I do not know the exact contributions but there is a whole series of factors including
1) base pop_growth_rate (which can be tweaked in the game files)
2) life rating in a given province (the higher the province's life rating the faster the population in that province will grow)
3) ability of POPs to get life needs (if the lowest POP classes can not get their life needs, they will begin to die off and shrink in size)
4) technology advances that boost the base life rating of the country as a whole
5) state vs colony - i'm still testing this to prove for a fact, but it does seem that colonial POP growth rates are lower, all other things equal, than state POP growth rates
6) the existence of specific reforms such as health care, which at higher levels will boost POP growth (better health care = less infant mortality, longer life for POPs etc)
and to Oerdin - if you look at the range of responses in this thread you'll see that in fact there is a very wide variety of population results, most of which tend to be on the high side. Victoria is not a historical simulator, it is a game set within a historical era that attempts to capture the broad themes of the period. For the United States, this means having huge waves of immigrants arrive that allow the USA to be transformed from a second-rate regional power at the start of the game to a true global power by the end. Attempting to portray even more historical results than this would have required the development of separate algorhythms for immigration for the USA (and thus likely other countries, why should the USA be the only one to get special treatment to try and model historical patterns) that would have resulted in a great deal more computation of statistics each game day.
And considering that Victoria is designed to run at a 128 MB RAM (the game was designed back in 2002, when that was considered the global standard low-end level of RAM in a computer) adding much more to the game engine to compute on a regular basis, given how slow the game already runs on low-end systems, would probably be impossible to achieve and still keep the game within its base minimum prerequisites.
For the overall game purposes based on the game engine Victoria has, what Victoria reproduces for the USA in terms of population growth and immigration is more than sufficient to capture the nature of the historical transformation of the USA that happened in the 19th and early 20th century. The broad themes are there for the player to use, even if the specific historical details of how that process worked are not able to be depicted.
Now, should the gods of Paradox decide to revamp the Victoria timeperiod into a new game title based on the new game engine and the massive increase in minimum computing power that has occurred over the past five years since the design of Victoria, then perhaps greater emphasis on trying to recreate more clearly historical patterns could be attempted. Paradox has learened a great deal over the past five years in terms of game design, as well as what works well and what needs improvement in Victoria, so a redesign of the title would definitely be able to draw upon a mountain of experience of gamers over the past four years since the release of Victoria commercially in 2003. And with the much greater power of the average personal computer today in 2007 compared to when Victoria was designed in 2002, the ability to be able to handle more complex data for the game will also be significantly expanded.
