This article covers both the basic gameplay considerations of handling population growth as well as the more technical underpinnings of the system [Formulas and such to be added later].
Rural and urban populations have a certain Ideal Population, or carrying capacity, that they will be drawn towards. The further below the ideal level, growth will occur faster, while conversely the further above, growth will occur slower.
What this means is that populations which suffer significant casualties due to disaster will not be permanently diminished. So long as the underlying fundamentals of the province are favorable, the province will be able to recover its population within a few generations. Conversely, if a province's population isn't damaged by plague or war or famine, it will continue to grow bigger and bigger, but the further the number gets from Ideal Population, the slower and slower that growth will be. In theory, if you take extra, extra care of your people, you can keep their population artificially above the Ideal Level of Population.
Urban populations' ideal value is Urban Gravity, representing how strongly a city could attract inhabitants based off its importance, opportunity etc. This is directly improved by Wealth, buildings, Centers of Trade and Production and a number of other factors. As with most factors tied to Urban Pops, Urban Gravity is more easily built up and lost compared to its rural counterpart.
For rural populations this ideal level is simply called Ideal Rural Population (shocker!). This represents the population supported by the arable land in the province. While this slowly ticks up with increases in technology and long periods of stability, it can be reduced by Trauma.
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