Population represents the population of the primary settlement of a province. Population determines the type of settlement: colony, colonial city, or city. Province income increases with increased population.
Population is a number which abstractly represents the population of the primary city of a province. It is not the entire population of the province itself; this amount is not represented in the game. Note that the richness of the province as a whole (as opposed to its primary city) is abstracted as the base tax value for the province; unlike most of the income from a province, the census tax is computed independent of its population. However, most province income is scaled up with population.
To see the population of a province, you want the province screen. For a non-owned province, you get this by just clicking on the province. For your own provinces, you can right-click and select View, or else click the province (you get the picture view of it), then click the church icon. (Note that population, but not growth, is shown on the picture view at the top.) The province screen shows, among many other bits of information, the province's population, along with the rate of increase or decline.
Effects of Population
The most important effect of population is determining when a colony turns into a colonial city. This happens at 1000 pop, or 900 pop if there are natives present. This transition has many effects; for example, you can only promote officials in a city. Cities pay census tax; colonies don't. Cities are worth more warscore and also cost badboy to take in war.
Population also is the difference between being a colonial city (pop 1000-4999), and a full city (pop 5000+). Cities and colonial cities mostly have the exact same rules; however, there are several ways in which they differ. Colonial cities can have their culture converted under certain conditions, whereas the culture of a city cannot be changed unless it is pagan. And colonial cities cost 1/5 as much to religiously convert, if they are on a different continent than the capital of their country. Colonial cities are subject to a few different growth modifiers than cities; see below.
As a city increases in population, when it reaches certain population levels (5000, 10000, 20000, etc.) it will increase its income. Most income generated by a province is affected by its population, including production income, gold income, trade tax, and generated trade. Additionally, at certain population levels (1000, 20000, and 200000) the manpower supplied by the province increases.
Population makes religious conversion attempts both more expensive and less likely to succeed.
Population of all settlements is recomputed at the start of each month, to account for the natural growth (or sometimes decline) in population due to immigration and reproduction. The rate at which population grows or shrinks is called the population growth rate.
Provinces with positive growth rate continue to grow up to population 999999, where growth is capped. Provinces with negative growth rates decline in population, with two exceptions. A colony can never go below 1 pop, so you cannot lose a colony to negative growth, no matter how awful its climate is. Also, a city cannot revert to a colony: no city province can decline below 1000 pop for any reason.
Computation of Pop Growth
The growth rate displayed on the province information screen is a per-decade approximation of the actual growth. Population growth actually occurs at the start of every month, using the displayed growth rate divided by 120. (There are 120 months in a decade.)
For example, a city which has a displayed growth rate of 12% will grow by (12%/120)=.1% per month. If the city has 1000 people, then it will grow by (.1% * 1000 pop)=1 pop per month. Population is kept as a floating point number internally, which results in smooth growth. For example, a colony at 500 pop and 12% growth will grow 0.5 pop/month; in the game you'll see it at 500 for two months, then 501. Internally, it is at 500.5 after the first month.
Factors in Population Growth Rate
A settlement's growth rate is determined by several factors. The base growth rate determined by the stability of the owning country: it is 1% per decade, plus 1% for each point of stability above -3. That is:
Stability Base Pop Growth Rate -3 1% -2 2% -1 3% 0 4% 1 5% 2 6% 3 7%
For example, if your country's stability is -1, all of your cities will grow at a rate of 3%, assuming no per-settlement factors apply.
The per-settlement factors are as follows:
Province is looted: -5% Province is occupied: -3% Province is covered/sieged: -5% Enemy troops present: -5% CoT in province: +5% CoT in adjacent province: +2% Colony or colonial city: +5% Province has governor: +1% Province has manufactory: +2% Location malus: varies; -1% to -14%; see below
On the province information screen, if you mouse over the population growth rate display, a tooltip will appear showing the growth rate broken down according to the factors listed above.
The location malus applies to all colonies and (in reduced form) colonial cities, which are on a different continent than the country owning them. The colony bonus applies to all colonies and colonial cities on a different continent. On the home continent (that is, the continent where a country's capital province is), there is no location malus or colony bonus in any province.
Computation of Location Malus
The location malus is based on a province's "Difficulty for Colonization" number, which is found in province.csv. This number is divided by three. DfC is 0 for many European provinces. It is 2 for a handful of very easy provinces, and usually 3-9. There are no provinces with DfC of 10 or more. Then subtract the following additional penalties:
Province is in Africa: -12% Province is in Asia: -3% Province has tropical climate: -8%
Tropical climates are climates 4 and 6, in province.csv. The resulting number is the base location malus. The base location malus (capped to -14; see below) applies when a province is a colony, and also (strangely) for colonial cities at exactly 1000.000 population. Once the province becomes a colonial city with pop of at least 1000.001, the malus is immediately reduced to 2/3 of its base value. It is also reduced at a few other key population levels, as the colony grows in pop, being eliminated altogether when the colonial city becomes a city at 5000 population. The formula for the malus is this:
location_malus = location_malus_multiplier * base_location_malus
Pop Location Malus Multiplier 0-1000.000 1.0 1000.001 - 2000 0.66666 2000 - 2500 0.5 2500 - 3500 0.33333 3500 - 4999 0.25
Finally, location maluses are always capped at -14. If a malus would be worse than that, -14 is used instead.
Being an island matters. Islands (defined as any province which has no land connection to another province), have a location malus that is drastically reduced from what they would otherwise be. Sometime like a quarter, maybe. Although that's not exactly right, it's a reasonable approximation. The worst island in the world is Fernando Po, and its malus is just -3, when it ought to be -14.
