While food is a primary function of increasing growth your Faction Prestige also counts toward gaining new citizens from the Wiki description I found:
Faction Prestige is a measure of the pull your nation has towards drawing in new citizens. The more prestige you have, the more POPULATION you will get each turn in your cities. Keep in mind that gains from your Faction Prestige are SPLIT EVENLY amongst all your cities, so the more cities the LESS of an increase you will see in each of them per turn.
So, according to this just because you have an abundance of FOOD doesn't mean you will get growth if your prestige is low and you have a lot of cities.
