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Douglas_Knight comments on Non-Malthusian Scenarios - Less Wrong
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These are answers to a different question: how could a singleton limit population? More precisely, they're answers to the question of what a singleton could do now, since in the long run, people would evolve around any particular mechanism that doesn't wipe them out, so the singleton would have to adapt.
This assumes high genetic heredity of fertility decisions. Binary fertility does seem largely like it has a strong genetic component, but once it's there, the decision to have two children versus six children seems to be influence overwhelmingly by non-genetic factors. Once industrialization took root, fertility fell quite heavily. Since there would be rather strong selective pressures favoring "have more kids when resources are available," this suggests that such an impulse, if genetic, is very easily outweighed by other factors.
If it's memetic rather than genetic, the argument requires extraordinary stability, for which I see little evidence.