We don't. But Earth's current population is currently over 7 billion and the UN predictes that by 2300 there could be as many as 36 billion humans (http://www.un.org/esa/population/pub...p2300final.pdf
But if that is our population, on worlds that are as/more advanced than ours, their populations would also continue to grow as medical technology improves, life expectancy increases, etc. Granted some alien races may live considerably longer than us (in which case they could have many more children over the centuries), whilst others would have shorter lifespans (which would mean that conceiving and raising children to continue their society is of great significance). Or other worlds like Vulcan where fertility cycles play an important role in population growth.
By the time of Trek colonisation of other worlds has occured, as has terraforming planets to be made suitable for future settlement, so overcrowding on one planet isn't an issue.
If 149 other planets could have populations that varied from 1 billion to 100 billion, which would leave humanity very much the minority.