Science fiction stories often suggest that ETs, and our future selves also, would be expansionist, colonizing the galaxy, taking over worlds, and so forth. It's natural enough, because we are expansionist ourselves. But it's actually quite easy to see that ETs simply can't have expanding populations, at least not for very long. Not if they are anything like us.
It's a simple calculation which I covered before. If their doubling time is once a century, say (for ease of calculation) - then in a thousand years, their population multiples by a little over a thousand (two to the power ten). So after two thousand years it has multiplied by a million, by a billion after three thousand years and so on.