The LTG study was based on a rather complex model which, however, can be summarized in terms of five main elements. The five elements are 1) population, 2) mineral resources, 3) agricultural resources, 4) pollution and 5) capital investments. This is just one of the many ways to build such a model. Other choices are possible, but the LTG model, improved over the years, is a good way to capture the essential elements of the world's economy. Despite the persistent legend that the LTG study was "wrong"; the results of the study have been found to be remarkably accurateNone of the five elements of the model is a problem in itself. But each one can become a problem. In that case, we speak of 1) overpopulation, 2) mineral depletion, 3) famine, 4) ecosystem collapse and 5) economic decline. Often, these five problems are considered as if they were independent from each other. People tend to attribute all what is going on to a single problem: peak oil, climate change, overpopulation, and so on. In particular, economists tend to see the economy as independent from the availability of natural resources. Of course, this cannot be true and in a "dynamic" model, such as the LTG one, all the elements of the economic system interact with each other; either reinforcing each other (positive feedback) or weakening each other (negative feedback).
In the LTG world model, "capital" is created by investments generated by industrial activity. Capital is assumed to decay at a rate proportional to the amount of existing capital. This is called obsolescence or, sometimes, depreciation. To keep capital growing, or at least not disappearing, investments need to be larger than, or as large as, depreciation. Since investments depend on the availability of natural resources, the buildup (or the dissipation) of the capital stock depend on the progressive depletion of these resources. In the original LTG model of 1972, there were three kinds of capital stocks considered: industrial capital (factories, machines, etc.), service capital (schools, bridges, hospitals, etc.) and agricultural capital (farms, land, machinery, etc.). In the latest version (2004), industrial capital and mining capital are considered separately, as you see in the following figure ( from the synopsis of the 30 year update of LTG). Note how the "capital" parameter (in its various forms) affects the parameters which determine the GDP.
Here are the results of these interactions, expressed in graphical form as what is called the "standard run" or "base case model" of the LTG study (from the 2004 edition)
In the graph, you don't see the "capital" parameter plotted. However, industrial capital follows the same curve of industrial production. The other forms of capital have a similar behavior. All reach a maximum level and then decline, carrying the whole economy down with them. Overall, it is "peak capital."
When do we expect peak capital to occur? According to the "standard run" of the LTG report, it may arrive during the first two decades of the century. It may very well be that much of what we are seeing now is a symptom of peak capital approaching: airports, roads, bridges, dikes, dams, and about everything that goes under the name of "infrastructure" are decaying everywhere in the world. The whole economic system is becoming unable to maintain the level of complexity that it had reached just a few decades ago.