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policies from the government page (costing 50 oratory) can give you +3 route in capital or +1 route in every province if you reach the good technology (6 ans 12 if I remember correctly)
An other way is to grap the ''plutocratic monarchy'' (don't know if ''plutocratic republic'' exists, but in logic, it should)
so, main are tech, and government (event can provide you some perma buff giving supp route, but nothing you can influence yourself)
hope it helps ^^
- "Entice Business Investments" in the Province's own tab will add 1 new trade slot for 72 Political Influence points.
- I don't know what Technology or Government Law adds an Import slot.
The other thing that adds trade routes is POPULATION. Every 15 pops or so (someone correct me) you get another trade route. I can't quite remember which pops you need, but I think its citizens.
in your capital province, you should get as much nobles as you can get there (so it's good to build the associated building in all cities). In the population panel of cities, you'll see how much trade routes your nobles produce (citizen too but a lot less).
Basically, with enough nobles and trade routes in your capital province quickly enough you'll get a lot of innovations and bonuses from trading. And if you really boost your capital province population, a lots of troops.
It seems that normally one would want to provide lots of food and population capacity, and then the city would grow naturally. Maybe farms and slave estates would help growth too.
Further, in order to convert more people into freemen/nobles, you build more libraries and academies. There might also be some "omen" or diety with an integration bonus that might have something to do with it. I notice that there is a provincial governance policy that increases promotion/demotion. Maybe one should choose that, and then after one gets enough nobles, then switch to an Encourage Trade policy.
https://imperator.paradoxwikis.com/Population
That's why usually one of my first goal is to have only cities on non-food provinces in the main province as well as the whole main region. With plenty of granaries you increase the pop growth and get a huge main army by mid-game. You specialize your buildings then: the capital province will have nobles mainly to increase the number of trade routes faster and get country bonuses, other citizen and freemen for manpower and other bonuses, cities with a high valued ressource slaves.
And you'll need trade routes to import food to feed the growing population.
The stat for population growth should on the main city panel. You'll see that having a lot of food reserve is a good way to increase population growth aside from other bonuses. To increase it, you need granaries.
If I remember, it's a monthly growth stat per province as it depends on available reserve. Note that a big populated province consume more food so has less reserve even if you have a lot of granaries. It means a weaker population growth at one point.
As for promotions, you get it. Policies, building and innovations will help in accelerating the process. Integrating a culture and giving it the noble status instead of the citizen one helps too as you'll get more nobles.
But in my opinion, a soft rate is better. I like slaves, they help producing more, so that's more intern trade route for rare ressources in your empire and you'll export or stack bonuses in productive provinces. Usually, I rely on citizen for science output as they increase manpower. Nobles are important to me in the capital province and then in one city, sometimes two, to get some specific bonuses (mostly population happiness for the main group). Overall, they ensure me to produce more science than I can benefit from.
You expand depending on your needs. Most games, I don't have a fleet, so I rarely import wood. I has to be a province with a lot of freemen or citizen to do so and get a boost in manpower. And in this kind of regions, I do not hesitate to produce wood, a lot of it, and to import more wood for the wood bonuses to stack in the province.
You'll get more trade routes than you need overall by doing so. You can therefore specialize in almost anything in the capital province.