[jerf]

"If one believes that this is a reasonable model to apply to the human population on Earth,"

It almost certainly isn't. The extremely strong propensity for rich countries to have fewer-than-replacement children kills this model. Animal models have no equivalent to this.

We're headed into uncharted territory with human population. Usually this is supposed to be a sort of implicitly scary thing to say, but since the charted territory here is "guaranteed major ecological catastrophe", it's net good news. Disaster is not assured! (Of course, it's still on the table. It's always on the table.)

On the flip side, we're in thoroughly uncharted territory in terms of carrying capacity as well. On the relevant timeframes (decades, minimum), nobody can correctly predict what our technological carrying capacity will be. There's no guarantee it will continue going up, but contrary to the doommongers there's no guarantee it will stay static or go down significantly either; if in 40 years we've licked nuclear energy and cheap robots we could well be growing huge amounts of food in robot-tended greenhouses stacked into skyscrapers, powered by the nuclear energy, or growing meat in vats with chemical energy more efficiently than going through the full biological cycle. And while that may sound like sci-fi, those actually feel like conservative extrapolations of existing trends. (Just about the only prediction I won't buy is the one where we make no further progress and everything stays the same but we keep consuming resources at the same rate, but that's the one you hear most often.)

[chad_oliver]

I'm not a biologist, but surely the fewer-than-replacement birth rate could be considered as just a new way for the population to drop to carrying capacity? It may be a response unique to humans, but wouldn't the effect be the same?

[afterburner]

It's not a response to the carrying capacity of the planet/environment, though. It's a response to the pressures and culture of human societies in developed countries.