Saturday, 2 January 2021

Collapse you say? Part 4: growth, overshoot and dieoff

Nature's Ice Sculptures Along Lake Huron

On the rare occasions when the subject of collapse comes up in polite conversation, a kollapsnik like me is liable to get responses like: "Collapse you say? Surely not!" Thus the title of this series of posts. But I've found that responding with "Surely yes!" isn't very effective (as well as sounding rather childish). The pandemic this year (2020) has got some people thinking a bit more, but most still expect things to get back to normal any day now.

So in this series of posts I've been talking about what collapse is and why I think the our civilization has been slowly collapsing for several decades and will continue doing so. This in the hope of laying out the facts clearly enough that just about anyone should be able to recognize the seriousness of the situation.

In the last two posts(Part 2, Part 3), I looked at problems with the inputs to and outputs from our civilization, and pointed out a number of issues, any one of which alone should be cause for great concern. And taken together, well....

Now I think it is time to have a look inside the box labeled "Industrial Civilization". When you look around you from within this civilization, you are confronted with a complex and confusing sight, of which I don't have any sort of complete understanding. But there are some aspects which bear more directly on collapse than others, and I'll have quite a bit to say about them in the next few posts.

The problems we've looked at so far—resource depletion, declining surplus energy, climate change, overshoot and decreasing carrying capacity—all seem to be a result of the ongoing growth of our civilization, both population growth and growth in affluence. So you would think we'd be making a serious effort to get growth under control, maybe even initiate "degrowth", in order to cope with these problems. And yet, over the last few decades economic growth has come to be seen as a necessity. If you paid attention to election speeches, you'd conclude that the most pressing problem we face is maintaining and further stimulating such growth, not preventing it. It seems to me that this obsession with growth is a built in feature (dare we say a fault) of our civilization.

To more clearly understand our impact on the planet—our footprint—we need to review the subjects I touched on at the end of my last post: eco-system services, carrying capacity, and overshoot. Eco-system services are things like breathable air, potable water, a reliable climate and moderate weather, arable soil, grasslands, forests and the animals living on/in them, waters and the fisheries they provide, and so on. And also important, though I neglected to mention it in my last post, is the ability of the eco-system to (within limits) absorb and process our waste products. All these things are available to us free of charge and we simply could not do without them.

It is reasonable to call the rate at which the eco-system can supply those services to us its "carrying capacity". The portion of those services that the human race uses can be called our "footprint"—the impact we have as we walk upon this planet.

According to the Wikipedia article on carrying capacity, credible estimates of carrying capacity range from 4 to 16 billion humans, with a median around 10 billion. The literature I've read on carrying capacity and dieoff typically talks about us currently being at around 165% of the planet's carrying capacity. If such estimates were made when our population was around 7 billion, then the carrying capacity was a little over 4 billion. That's at the low end of the range of estimates, which seems prudent. Using the high or even median estimates would lead us to do nothing in the belief that everything is OK and may well continue to be OK. Instead, we should be setting ourselves up to run well below carrying capacity, allowing us to live on this planet without damaging it and with a comfortable margin to allow for unforeseen circumstances.

Being over carrying capacity is called being in overshoot, and it leads to collapse. Some of the extra over 100% comes from consuming non-renewable resources, and some of it comes from using renewable resources at greater than their replacement rate, so that they too are irreversibly consumed. This means that we are actually reducing the carrying capacity of the planet and digging ourselves into an ever deeper hole. Certainly judging from the resource depletion and pollution (mainly climate change) problems we're currently experiencing, it seems that we are indeed in overshoot, and the condition of the ecosphere is definitely worsening.

If we are to solve the problems caused by our overshoot we need not just to reduce our impact below the current carrying capacity of the planet, but rather to go below the smaller carrying capacity that will be left by the time we get to where we are aiming. Further, since it is a big planet with different conditions in different places, we can't just look at global averages, but must consider impact versus carrying capacity on a region by region basis. This to avoid being fooled if we are lucky enough to live in an area that is not as yet hard hit. In much of Europe and North America, it seems we are currently being fooled.

Our footprint (impact) is expressed in the following equation: I=PAT.

