The endangered species act outlines empiracle data that at least 1000 individuals are needed for short term self-sustainability ~100 years, but due to environmental disasters, a colony would need to start with 10,000 individuals at first to guarantee survival for 1000 years, assuming they are living "in the wild" without anyone artificially re-supplying them or otherwise helping them. That's just statistical extrapolation with animals. Perhaps we could do with less because we are tool-users, and tools can be used to build more and better tools.

For space colonization we are trying to choose between:

1. Sending 3 people as far away from Earth as possible.
2. Putting as many people in space as possible.

For any estimate on colonization, you have to choose the second option. The first option would be just a temporary scouting party, with emphasis on *temporary* !