Why a small Earth colony is a poor Mars model

Could a few hundred settlers sustain an off-world colony, as some small populations did on Earth?

Not on the same terms, because an off-world colony has no local population, environmental knowledge, labor pool, or easy replacement for casualties.

Historical settlements rarely began in a genuinely empty human landscape. Local people could identify water, seasons, hazards, useful resources, and workable practices, while also supplying labor and new members of the community. Mars offers none of those buffers, and radiation, accidents, illness, or infertility would make a small starting population more fragile. The comparison turns population size into a logistics and resilience question that extends well beyond a genetic minimum.