A Use Case - might be able to work out some rules.
I am assuming a non-garden of Eden (not Earth like ) environment so requires significant technology to survive for example Mars or in Space.
100,000 general purpose population (they can do any job with minimal training).
1% population expansion and as it takes at least 20 year to mature 20% or 20,000 children extra.
Assume 1 Specialist(Doctor, Mechanical Engineer etc) for each 200 people,
therefore 500 people in each specialty. If there are as many as 50 sub-categories, then at least 10 are available in each sub-category.
For 20 specialties (500 * 20) => 10,000 ;
The total is at least 100,000 + 20,000 + 10,000 => 130,000.
If we assume that 3 or 5 in each specialty is the minimum needed then 39,000 or 65,000 respectively would be a minimum sustainable population.
Conclusion: The minimum is at least 10s of thousands.
Note: The more people the better, certainly 1 Million will significantly reduce the risk of a colony dying compared to 130,000.
1I'd say the answer is 0. Or 1 if it doesn't count unless you have a human. The rest can be filled with technology. Just keep cloning the 1 person. – A. C. A. C. – 2017-12-05T23:49:52.523
1What is the colonys technology level? How would you define comfort? If you want a simple farmer style village it won't be that high. As your level of technology increases so too does the number of people required to run it... edit: Grammer – Shadowzee – 2017-12-06T00:13:48.080
You might want to improve your question, by setting specifics (such as minimum population growth rates and wealth growth rates ) and refine the terms, for example self sufficient colony, is a society that trades to mutual advantage with its host (country or region) but does not need the host for its continued development. – LOIS 16192 – 2017-12-06T00:53:46.547
Welcome to the site, Braxton! Your questions are good ones. Keep them coming. – Willk – 2017-12-06T01:01:09.103
When you say "run", do you mean operate long-term (i.e. many generations) as a closed system (no immigrants)? If not, what are the parameters? – Monica Cellio – 2017-12-06T04:33:49.240
"and still be a colony" - is your definition of a colony size dependent? If it has a limit, just max it. The more people, the bigger chance some of them will be able to work for comfort. – Mołot – 2017-12-06T07:46:02.027
By the way, my vote was "unclear what you are asking", because it seems you have something particularly defined in mind, but you didn't share your definition of a colony. Also, it is unclear to me if you want them genetically stable or, for example, able to survive X years and prepare for other settlers. We also need to know what you consider a comfort and what's tech level and environmental conditions... – Mołot – 2017-12-06T07:50:14.050