"I" stands for impact, or footprint, which is the product of three factors:

  • "P", which stands for population.
  • "A", which stands for affluence, or consumption of resources.
  • "T", which stands for technology, and is included in the hope that improving technology can reduce our impact

We seem determined to do whatever it takes to increase "I", no matter how negative the results. Is this because of something inherent about human beings, or the way we organize ourselves, or the circumstances we find ourselves in? Or perhaps all three combined together?

In the rest of this post and the following one we'll look at this from the viewpoint of our growing population. In future posts we'll look at the role affluence and technology play in our problems.

But first I think we need to understand something about the mathematics of growth. In cases where the rate of growth is related to the size of what's growing, growth is "exponential". If you chart such growth on a graph, it looks something like this:

Figure 1, The Exponential Function

This is the kind of growth you get with a compound interest savings account, where even if the interest rate stays the same, the balance in the account increases dramatically over time. It is convenient to look at exponent growth in terms of the doubling rate, the amount of time it takes for that bank account to double. A rule of thumb is to divide 70 by the percent growth rate per year, and that gives you the approximate doubling period in years. If you are lucky enough to get 10% interest, your savings will double in 7 years. At 5% interest it takes 14 years to double and at 1% interest, it takes 70 years to double.

What may not be clear from Figure 1 is the degree to which the curve takes off as it moves to the right. Growth is very slow at first until we reach the "knee" of the curve, then it goes right through the roof, so to speak. A great deal has been said about how exponential growth is counter-intuitive for most people. Here is a short (not quite two minutes) YouTube video about the subject. If you have a little more time (11 minutes), this video goes deeper into it.

But in the physical world, growth consumes resources, which are only available at a certain maximum rate and can a only support so large a population. At some point the rate of growth starts to decrease and the curve levels off rather than continuing upwards. So the exponential curve doesn't really give us a very good picture of how growth actually works. For that we need to look at the logistic function.

Figure 2, The Logistic Function

Of course the logistic function assumes a constant supply of whatever it takes to support a population, so that the right side of the curve levels off and stays flat. Again, the real world doesn't exactly work like that. In the real world it is possible to go into overshoot, and over consume resources so that the rate at which the system can supply them is reduced. This results in something like the curve shown below.

Figure 3, Overshoot and Dieoff

The population in this case is of some sort of simple organism with a more or less fixed consumption rate per individual, and a growth rate determined by the availability of food. I have chosen to show the worst case scenario where the population we are considering declines to zero because of decreased carrying capacity and the rest of the ecosystem is so badly damaged by the overshoot that it dies out as well.

Fortunately, this is not necessarily the case—as the population goes into dieoff it eventually goes below even the reduced the carrying capacity of the environment and quits damaging the environment. The environment, if the damage is small enough, may be able to recover, even if the species that was in overshoot doesn't. If it recovers enough before the population under consideration goes extinct, that population may be able to recover as well, something like this:

Figure 4, Overshoot, Dieoff and Recovery

What happens as time progresses off the right end of the graph varies. The population may go into overshoot again, then die off and recover, and this may be repeat on an ongoing basis. Or, at any point along the way, a dieoff could lead to extinction. In any case the idea that there is a "balance of nature" that would cause the population to level out just below the carrying capacity is largely bogus. Things are always changing and don't stay balanced forever, or even for very long.

So now that we've looked at growth in general, we need to look in detail at the growth of the human population of this planet. Because human populations can change their growth rates, their levels of consumption and even the carrying capacity of their environment, this is complex, and I'm going to devote the whole of my next post to the subject. In short, though, based on the ideas of carrying capacity, overshoot and our capacity for growth, I am not in the least dissuaded from my predictions of collapse,"dieoff" in the language we've been using in this post.

This has turned out to be quite a short post, mainly because I have split it in two and saved the slightly longer second half for next time. So, there is room here for a couple of graphics about carrying capacity and ecological footprint.

