Spruce budworm and oil price: a biophysical analogy

Trying to modeling some dynamics of the energy market, especially for the largest part consisting of oil and gas, we looked to some simple traits, useful to compare these dynamics with something that happens in Ecology. In particular, in the simplest case, the oil market dynamics are marked out by two variables: one, the price, is able to vary quickly and the other one, the EROI, slowly. The EROI (acronym of Energy Return on Investment) is an index used to measure the quality of an energy resource. This is an adimensional index that can be measured using directly the energy, but also with energy proxies like CO2 [1] or the monetary one [2]. The EROI depends on a huge number of (sub)variables, some of them geological (the availability of the oil fields), some other technological (the efficiency of drilling, the technological improvements) and so forth. For this reason, it is quite difficult to know what are the laws that the variables (price, EROI, production) obey. Therefore, a phase-plot diagram has been used to represent variables as price and production from 1965 to 2018 [3]: it shows an "erratic walk" but also some regularities with two ascending movements and two descending ones. Some considerations can be done on this behavior, but for our aim, the most important is given by the inelasticity shown also in the following example. For simplicity's sake we can suppose having two oil wells: one at a lower cost of extraction (e.g., 100 $/barrel) and one higher (200 $/barrel). If in our hypothetical world the consumption is in the range between 0 and 1,000 barrels/day, we use the oil at a lower price, with a price (ideally) inside the range 0-100 $/barrel. If the intensity of consumption grows, we need to use the second stock of oil, extracted at a higher price. In this case, the oil price increases rather rapidly, and the dynamic, in this case, show four movements: two with a very fast variation (oil price) and two slow (the production intensity). If the oil price increases rapidly, the consumption decreases and, sooner or later, society comes back to the previous range of extraction intensity. A model suggests the analogy between this feature of the oil market and some dynamics well studied [4] [5] [6] in Ecology, where we have three species in mutual competition, following a variant of the Lotka-Volterra model: 1. Prey: the American spruce, whose needles are the food of caterpillars of the species Choristoneura fumiferana (this is the slow variable since the regeneration of the leaves - and not only - is a process that lasts several decades); 2. Predator: the population of the caterpillars Choristoneura fumiferana, considered able to vary rapidly (fast variable, since demographic outbreaks of this species, periodically observed, are considered a real scourge); 3. "Super-predator": the population of birds, which eat the caterpillars, but do so at a rate that we can consider constant (identified as a "natural" rate of mortality of the caterpillars themselves) because this predator actually does not feed exclusively on these caterpillars. The demographic explosion of the latter, however, saturates the space for all prey (the needles of the spruce). In this sense, we will not take into account, in the following discussion, this variable. The ecological model is briefly described in this way: the needles area surface grows, but also the caterpillars' population. They eat all the needles of the spruce and, at a certain point, there is a population outbreak: the needles decrease until the caterpillars die for starving, and therefore the population decreases very fast. At this point, there are no needles and no caterpillars and the woods need more or less forty years to regrow and start again the cycle. To switch from ecological t