Disclaimer: This represents my current understanding of the mod mechanics, and will likely change upon seeing the actual scripts and events.
Each 1 rural pop represents 10,000 inhabitants of the province living in the countryside producing Food or Rural Production. They make up the vast majority of people in the world and for most places during most periods existed barely above subsistence. They are the foundation of society, but are far less productive and useful to the crown than urban dwellers.
Ideal Rural Population Edit
The Ideal Rural Population (IRP) is the underlying potential that each province has for population growth. The further the rural population is below this number, the faster the population grows, and conversely, the farther above, the slower it grows.
Optimal Foraging Theory applies to both animal and human behavior, and both tend to prioritize the pursuit of food or resources in such a way to maximize efficiency. In any given province, there is going to be varying degrees of fertility in the farmlands and it stands to reason that the more people you pack into the province, the more you begin to rely on less fertile and less ideal farmland. This results in less efficient food production and slower growth in that province for each additional person that lives there.
The effect of Ideal Rural Population is that after a plague, famine or looting ravages a province, killing or displacing its Rural Pops, the underlying potential is still similar and the population will begin to rebound. After a generation or two of peace and calm, the population will return to roughly its IRP.
Changing Ideal Rural Population Edit
While far less variable than the actual Rural Population at any given time, the Ideal Rural Population will dynamically respond to longer term events. Perhaps the greatest driver of IRP growth over time is steady improvement of Farming Efficiency
Innate Fertility Edit
While IRP will dynamically change in response to a variety of factors, Innate Fertility (IF) represents the unchangeable conditions of a province. A province's Innate Fertility is largely determined by climate and terrain.
If you have a 10 Innate Fertility province but it currently has 5 Ideal Population, the Innate Fertility of the province will act to push up your Ideal Population Growth faster than normal until it is back at equilibrium. Conversely, if that province has 10 Innate Fertility and 20 Ideal Population, Ideal Population will increase much, much more slowly. This makes regions enjoying a "population golden age," like the Medieval Andalusia and Sicily, relatively vulnerable should they be wracked by discord, while also allowing regions that have been ruined by war capable of eventually pulling themselves back up.
Growth Model Edit
So how is population growth calculated? Universal Growth Factor 1.01
Provincial Fatigue (or whatever it's called) Edit