Figure 5, Biocapacity and Ecological Footprint

This an interesting and possibly misleading graph, which compares the carrying capacity (biocapacity) of various countries with their consumption, on a per capita basis. The units on the vertical axis are "global hectares per capita, Gha".The Wikipedia article on GHA is a short and informative read. Here is one central paragraph:

"Global hectares per person" refers to the amount of production and waste assimilation per person on the planet. In 2012 there were approximately 12.2 billion global hectares of production and waste assimilation, averaging 1.7 global hectares per person. Consumption totaled 20.1 billion global hectares or 2.8 global hectares per person, meaning about 65% more was consumed than produced. This is possible because there are natural reserves all around the globe that function as backup food, material and energy supplies, although only for a relatively short period of time. Due to rapid population growth, these reserves are being depleted at an ever increasing tempo. See Earth Overshoot Day

To understand what I mean by misleading, take a look at Canada, the country where I live. The graph might make it seem that we are doing fine, since we have a large biocapacity compared to our population. but our per capita consumption (ecological footprint) at 7 Gha is among the highest in the world.

Figure 6, Footprint in terms of "Planets"

Another way of looking at footprint is to calculate how many planets like Earth it would take if everyone on Earth today lived like they do in a certain country. As is so often the case, Canada is left out of Figure 6, but a little calculation using the numbers in Figure 5, leads me to believe that if everyone lived like we do in Canada, we'd need around 4.4Earths. I find that quite a sobering idea.

Links to the rest of this series of posts, Collapse, you say?


Bev said...

Excellent as usual, Irv. I'd be interested on what you think of this idea.

Years ago when I first read Daniel Quinn's 'Ishmael' (I'm sure you know it), I joined the Ishmael Community website and took part in discussions there for many years. I think the concept of 'ecological footprint' might have just come in. There was one commenter whose ideas went against the mainstream. In the accepted view, a large number of people (many feet) means a large EF, but in this scenario each 'foot' only has access to a small part of the total resources available (per capita or per 'foota' as it were). So he called that a 'small footprint'. His reverse idea (and this pertains to hunter-gatherer societies), is that since each H-G needed to access a large territory to get the scattered resources available, then he had a 'large footprint', i.e. needed more territory. I hope I've explained this as he did, basically he meant, large numbers of people = small footprint and small numbers of people = large footprint. Since this went against what I was reading at the time, I nutted over it for ages. I even wrote to Mathis Wakernagel, the co-originator of the idea with Bill Reeves, but I never got an answer.

What's your opinion? I know access to fossil fuels has made us able to access huge numbers of resources, but when you factor in numbers of people, then on a finite planet, per capita resource use will decline, which it is.

I still think about his idea but mainstream use of the term EF swamps all else. When the situation is reached where we have a small number of people (survivors) trying to access poor and scattered resources each one will need a large EF to supply them.

I think the commenter was going wrong somewhere and so am I.

Steven B Kurtz said...


One of the chap's errors , according to your explanation, is that he considered only the territory needed to supply adequate inputs of nutrition, water, energy like firewood, etc. Footprints include waste sinks. That H-G produced little waste so didn't overload the territory. Whereas densely populated areas produce far more waste for the territory. As well, to the extent possible they import food/water/energy/materials...from external places. Their footprints are not just local.

Anonymous said...

I'd add that fossil fuels allow us to concentrate those resources. For example, we can walk/drive a mile to the store and buy a banana from thousands of miles away, whereas a H-G (in the same original location) would have a considerably more difficult time acquiring the same banana.

In this instance, the modern world appears 'efficient'.

However, if we account for the energy embedded in the delivery system for bananas, as well as the marginal energy to deliver that specific banana, the calculus does not look so favorable for us vs the H-G. We could add to that the social-political costs as well, such as 'Banana Republic' governments propped up by the U.S., low-wage labor for banana harvesters, etc...though those are more difficult to quantify in equivalent terms.


Robert Callaghan said...

