This isn't about population growth, it's about the maximum period of "sustainability".
Perhaps I could phrase it better as the maximum period before obvious unsustainability: "The maximum time a given population at a fixed level of technology/affluence can exist before the first sign of involuntary population decline appears."
Essentially this refers to how long a population/consumption combination can last before it hits reach the peak of the bell curve you're used to seeing.
How long that period is depends on the level of consumption technology or affluence, which is the isomorphic to the drawdown of natural capital. The drawdown of natural capital is the sum of the non-recoverable use of non-renewable resources plus the use of renewable resources above the natural replenishment rate. This amounts to a re-statement of the I=PAT equation.
I assume that the Earth has a fixed capacity for absorbing human impact. That means that when we have been around long enough to generate that much impact, we will begin to go away. What that maximum capacity is, is also open to debate.
The time period after we hit that MaxImpact point, during which our population declines, forms the other half of the bell curve you' saw in Bio.
The maximum impact point under current conditions could (perhaps) be estimated by balancing global warming, fresh water drawdown, the EROI of fossil fuels, and the unaided average productivity of agricultural land (without the help of nitrogen fertilizers or irrigation).
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