odumchi: I'd like you all to give your own thoughts on how the populations of these three ethnic groups came to be so large. But here's my own theory:
Hausa: The Hausas have had strong united traditions. The Hausas were originally a trading people in the Sudanic region of Africa and might have possibly started out with a rather small population. As their trading cities grew in influence, they became centres of migration for traders and merchants all across the Sahel. These traders might have had different backgrounds but all spoke Hausa as a trade language, making "Hausa" more of a linguistic group than an ethnic group. By the time Islam arrived in the Sahel, the Hausa elite and then the commoners converted to the religion and assumed a united "Hausa" identity since after all, they lived in the same place for hundreds of years, spoke Hausa and worshipped Allah. As the trading cities expanded, they attracted more and more people from al across Sudanic Africa and soon they too experienced the cultural diffusion and mixed into the Hausa population.
Igbo: The Igbo as we all know were never united into one kingdom. They might have xisted in many small independent city-states just like the Germanic kingdoms of the Holy Roman Empire. Trade was also very important in Igbo culture and might have helped increase the Igbo population also. As Igbo-traders expanded outward and settled in various other cities, their influence spread and soon Igbo might have also been adopted as a second language by the peoples and as the Igbo population grew, it might have become the primary language of these poeoples. I m also hypothesizing that the yam has played a large role in the population growth of the Igbos. Yam, was easy to grow and required little land as compared to crops such as sorghum, bailey and etc which grew in the North. This reduced the need of land to feed large populations and effectively dictated the size of modern day Igboland. Yam could not be grown succesfully in the Northern plateu of the country thus making Igboland a "tropical" land.
Yoruba: The Yorubas, like their Hausa counterparts, also had strong communal traditions. Much of Yorubaland has been united twice, first under the Yoruba kings of Ife and Oyo and twice under the Binis. The Yorubas had minor trading cities but trade did not play as much importance in its culture as it did to the other two. With the empire secure, and all Yoruba speakers united under one ruler, the people were free to multiply and epand, and with the arrival of Islam, polygamy spread much further allowing for a large population boom.
Good topic. I agree. I mentioned in another topic the Igbo expansion from Central Igboland to areas of present day Ebonyi and Abia States where they encountered many non Igbo groups. The Igbo speakers eventually became dominant and assimilated a lot of people. There were also non Igbo groups that moved into areas dominated by Igbo speakers. These migrations probably played a role in the large population of Igbo people.