*1.5 °C Threshold = 2030 | Solar Wind < 3% of Energy*
-- Electricity is 20% of energy ∴ 100% renewable electricity = 20% of energy
-- Fossil fuels have been about 80% of energy since 1971
-- Wind turbine plans for 2030 = 800 million tons of coal emissions
-- Wind turbine demand for rare earth production will grow up to 26X by 2040
-- The market for magnetic rare earth oxides is to increase 5X by 2030
-- EVs will fuel a 275% increase in demand for rare earths by 2025
-- Basic resource depletion and insecurity are up while supply & demand will diverge
-- Batteries and hydrogen can't scale up in time to prevent 1.5 °C
-- EV and wind rare earth demand will overwhelm supplies
-- If batteries were 60% more efficient we would use 60X more of them
-- Over 60 yrs jets are 68% more fuel efficient and fly 60X more passengers
-- 2.63 billion air trips were taken in 2010 -- 4.4 billion trips in 2018
-- Euros burn imported trees and seed oils for energy & recycjed garbage for electricity
-- Yanks pump groundwater underground for gas to charge EVs in a megadrought
-- Fracking and conventional enhanced oil and gas both use lots of water
-- EV battery and bio-energy demand will landstrip water and wildlife worldwide
-- By 2035 US farms will lose up to 8X the soil The Dust Bowl
-- Wetland loss is greater than tree loss
-- Inland sea & lake levels will drop globally -- ofen dramatically
-- 40% of Amazon rainforests don't know their ass is grass yet
-- AC cooling energy demand will grow 3X by 2050 = US EU Japan electricty use
-- 24% of energy will be electricity by 2040
-- Not even 3% of energy is solar & wind -- 1.5 °C likely by 2030
-- Earth is heating by 400,000 Hiroshima nukes / day
-- Earth was heating 1 nuke /sec 60 years ago -- 5 nukes /sec now
-- 1971 - 2018 global heat forcing averaged 0.47 watss/m²
-- 2010 - 2018 global heat forcing averaged 0.87 watts/m²
-- 4% of mammals are wild by weight
-- 96% of mammals are livestock and human
-- With 23 billion chickens on earth, if one sneezes we all get the flu
-- Greenhouse gases went up 45% in 30 yrs
-- We kill trees 2X faster than we plant them
-- Net tree loss is about 1 football field per second
--Trees grow faster die younger in heat fire flood & drought
-- Battery & Bio-energy extraction destroys native land water & wildlife

Steve Salmony said...

Joe Clarkson said...


It is true that hunter-gatherers have a very large footprint. The carrying capacity of the earth if everyone is a HG is very small. The question is, "Can the carrying capacity of the earth be increased on a sustainable basis to allow a larger human population"?

I think the answer is "yes", but only a little. Horticulture/agriculture converts "wild" biomass to food resources that humans can use. But it is hard to determine how much agriculture the earth can tolerate without disrupting the ecosphere. When we look at regional populations that were stable over millennia, such as in pre-Columbian America and parts of Asia, we get an idea of how much agriculture the earth can tolerate on a permanent basis. And there are many examples in which too much agriculture was attempted and carrying capacity was gradually reduced (Mesopotamia, Central America).

So how many people can the earth sustain permanently? I think a good approximation is to look at the historical population after agriculture was invented but well before fossil fuels distorted our ability to expand agriculture. One thousand years ago the human population was no more than 300 million. Even if we "round up" to 500 million on the assumption that not all land area was efficiently converted to human use, the sustainable population would be far lower than today's 7.8 billion. This would mean that we have overshot the sustainable population by roughly 15 times. If so, the 165% of carrying capacity that Irv cites is a huge underestimate. I think it is more like 1,500%.

And as Steven Kurtz points out, this is only considering the supply side limitations to carrying capacity. However, I think that consideration of waste absorption only comes into play at population levels that are already far into overshoot from supply limitations.

Irv Mills said...

@ Bev
Footprint isn't just about the area used per capita, but also includes the depth of the footprint. So, yes the per capita land use of hunter gatherers is large, and that of agriculturalists is smaller. But the equation used to calculate ecological foot print or impact is I=PAT. That's Population times Affluence times Technology. To do this calculation, we consider the impact on a fixed area of land, be it a hectare, a country, a planet or whatever. Approached this way, you can see that hunter gatherers who live quite thinly on the land, which would have a much smaller population to enter into the equation and accordingly, a smaller impact or footprint. Agriculture allows a higher population density, so agriculturalists would have a higher population for a given amount of land and, the other two factors being equal, would have a larger footprint.

Of course, affluence, technology and carrying capacity also enter into this, and I am going to be going into those factors in future posts. And possibly in future comments on this post.

But first I'd like to know if my explanation of footprint makes sense to you--please reply.

