Quote:
Originally Posted by cdcox
The real tragedy is that with two data points they can't even be sure that they've selected the correct population growth model.
Obviously they chose a linear growth model:
dP/dt = k
But their estimates would be different if they had chosen a geometric growth model:
dP/dt = kP
or a decreasing rate of increasing progression model:
dp/dt = k (Z-P)
You'd need at least three data points to accurately select the correct model. Taken together the three models make the classic S-shaped population curve (Geometric -> Linear -> Decreasing Rate). Any of the three models might be applicable, depending on the amount of resources available relative to the population, demographics, and social attitudes. Also, none of these models should be used to project populations more than 10 years into the future.
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Interesting. On population projections of humans, I've typically used either a simple exponential model (short-term only), or a ... what's it called. P2=P1*e^(-kt). That one. Can't remember the name. For population growth they tend to work pretty well because the growth rates are relatively small numbers.
What's Z in your third model?
I know this firm, and they have no ability to do projections at all. In fact, all they were trying to do is say that the population has grown X percent over a 7 year period, and they couldn't even do that.
This one particular firm is a joke. They don't do research and have no researchers on staff, but if a client wants it they'll make all sorts of claims and take their money. And then they do stuff like the calculations above. And don't even get me started on their surveys. I wish my business had some sort of entry requirements.