I started from the somewhat iconoclastic hypothesis that the different primary energy sources are commodities competing fora market, like different brands of soap or different processes to make steel, so that the rules of the game may after all be the same. These rules are best described by Fischer and Pry, and can be [summarised] in saying that the fractional rate at which a new commodity penetrates a marketis proportional to the  fraction of the market not yet covered.

F'/F = a(1-F)

He then shows some examples from actual data, and says

All of them refer to competition between two products. In the case of energy we have three or four energy sources competing most of the time and it is mathematically impossible that [the sum of all the F's equal 1], so I had to extend the treatment slightly with the extra stipulation that one of the fractions is defined as the difference to one of the sum of the others. This fraction follows approximately an equation of [the above type] most of the time, but not always. It finally shows saturation and change in coefficients. The fraction dealt with in this way corresponds to the oldest of the growing ones. The rule can be expressed in the form: First In, First Out.

With two products, with market shares F and G adding up to 1, one can write

F'/F = a G

which implies

F' = a F G

and, given that F' + G' = 0,

G'/G = -a F

So, in the case of two commodities the Fischer-Pry model is compatible with F + G = 1. Now, suppose we have F1, F2, F3, ... Then, Marchetti is right that

F1'/F1 = a1 (1 - F1)
F1'/F2 = a2 (1 - F2)
...
Fn'/Fn = an (1 - Fn)

is incompatible with F1 + ... + Fn = 1. However, realising that 1 - F1 = F2 + F3 + F4 + ... + Fn, one can see that the "proper" generalisation of the Fischer-Pry model to n > 2 commodities is

F1'/F1 = a12 F2 + a13 F3 + ... + a1n Fn
F2'/F2 = a21 F1 + a23 F3 + ... + a2n Fn
...
Fn'/Fn = an1 F1 + an2 F2 + ... + an{n-1} F{n-1}

which is compatible with F1 + ... + Fn = 1 as long as a{ij} = - a{ji}.

The coefficients a{ij} are a measure of the rate at which the ith commodity takes market share away from the jth one (or loses market share if the coefficient is negative).

So, question: do we have the necessary data to fit this extended model and compare it with Marchetti's simpler one?

Can the last politician to go out the revolving door please turn the lights off?

Our civilization, throughout its history, has treated ALL energy sources as non-renewable, and exploited them to exhaustion, even when they were not intrinsicly so.

Jared Diamond gave examples of Japan in the Edo period (reversed deforestation) and then some Pacific island where they decided to limit the population to 1000 or so, and get rid of all pigs. Societies can be aware and manage the resourses.

But aghr... those examples are not exactly of "our" civilisation, or are they?

Your evidence that all these curves are logistic points to a deeper problem: Our civilization, throughout its history, has treated ALL energy sources as non-renewable, and exploited them to exhaustion, even when they were not intrinsicly so.

Given the information in this diary and in Marchetti's first paper it is not obvious that the absolute consumption (as opposed to "market" share) of each energy source is logistic.

But you are right, from other sources we know that we are perfectly able to exploit renewable resources to extinction (fisheries and European forests are good examples).

Can the last politician to go out the revolving door please turn the lights off?

2006. F = 0.3% <> F/(1-F) = 1/332 = 10^{-2.5}

2012. F = 1% <> F/(1-F) = 1/99 = 10^{-2.0}

2018. F/(1-F) = 10^{-1.5} = 1/32 <> F = 3%

2024. F/(1-F) = 10^{-.5} = 1/3.2 <> F = 24%

2030. F/(1-F) = 10^{.5} = 3.2 <=> F = 76%