The Oil Drum

I'm actually a physicist, and I agree with your requirement of defensible reason being more important than quantitative, but there is, as a physicist, some wriggle room. It depends on the quality of the data and the stage of development of the theory. For example, in Verhulst's time, there was no data with which one could do a reliable study of the effect of starvation alone, as opposed to starvation and disease, or starvation and war, etc. So Verhulst chose to simply posit that population tended toward a saturation number that was a new parameter in the Malthus model. In the absense of any real data, this was little more than an intellectual place holder for the idea that this model can't possibly be complete.

Then a century later Hubbert needs a simple formula for a time dependent quantity that starts very small, grows to a peak and then declines, ultimately to zero. He sees that Verhulst equation meets his criteria and uses it.

The Gauss normal curve also meets these theoretical criteria. I tried Gauss curve when first learning about PO. It leads to very messy algebra. There was no theory that supported using Gauss in this situation. The central limit theorem applies to large numbers of statistically independent events. Since I didn't want to use Gauss because the algebra was messy, it was easy for me to convince myself that there were surely not a large number of independent events in this situation.

He, like a physicist, doesn't have to justify trying it. Using it only needs justification if it works, and then the justification is more a discussion of what work needs to be done to develop a proper theory. Among other things, one needs to develop a good procedure for selecting data.

Elsewhere in the discussion I've posted a comment about how troubling it is that Hubbert linearization requires that the Hubbert peak be symmetric.

I think that we may very well witness the post peak decline in real life before we have a adequate theory of how to predict it. What we have now is good enough for economic hand waving, but as soon as decline is real there will be rapid changes that will lead to big forced changes in human behavior.