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If you ask this question of the archeological establishment today, the answer you are likely to receive is something like "Darned, if we know!"
Whoever they were, they appeared and disappeared suddenly with about 1500 years in between. Phoenix where the Salt and Gila rivers meet was their center, and the site of the present-day Pueblo Grande Museum and Archeological Park near Sky Harbor is believed to have been their capital city, with an area population at its height of 50,000 people--the greatest civilization of North America, excluding Mexico.
Their name means "the vanished ones" in the modern Pima Indian or O'odham language. The Salt River Pima-Maricopa Indian Community located in the metropolitan Phoenix area now occupy the Hohokam homeland, although they and the related Papago (Tohono or Desert O'odham) are ambivalent about whether they are the descendants or conquerors of the Hohokam.
Harold Sterling Goodwin, who first discovered the Hohokam in his excavations of Snaketown in the 1920s, thought they were a Central American culture like the Maya or Zapotec. It is true that when they showed up about a century before the Common Era, they brought pottery, corn and beans agriculture and sophisticated canal irrigation, and that none of these arts indicate any preliminary or introductory stages of development in the Arizona archeological record. It would be 800 more years before the truly indigenous Indians (called Basketweavers) acquired pottery and the other appurtenances of civilization, including the village architecture we call Puebloan.
A giant in Southwestern archeology, Goodwin fell from grace in the 1940s when he had the audacity to disagree about the emerging picture of Basketweaver-Pueblo-Spanish cultural phases and persist in a diffusionist theory of prehistory emphasizing Austronesian migrations rather than Asiatic influences. He went on to write a synthesis of American Indian studies titled A History of the Ancient Southwest (1957), a straightforward survey of the ancient civilizations that were overrun by the Uto-Aztecan, Navajo and Apache intruders beginning about 1100.
Another bad boy of academia, Barry Fell, believed the Hohokam came from the Middle East and North Africa, where they had perfected adobe construction and canal irrigation of crops. Fell pointed to the parallels between Pima and Papago and Berber languages.
The Salt and Gila Rivers ran year round when the Hohokam built their system of government and katchina-based religion. Some of the canals were 50 feet wide and 16 miles long. There were four or more networks of irrigation canals totaling more than a thousand miles long. Since they built grass huts and caliche-plastered mud mounds and villages, though, the footprint of the Hohokam today is mostly melted away by erosion, and their earliest habitation spots are forever lost in the changing shoreline. They used few timbers, so tree-ring chronologies cannot be applied to them.
Thus the Hohokam are likely to remain permanent mysteries to us. But a little hint: if you read their name as Semitic, it means "Sea Peoples." Snaketown can be understood as "boat-town" as well as the modern local Indians' calque "place where there are lots of rattlesnakes."
Their genetic signature, at any event, seems to be haplogroup B, like the Maya, other Pueblo Indians and Southeast Asians.