Earth was doomed in any case; space travel just hurried it along.
...Space travel can't ease the pressure on a planet grown too crowded, not even with today's ships and probably not with any future ships–because stupid people won't leave the slopes of their home volcano even when it starts to smoke and rumble. What space travel does do is drain off the best brains: those smart enough to see a catastrophe before it happens and with the guts to pay the price–abandon home, wealth, friends, relatives, everything–and go. That's a tiny fraction of one percent. But that's enough.
...If–as Lazarus thinks, and statistics back him up–every migration comes primarily from the right-hand end of the normal-incidence curve of human ability, then this acts as a sorting device whereby the new planet will show a bell curve with a much higher intelligence norm than the population it came from . . and the old planet will average almost imperceptibly stupider.
...That tiny fraction that hardly shows statistically is the brain. I recall a country that lost a key war by chasing out a mere half-dozed geniuses. Most people can't think, most of the remainder won't think, the small fraction who do think mostly can't do it very well. The extremely tiny fraction who think regularly, accurately, creatively, and without self-delusion–in the long run, these are the only people who count . . and they are the very ones who migrate when it is physically possible to do so.
From "Time Enough for Love" by Robert A Heinlein.