Note that the in-game display of the location malus is rounded to the nearest integer. Occasionally you'll notice a city shrink even though it displays 0% pop growth; this is why. (It's actually -1/3% in that case.)
Other Changes to Population
There are several ways other than population growth in which the population in a province can change.
First, colonization. When you build trading posts or colonies, you add population to a province. Trading posts have 10 people per level. Each successful colonization adds 100 pop to a province. You can colonize all provinces except full cities, although doing so in colonial cities is rarely if ever cost-effective.
A colony can also incorporate the province's native population when the colony becomes a city. Native incorporation happens whenever the colony hits 900 people, either via colonization (typical) or population growth. For example, I colonize a province with a colony at population 822, containing 2000 natives. The colonization attempt succeeds: now I have a colonial city with population 2922 (822+100+2000), and no natives.
Second, warfare is generally bad for population. Whenever a siege results in the capture of a city, there's a chance of population losses. Also, countries can burn trading posts, which eliminates them. AI countries will automatically burn any trading post they capture on the next day.
Natives can also reduce the population of trading posts and colonies in their province, or eliminate them entirely, when a native attack happens and there's no friendly army to fight the natives (or the army retreats). If you get military access with a colonizing country, it is possible to (ab)use it to repeatedly provoke natives and run away, to clear off trading posts and colonies so that you can colonize the province instead. (This tactic is vital for native American countries.)
Finally, events can add to or subtract from a province's population. Some countries have scripted events which may affect their population, and sometimes also a neighbor's. For example, in vanilla EU2, France has an event in 1681 called Protestants expelled from France. If the player (or AI) selects the first choice, five randomly chosen provinces will lose 10000 pop, convert religion, and have their base tax value reduced. Meanwhile, the event triggers an event in Holland which adds population to provinces there.
There are several random events which affect population. For example, the New Land Claimed event adds 2500 pop to a random province (along with some other effects).
In general, population takes care of itself. You should be aware of the population and pop growth rate of colonies, since sending colonists is expensive. Once a colony turns into a city, you should usually just forget about it.
Cities that Aren't Growing
In some places, particularly tropical Africa, colonial cities don't grow. They'll just sit there at 1000 population and a negative growth rate.
The best "solution" to this problem is just to forget about it. In general it's not that important to get colonial cities growing, because even at 1000 pop you get a good fraction of the income you could ever get from the province. Furthermore, the marginal income you'd get by growing the city to 5000 pop is small, and it's also way off in the future, especially if you're having trouble growing the city to begin with. Thus, it's not worth paying much to get -- and sending extra colonists is expensive. Maybe you'll be lucky and get a "New Land Claimed" event.
There are a few provinces which, at exactly 1000.000 pop, won't grow, whereas they will at 1000.001. (Most non-tropical provinces in Africa are like this.) For these provinces, sending an extra colonist might possibly be worthwhile.
One good colonization tactic in the tropics and in Africa is to send a trading post to a province first, even when you plan to colonize immediately. The TP boosts colonization chances slightly for your first colonist, which is nice. But the main reason for it is that your colony will decline in population while you are building it, because of the tropical growth malus. Thus, your 100 pop would decline to 99 shortly, and that means it would take 11 colonists, not just 10, to get it to a city. By sending the TP first, with its 10 men, the small growth losses you take during colonization will not reduce the colony size. Thus, it takes 1 TP and 10 colonists to make the colony a city, which is cheaper.
I don't care about money! I want my city to grow!
OK, OK. See the "location malus" mentioned above? Well, the good news is it will go away, if you can just get the colonial city enough population. So, get your stability up. Still not growing? You definitely want a governor. And maybe a manufactury. Now, if you have spare colonists, send them. Each of them raises pop by 100, which will eventually lessen the malus.
Demoting Full Cities to Colonial Cities
When you capture a city on another continent, you'll usually get its cultural conversion in 30 years. However, sometime the population is too great for that. In this case, if the population is not too much above 5000, you may want to try to lower its population.
There's no easy way to lower the population of a city. However, if it has a fortress, and you can afford to give up its income for years or decades, then you may be able to engineer a significant population reduction by using rebels to cover and loot.
To do this, of course you need some rebels. If you're lucky, you'll get a random rebellion in the province. You might send a missionary; rebels will naturally appear if the attempt fails. You can also try zeroing out religious tolerance to the city's religion; the downside here is that (a) you have to have a slider for that religion, and (b) intolerance will cause revolt risk in all cities you have with that religion, which you may not want.
Note that when a rebellion happens, the rebels are generated with enough men to siege, not just cover, the province they appear in. You don't want a rebel siege to complete, because then you would have to take the city back, to prevent it from defecting or revolting. Sometimes the supply limits of the province will attrit the rebels down below siege levels without you having to do anything. You may also be able to use your own armies to attrit the rebels, by entering the province and then immediately retreating, planning the movement times so your armies are still in the province at the end of a month. But typically, you'll have to cull the rebels by combat, fighting for a while, then running away. Don't let the rebels' morale drop to zero, or they'll all die. To be safe, run away when their morale gets a bit below the halfway mark. You may have to engage them several times until enough rebels are killed that they are below siege amounts.
Once you get rebels in the province, they will cause the looting, siege, and enemy army maluses to growth, for a total of -15% growth. This will cause any city except a high-stability colonial CoT to go into decline. Just remember that even a fairly large negative number is growth per decade, not per year, so it just isn't going to be fast.