From Scientific American:
The problem that tends to underlie all the other problems with the idea is the sheer size of the universe, which was not known when people first imagined we would go to the stars. Tau Ceti, one of the closest stars to us at around 12 light-years away, is 100 billion times farther from Earth than our moon. A quantitative difference that large turns into a qualitative difference; we can’t simply send people over such immense distances in a spaceship, because a spaceship is too impoverished an environment to support humans for the time it would take, which is on the order of centuries. Instead of a spaceship, we would have to create some kind of space-traveling ark, big enough to support a community of humans and other plants and animals in a fully recycling ecological system.
On the other hand it would have to be small enough to accelerate to a fairly high speed, to shorten the voyagers’ time of exposure to cosmic radiation, and to breakdowns in the ark. Regarded from some angles bigger is better, but the bigger the ark is, the proportionally more fuel it would have to carry along to slow itself down on reaching its destination; this is a vicious circle that can’t be squared. For that reason and others, smaller is better, but smallness creates problems for resource metabolic flow and ecologic balance. Island biogeography suggests the kinds of problems that would result from this miniaturization, but a space ark’s isolation would be far more complete than that of any island on Earth. The design imperatives for bigness and smallness may cross each other, leaving any viable craft in a non-existent middle.
The biological problems that could result from the radical miniaturization, simplification and isolation of an ark, no matter what size it is, now …