicing more intensive agriculture, clearing river bottomland to plant fields, something which other groups didn't do as much. They also ate squash and beans and sunflower seeds and certain grasses as well as gathered foods like blue and blackberries and walnuts and acorns.

Most of what we know of the Mississippians comes from archaeology and archaeology cannot easily tell us directly how much protein vs carbs someone might have eaten, but it is a reasonable inference that if their society focused heavily on the cultivation of corn/maize, they would have eaten more carbohydrate heavy diets than other woodland cultures.

We do know from Archelogical evidence (generally bones and remanants in trash piles) that the natives ate white tailed deer as a significant source of protein, but that they also ate Rabbit, Muskrat, beaver, Raccoon, Turkey, and significant amounts of waterfowl, fish and amphibians.

So again, reasonable inference. We can assume that an average Mississippian native might have eaten much of their daily calories from various foods with corn/maize in them, and eaten deer, duck, fish and turtles as major meat sources.

I don't think any estimates of impact on prey animals exist, or at least I'm not aware of any, but using modern methods we can make some educated guesses.

In my home state, Arkansas, which was part of the Mississipian territory, the ecologists at the game and fish commission have determined that harvesting approximately 200,000 deer per year is necessary to keep the population at an optimal level. they keep track of harvest numbers and use the information to issue hunting permits less harvested than that, deer will begin to starve from overpopulation, more harvests, you don't have sustainable hunting. Keep in mind, this is the deer population at current human settlement levels, but also with far less predator pressure than would have likely existed in the 10th century.

Give or take, assume an average white tailed deer will have about 55 pounds of lean meat. That's about 40,000 calories. This is actually very conservative because it is likely that natives would be using more of the animal resources than modern butchering practices. I.e. they'd eat organ meats, use the bones to make stock, things many modern hunters would not bother with. That's all extra calories.

So if we assume that someone gets about half their calories from carbohydrate sources that's about 1000 calories per day that would need to come from proteins and fats. One deer would be sufficient to provide protein for about 40 people for a day.

Edit: to clarify 1000 calories is a huge assumption, probably multiples higher than reality, but the lower the meat consumption, the lower the harvest numbers as well.

To provide sufficient protein for 40,000 people, the Cahokians would have had to harvest about 1000 deer a day across their population area, and that would result in harvests of 300-400,000 deer per year. Definitely enough to result in local depopulation.

If they got half their protein calories from Venison and the remainder from fish, turtles and ducks and small animals, we take the deer harvest down to about 200,000 per year, about what we're doing at modern levels.

Adding into this, waterfowl are a huge resource for Mississippi delta areas. Arkansas, again, allows hunters to harvest close to 1 million ducks a year from migrating waterfowl. Importantly, ducks are migrating through in the winter, when other food might be difficult to obtain. A fatty duck might feed 4-5 people for a day protein wise. If they harvested even half modern levels, 500,000 ducks would feed the population for 40-50 days. Again, this is a level where over-harvesting is definitely possible but might also be sustainable.

So all in all, when you consider that there were likely quite a few different sources of protein, it's not too hard to figure out even how a city the size of Cahokia might have gathered enough wild protein to feed its population.

I am not personally an expert in the topic, but I do have a relevant article with me that I can summarize: Kelly, Lucretia S. "Patterns of Faunal Exploitation at Cahokia." In Cahokia: Domination and Ideology in the Mississippian World, edited by Timothy R. Pauketat and Thomas E. Emerson, 69-88. Lincoln: University of Nebraska Press, 1997.

Kelly is a zooarchaeologist who specializes in Mississippian animal remains. Her article synthesizes all of the studies that were then available of animal bone deposits in and around Cahokia. It may be a little out of date, but her data and conclusions are illuminating. She looks at what bones can tell us about the diet of people before and after the rise of Cahokia as a city and large chiefdom, and also at the different diets of the elite and common people.

For the Emergent Mississippian period, it seems that the villages of the Mississippi Bottom region incorporated far more fish than deer. In the different Emergent Mississippian phases that she describes, fish bones make up 76% to 95% of identified bone specimens. This was a time when the people of the region were shifting to more intensive maize agriculture. This meant that not only did the people probably have less time for hunting, they also cleared local woods for the first time, which meant there were less places to find deer.

So fish were the most important source of animal protein before the "explosion" of Cahokia. But there were enough deer bones present for archaeologists to analyze them. They found that in a site in the uplands a bit away from Cahokia, there were bones from every part of the deer. In (not-yet-a-big-city) Cahokia itself, down in the floodplain, they mostly found bones from mid- and high-utility parts of the deer, meaning not the neck, head, and extremities. This is because Cahokia was further away from any large stands of trees, so any meat that was brought in was field-dressed, and the less choice parts left behind. However, in all cases the deer was probably hunted locally.

However, when we switch to the Mississippian period - after the explosion of Cahokia as a city and a large chiefdom - the bone deposits change dramatically. Deer bones now make up 55% to 91% of identified bone specimens. Fish drop to as low as 7% of specimens, rising back to 43% at the end of the period. Almost none of the deer bones come from low-utility parts of the animal, showing that they were brought in from some distance.

Combining this evidence with what is known about the economies of chiefdoms, and what we know about other kinds of goods such as wood, Kelly concludes that Cahokia imported almost all of its meat. Hunters from other places killed and dressed deer and brought it to Cahokia as tribute.

Looking at how specific parts of the deer are distributed, there is even more evidence that the rulers of Cahokia directed the distribution of meat. Bones from the deer's hindquarters, considered the highest-utility part of the animal, are concentrated in elite areas of the city, such as finds associated with the mounds themselves. In average parts of the city, they have mostly found bones from deer's forequarters and backs. So Kelly hypothesizes that people brought in deer meat as tribute; chiefs then divided the meat up, keeping the choicest cuts for themselves and distributing the rest to the people. This appears to be how Cahokia's people got their protein.

In the final phase of the Mississippian era, there are signs that the trade and tribute network declined. More bones are seen from the entire deer, which suggests that they were hunted locally. There is more local and less imported wood.

So that's Kelly's article. I apologize that it may be a bit out of date. To me it's still really interesting. I tend to think of "tribute" as involving prestige goods and luxuries, but it seems that it may have literally been necessary for the people of Cahokia to feed themselves. I'm left wondering how far away the meat came from. How far could a pre-columbian person transport a deer carcass before it went bad? That's probably something that could be answered from historical sources and not just archaeology. (edit formatting)

Are there any anthropology books on this topic? Or more about these cultures in general? I want to learn more

Edit: thank you everyone for your recommendations.

That reply was worth the wait and definitely answered all facets of my question!! Thanks so much I really appreciate it, that’s fascinating.