First, it should be clarified that the Mississippian civilization is not, and was never, a single unified cultural or political entity. "Mississippian" is a modern term imposed by archaeologists and historians on past peoples possessing shared cultural characteristics who populated much of the modern US southeast from around 900 AD. There was no "Mississippian tribe" - rather, there were a number of smaller competing polities spread across the landscape. Some grew substantially more powerful than others, but at no point was eastern North America ever culturally or politically unified.
With that in mind, it's worth examining how the Mississippian culture emerged. Moundbuilding, the hallmark of Mississippians, has roots stretching back thousands of years in North America, with well-established sites dating back 5,400 years and others possibly as old as 11,000 years. Eastern North America had seen gradual sociopolitical complexity emerging in the thousands of years since the first mounds were constructed, as trade routes grew, mound construction grew more elaborate, and peoples adopted the Eastern Agricultural Complex - making the region one of the few independent centers of plant domestication. These crops included well-known ones like sunflowers or squash, but also more obscure ones like goosefoot or marsh elder.
It was with these new crops that complex cultures began to emerge, most notably the Adena and Hopewell peoples whose cultures centered around modern-day Ohio. They built massive earthen astronomical observatories (see the Newark Earthworks), and traded as far away as California. The Adena, and particularly the Hopewell, marked a massive development in the history of North America, but still possessed many of the hallmarks of prior eras. They moved frequently, staying in a single spot likely for only a generation or so at a time; and their communities were small, in the low hundreds at most, with a relatively egalitarian social structure.
The Hopewell seem to vanish around 500 AD. During the intermediate period between the end of the Hopewell and the rise of the Mississippians, an important new crop entered eastern North America from Mesoamerica - maize (or corn).
Maize enabled permanent sedentism and the development of large urban centers with thousands of inhabitants. The largest and most famous of these was Cahokia in modern Illinois, which I assume is what you are referring to by "mega city". With somewhere between 20,000-50,000 people in the city and its surrounding, it was the largest urban community north of the Rio Grande until the late 18th century.
Cahokia rose rapidly and then fell. We're not exactly sure why it fell. Scholars have promoted climactic issues, environmental depletion in the surrounding area, internal rebellion - any number of possibilities. In any case, Cahokia was a massive departure from previous lifestyles in the region, and many believe that it must have had to make use of force to maintain the power it held. It's very likely it had plenty of enemies, internal and external.
The region around Cahokia slowly saw its population decline, but this was not the end of Mississippian civilization. Rather, power shifted elsewhere - Moundville in Alabama, Winterville in Mississippi, Etowah in Georgia. Cahokia was the closest there ever came to being a unified Mississippian polity, and with its end the southeast would be continuously contested by smaller chiefdoms for centuries. All of these chiefdoms were still Mississippian, though.
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