Steve Salmony said...

The conundrum: increasing food production annually to meet the needs of a growing population is fueling a human population explosion. With every passing year more people are being fed and more people are going hungry.

Irv Mills said...

@ Joe Clarkson
I'm sorry I have to disagree with your first and last paragraphs. Mainly because of some confusion over terminology. Have a look at the comment I directed to Bev. The thing is that land area divided by population is not how you calculate footprint. Footprint, or impact, is I=PAT.
The A term in that equation, Affluence or consumption, certainly does include waste sinks as well as supplies of energy and materials.

Your middle two paragraphs I do agree with. This comes from the T in the equation. Agriculture is a technology that allows us to produce much more food on a suitable piece of land than we could by hunting and gathering. But you are right--we have to do it sustainably, and at the moment we aren't. I think that you are probably right that, done sustainably, agriculture could support less than 10% of our current population.

That's a lot less people than most estimates of the planet's carrying capacity, but carrying capacity is not a fixed thing, and our current overpopulation and over consumption is doing a lot of damage. By the time collapse reduces our population and consumption, carrying capacity will be significantly less.

Bev said...

Irv, I'm not sure.......did Wackernagel and Rees use Ehrlich's IPAT equation when formulating the ecological footprint idea? In any case, I agree with you that the 'depth' of the footprint matters too and that the equation is probably the quickest way we have to calculate it, despite the whole thing being more complex.

My way of looking at carrying capacity goes like this: I consider the earth at a time when all species, including humans, lived by hunting prey (killing other animals) and gathering (tubers, fruit, plants, etc). At that point, I assume there was a balance (albeit a dynamic one) and that no one species made so much impact on its system that the long-term functioning of the system was impaired. I would consider the number of humans existing at that time to be the planet's carrying capacity for the human species. Of course, different species of humans have existed, each with its own strengths and weaknesses and the one we call us, H. sapiens is the only one that has persisted. As soon as humans began to practise agriculture, some part of the system was co-opted for human use and that had the potential to impair the functioning of the whole. And the rest, as they say, is history. Estimates of that number depend on who is making them and what they consider as impaired planetary function.

Irv Mills said...

@ Bev
I am not sure how they calculate footprint either, but it has to take into account that same things that the I=PAT equation does, probably (one would hope) with greater finesse and accuracy.

I am always concerned when I hear the word "balance", even a dynamic one. There is a really good book (fairly short too) by John Kricher: The Balance of Nature, Ecology's Enduring Myth.

But at any rate, as soon as we started using tools, fire, organization and so forth it gave us an advantage that other species do not have. Some would say that the rest is just history, on the way to our eventual demise. I don't agree, for all that I talk about collapse. It is possible for humans to live sustainably--we have done so at times. But it is starting to look like we'll probably wait until collapse is over before giving it a serious try. Strong forces are at work within our society to keep our population and economy growing. A lots of money is being spent to convince us that it has to be that way.

Anyway, I'll be discussed all most of this in more detail in my next few blog posts, which I think you'll find interesting.

Irv Mills said...

@ Robert Callaghan
Good info! None of which I disagree with. We are already in the process of collapsing, and we'll continue to do so. Most of the things being suggested as solutions will turn into tomorrows problems.
But humans are nothing if not adaptable. I suspect a much reduced number of us will do just that post collapse--adapt to new conditions and carry one. Hopefully having learned something in the process.

Irv Mills said...

@ Steve Salmony
I read your post. Some good thinking there. I agree that excess food supply is a necessary condition for our population growth. But I am not so sure that it is a sufficient condition.

Our growth rate peaked out at around 2% per year in 1968 and has been declining ever since. In the developed world, where excess food is in great supply, causing an epidemic of obesity, populations are actually declining.

For a long lived species like ours, there is a big delay between reduced growth rate and an actual decline in population, so it is hard to see what is actually happening. If I was extremely optimistic I'd predict that our population will peak out around 2100 at about 10 billion. I am not that optimistic--I don't think the planet can support that many people, and I expect there will be a major dieoff of our species mid-century, with only about 10% of us surviving, mostly those in thinly populated areas away from cities. During this process I hope the survivors will learn a few things and strive to live sustainably.

