The physicist Enrico Fermi pointed out that an advanced spacefaring extraterrestial civilization could colonize the entire galaxy in only a few million years. On a galactic timescale, this is a blink of an eye. That no civilization has apparently done so already is the Fermi Paradox
The Drake Equation
is used to calculate the likely number of extraterrestrial civilizations in the galaxy on the basis of a number of astronomical assumptions. If the assumptions are reasonable, the result is not a crowded galaxy. However, the assumptions don't take the factor of colonization into account.
The star nearest to Earth is about four light years away. A spacecraft traveling at 10% of the speed of light (well within the realm of plausibility, unlike warp drive, hyperspace, etc.) could reach it in a few decades. Would you expect this to be beyond the reach of a civilization 10,000 years more advanced than our own? Suppose this society could colonize a new star system every 10,000 years (allowing time for ship construction, travel, and the adaptation of suitable planets), and every colonized world could colonize another every 10,000 years. They would run out of space relatively quickly.
It seems that nearly every conceivable approach to the paradox, plausible and otherwise, has already been advanced. A list of them is here
. But for some reasonable explanation, it should be rather easy to detect an extraterrestrial civilization. Whatever the reason we have not detected this extraterrestrial civilization may be, this does not bode well for the SETI
program. Either there's nothing to find, or no one wants to be found.