Just watched Children and Time [DS9], and the growth rate astounds me…
So, when they crashed, there was 49. Shortly thereafter, Kira died and there was 48. In the matter of 200 years, their numbers increased at an astounding rate. They went from a population of 48 to 8000. That's got be some insane reproduction.
I'm not very experienced at population growth rate, but according to this formula that means that their population increased by:
PR = (((8000 – 48)x100)/48)/200) = 82.83%. Their population increased by, on average, a nearly 83% yearly. That means that the crew of the Defiant must've been a very… fertile… bunch.