Unfortunately, that analogy has a very limited range of validity, and it is frequently deceptive. A pioneer on earth does not have to bring his own air; he may have to dig for water, but that is usually readily available; and there is always a source of food (or else he will not settle there!). As a result, the minimum size of a successful colonization on earth -- in Polynesia, for example -- is determined by the minimum population needed to avoid disastrous inbreeding.
A self-supporting colony on Mars will be different, though. It will have to make its own air and make soil suitable for agriculture; it will have to provide pressurized enclosures where people can live; it will have to make potable water from dirty ice or brine. All these will require lots of machinery, which the colony will have to be able to build and repair; that means making lot of tools. That will require mining and refining iron, copper, tin, and zinc; it will also require making glass, ceramics, and of course silicon wafers. And, naturally, the tools needed for all these operations!
With a population this large, there will be a need for doctors, police, teachers, and clergy. It will not be possible to live on Mars as hunter-gatherers, because there is nothing to hunt or gather. In short, a city of tens of thousands would be required. My guess is that a population of at least 50,000 would be required.
This should be kept in mind when folks talk about colonizing Mars. The first colony will either be hugely dependent on expensive support from earth, or we will have to build and land a mothership. Neither one will be feasible until we come up with a cheap, safe, and practically unlimited energy supply -- probably fusion. That means neither will be doable until the end of this century at least.
By the way, I also wonder what size population would be needed to maintain a modern, technological society. The TV show Battlestar Galactica dealt with just such a situation; they seemed to have some hope of rebuilding their civilization on New Caprica from an initial 50,000 or so. Once again, that strikes me as a minimum size. When they went to (our) earth and split up, they really should have tried to lay the groundwork for falling no farther back than the iron age. (They fell back all the way to the paleolithic!)