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Hanley Sustainability Institute

A lesson about natural resources: Exponential growth and limits in a time of COVID-19

By Robert Brecha

Note: University of Dayton physics professor Robert Brecha is on leave serving as a European Union Marie Curie Fellow working with Climate Analytics in Germany on sustainable energy access and system transformation in Least Developed Countries and Small Island Developing States.

One of the foundational notions of sustainability is that long-term exponential growth in a finite world can only lead to catastrophe. In the last half-year or so we have seen a real-time example of exponential growth and perhaps most importantly, how this growth is most appropriately seen as being a characteristic of a diseased system, not a desirable goal.

Although we do not commonly think of it this way, anytime we discuss the need for continued growth, let’s say gross domestic product (GDP) increasing at 3 percent per year, we are advocating for exponential growth. At least as our society is now organized, the unstated consequence of continued growth is that we will run into the limits of our planetary systems to withstand anthropogenic impacts. And just as a side note, exponential growth does not mean “growth at a fast rate” as we often use the term; rather, exponential growth refers to something that is increasing at a constant percentage each time period. One of the pernicious consequences of exponential growth is that one is likely to be caught by surprise when growth “suddenly” becomes problematic.

Let’s imagine a pair of innocent bacteria, E.coli each with a mass of about one-trillionth of a gram. If we decide to properly feed and nurture them in a Petri dish, they will turn into four E.coli in about 20 minutes. Those four will become eight after another 20 minutes, and so on, doubling in number (and mass) every 20 minutes. At this rate of doubling, the time it would take for the bacteria to multiply such that the mass of bacteria is equal to the mass of a person is less than one day. This seems remarkable (and surprising). What is it that keeps these bacteria from overwhelming the body, since they do start out on that path of doubling in number every 20 minutes? Apparently, there is something setting limits to growth.

There is a simple rule that goes along with this kind of problem that says we can figure out how long it takes for the amount of something to double if it is growing at a constant rate – divide 70 by the growth rate. For a 7 percent annual growth rate, the doubling time would be 10 years. A few months ago (has it only been that long?), if you followed serious news outlets the concepts of doubling times, reproduction rates  (the R0 value) and flattening the curve all became familiar. These are all related to the bacteria example presented above, and more generally, to the idea of exponential growth. 

An obvious solution to the problem of bacteria taking over the body is to not provide them with ideal living conditions. When bacteria start to fill up a Petri dish, they run out of food and the growth rate slows dramatically. In fact, in a laboratory setting it is not unlikely that the resource-limited bacteria begin to produce poisons that actually lead to a collapse of the population. Thus, the exponential growth that proceeded along just fine for some time comes to a halt when the finite amount of fuel available for the bacteria is not enough for their sustenance.

For example, the bacteria doubling in number every 20  minutes will eventually fill their dish, but only 20  minutes (i.e. one doubling time) before the dish is filled, it is half empty, and 20 minutes before that, the dish is only a quarter full, and appears to allow plenty of room for further expansion. The bacteria do not realize that there are limits to growth until it is too late. This feature of exponential growth is what caused many careless commentators to be too sure early in the COVID-19 pandemic that all was going well since the number of cases was apparently small.

The spread of COVID-19 was presented initially in terms of doubling times; for example, the doubling time in reported new cases in New York City increased from two days to two weeks  early in the pandemic. That means that the growth was no longer exponential, and in fact, slowing of the doubling time is a typical sign of what is called logistic growth – something that starts out growing exponentially but is limited by external constraints. In the case of COVID-19, this has been crucial, and one of the basic uncertainties that comes into the models that are cited by government officials, journalists and scientists is how well will we block the virus by limiting transmission opportunities – controlling limits to growth. In the absence of restrictions on contact and movement of people, the virus has unlimited “nourishment,” at least until it would reach another limit, that of the total population of an isolated region or the world. Wearing masks, limiting physical contact and good hygiene practices have all been successful measures, when applied, to limit potential spreading.

On the other hand, when physical-distancing measures are lifted or not implemented with the virus still lurking in the population, then the exponential growth can take off again because of the inherent infection capacity of the SARS-CoV-2 virus. The effect of a vaccination, when one is developed, will be to rob the virus of nourishment in terms of possibilities to spread. In the absence of a vaccine, a number of “natural experiments” are being carried out around the world, with a great deal of uncertainty as to what is the best approach to stop the pandemic. It is clear, however, that we have the ability to set limits to growth on the spread of a virus, but only with great effort.

In terms of one of the other great challenges facing the world, that of the climate change emergency, we also know the cure for eliminating the exponential growth of fossil-fuel use. For more than a century, the trend for extracting and burning coal, oil and gas was a doubling time of about 10 years. We have learned using renewable energy would slow and limit the spread of climate change impacts around the world. Ironically, exponential growth can temporarily be our friend in this case – renewables such as wind solar photovoltaics have been growing at 20-30 percent per year and are now beginning to dominate energy systems in some countries and regions.

For example, 20 years ago in Germany, renewable energy (mainly hydroelectric) made up 3 percent of total electricity generation. Fossil-fuel based utilities were caught by surprise by exponential growth in renewables once favorable policies were put in place; they essentially disregarded the potential for renewables and are now faced with the fact that renewable electricity in 2020 makes up half of the total. We need to enhance our efforts everywhere and ramp up the use of renewable energy to replace all fossil fuels by mid-century at the latest. At the same time, we have to look for ways to increase human and ecosystem well-being without exponential growth in the use of resources, our only chance of staying within planetary boundaries.

For more sustainability news and information, visit HSI’s news blog, the Hanley Sustainability Institute website and the Sustainability Program website.

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