Yep, population dynamics is a lot of fun to think about, especially for those of us who loves to play "god" games like Sim City.
The thing with our current population explosion is that most of it happened over the past 100 years, even though we human beings have a recorded history of 10,000 years. We started the 20th Century with around 1 billion people if I remember right. Granted most of the population growth was in developing countries (China, countries of Africa, etc.)
If the population explosion model of growth applies to the Sirius Houses, I think Liberty is probably in the worst position, because it is hemmed in on all four sides, with no border systems to expand into like the other three houses can.
Damn, we humans sure know how to propagate!