Or as you might say, a crash in food supply will reduce our population, and the survivors won't likely be able to produce much of a surplus of food, so our population will not grow back quickly.

I'll have more to say about this in my next few blog posts. Stay tuned!

Irv Mills said...

@ Oji
Yes, energy from fossil fuels has been responsible for the amazing growth in both our population and economy over the last 300 or so years. This is a great pity since those fuels are a non-renewable resource and are in the process of running out.
Or to look at it a little more subtly, there are lots of hydrocarbons left in the ground but the surplus energy left over from the various processes we use to extract them is declining, and with it the economic growth our society needs to continue.
Without fossil fuels, agriculture can only feed a fraction of our present population. And the carbon dioxide from burning fossil fuels is going to cause enough climate change to make agriculture significantly more challenging.

And you are right, "efficient" is a word used support all sorts of bizarre notions. It sets off my BS detector whenever I hear it.

Interesting times lie ahead.

Joe said...


I always thought that "ecological footprint" was defined as the "impact of a person or community on the environment, expressed as the amount of land required to sustain their use of natural resources". There are two ways in which this land area can be expressed; as per capita footprint or as total human footprint.

Paleolithic hunter-gatherers had a huge per capita footprint because they needed a lot of land to "sustain their use of natural resources". This was due to their very low level of technological efficiency (the T in the I=PAT equation). They needed virtually no land to absorb their wastes, but even so their total footprint was approximately one earth, assuming most habitable areas were fully populated, which they probably were.

If the same population of hunter-gatherers had all transitioned to horticulture, their footprint would have been less, on both a per capita and total population basis. By using improved technology to obtain food the land area needed to sustain their use of natural resources is reduced. If you can "artificially" increase the carrying capacity of the land, you decrease your footprint.

Footprint is just the proportion of carrying capcity used. For hunter-gatherers, carrying capacity per unit of earth's surface was very low. They needed a lot of land per person in which to hunt and gather. They had a large per capita footprint. But because of the way they lived, they never had to worry about exceeding the carrying capacity of the entire earth for very long (as long as it takes to starve to death).

Because of fossil fuels, we have been able to exceed carrying capacity for far too long. It won't end well.

Steve Salmony said...

@Irv Mills,

Human Population Numbers as a Function of Food Supply

Steve Salmony said...

@Irv Mills,

Too much food, too many people on a finite planet – Steven Earl Salmony

Many thanks for your consideration.

Steve Salmony said...

@Irv Mills,

A tiny biomass of mammals on the planet is now made up of wild animals. The remaining ninety-six percent is Homo sapiens, animals we favor as pets and as sources of food. The spectacular increase in the food supply for human consumption comes from agricultural production and husbanded mammals that have caused absolute global human population numbers to explode, declining total fertility rates in many places on the surface of Earth notwithstanding. Available food is a primary cause of human population growth.

Bev said...

It all seems to depend on the definition of 'footprint'. I remember seeing ads for desktop printers that had a 'small footpint', implying that this was beneficial because it took up less space on your desk. So 'large footprint', in terms of population means taking up too much space....a bad thing, as other species matter if the system is to function correctly. I do accept this meaning, it's as I said in my original comment, that other chap's comments made me think "hang on a bit".

Yes, I realise there's no such thing as 'balance of nature'. It's often called a dynamic balance, meaning I think, capable of dramatic change but eventually returning to some sort of equilibrium.

Regarding the fact that population growth is slowing (which is sometimes quoted by defenders of population growth), if you consider the S-curve (or logistic curve), a slowing of growth can mean the species is approaching the carrying capacity of its environment and hopefully will stay under it. But humans have obviously gone above it into overshoot and now the slowing of growth means that a downturn i.e. collapse, is imminent. That's where we are.

Irv Mills said...

@ Bev
As to the definition of "footprint", I am guessing that the people at the Global Footprint network would be the ones to ask, though I reserve the right to disagree with them. Here are some links to their site:
How the Footprint Works
Data and Methodology
I haven't had a chance to read those yet, but I do intend to have a close look at them soon.
Not to be a pain, but equilibrium is just a big word for balance.
Yes, we've gone into overshoot, and collapse is imminent. If you and I can see it, why do so many question this?