Short answers, pulled from the story.
Classical demography is the study of how many people lived around the Mediterranean Sea between the Bronze Age and the fall of the Western Roman Empire. Researchers in the field also study birth rates, death rates, and the ratio of men to women in ancient populations.
Estimates for the Roman Empire's population range from 45 million to 120 million, with most historians favoring a narrower band of 59-76 million. The population is thought to have peaked just before the Antonine Plague.
Greek city-states began founding colonies along the Mediterranean and Black Sea coasts around 800 BC. By the 4th century BC, the area of Greek settlement stretched from the western Mediterranean to Asia Minor and the Black Sea, with a population estimated at up to 10 million.
The Phoenicians established colonies and trading posts across the Mediterranean, North Africa, and beyond the Pillars of Hercules into the Atlantic Ocean. Their most famous colony, Carthage, was founded in 814 BCE.
Historians disagree because ancient census figures do not specify whether they counted only adult male citizens or all adult citizens, male and female. One interpretation of a base figure near 4.063 million citizens puts Italy's population near 13 million if only male citizens were counted, or closer to 6.5 million if all adults were included.
The Greek historian Diodorus Siculus estimated that 7,000,000 people lived in Egypt during his lifetime, before the Roman Empire annexed the country. Of that total, he counted 300,000 citizens living in the city of Alexandria.