Population-Consumption Model v4


Over much of December 2013 and half of January 2014, I focused on updating and testing my simple "Population-consumption" model for projecting global population and resource consumption into the future.

I had been considering how to craft solutions to the problems posed by previous efforts and recent news. An obvious approach would be to somehow predict what people are more likely to do, given a set of conditions they live with. The concept of "happiness" once again came to mind, and the idea that people tend to seek out conditions that fit their particular sets of wants and needs.

In the simplest sense, people and their wants and needs fall into a statistical distribution, such as the totally random normal distribution (or "bell curve"). Superimposed on that, I imagined a complementary distribution of environmental conditions organized as a population of "environments," each embodying a unique combination of those conditions. If everyone was totally satisfied with their lives (a happiness of 1 on a scale from 0 to 1), they would each occupy an environment totally meeting their wants and needs.

Obviously, we're not all very happy. One way to increase our happiness is to find and access more environments, in the hope that one of them will suit us. If our happiness is 1/3, a simple strategy is to triple the number of environments; if we're only 1/2 as happy as we want, we can try doubling the number of environments. On a global basis, it appears that we do just that, so that at any time the number of environments we collectively "inhabit" approximates the ratio of people to happiness (with some extra that Nature apparently endowed us with).

Another way to increase the happiness of a population is to increase the number of people. The more people we have, the more likely some of them will match the environments we have access to. It turns out that this also happens. Of course, there is a limit to how fast we can grow the population, so we're always taking the happiness we have and seeking out more environments to increase it.

Having more people has the added benefit of enabling the population to acquire more environments because of their added capabilities, including labor. That's not all we need, though. Finding new environments (as well as living) requires resources such as energy and materials, preferably from environments we're not using, as well as some place to dump the inevitable waste. This has the effect of drawing down the number of remaining environments if we exceed the rate at which Nature replenishes those environments, which we have been doing for several decades.

Unfortunately, we gain less in happiness as we use progressively more resources (mathematically, the ratio of resources to happiness increases linearly with resources). This has the effect of limiting just how happy we can ever become, on average as a population. That limit, which I've calculated to be 0.82, also defines the maximum number of environments we can inhabit, the maximum number of total environments, and the maximum size our population can become in the process of finding more happiness. It is likely not coincidental that if we divide one Earth by the size of that maximum population, the amount per person approximates the minimum amount of ecological resources needed for one person to survive and procreate (as determined from the historical record).

Life expectancy has a similar relationship to resources used, and likewise has a maximum (358 years). It's not surprising that the more resources we use, the more likely we can keep people from dying at an early age, and the longer we can delay dying from old age – but only up to a point. This relationship relates life expectancy to happiness as well, along with population size. Multiplying all of these limits (happiness, population size, and life expectancy) yields the ultimate limit: 6.36 trillion happy-person-years (hpy). I estimate that we are currently at 329 billion hpy, which is 5.2% of the limit.

One of the main goals of my model has been to anticipate possible futures for humanity. As with previous versions, I extrapolated historical data for several scenarios, chose a best case and worst case for population growth, and created a composite scenario that represented what was most expected. This time, I extrapolated life expectancy and calculated values for other variables such as population size, ecological footprint (my proxy for resources), and happiness. As before, I used polynomial curve-fits over time, and all of the variables track closely with population size (which has been my primary focus over the years I've doing this).

In the last version of the model, population size reached a peak in 2030. In this version, the peak occurs earlier, in 2015 for the worst case and 2022 for the expected case, and we are all but extinct by 2109 or 2128, respectively. The best case is based on a linear extrapolation of life expectancy, and approaches the maximum value in 2821. I should note that none of these projections included provisions for external factors such as climate change; they merely reflected how life expectancy has varied since 1950, which has been influenced by all factors.

Investigating how we might experience the peak and fall in the worst and expected cases, I came up with an hypothesis for what might be causing it. To me, the simplest explanation for a peak was that the resources needed to grow had become too scarce. The decline from the peak suggested that resources to survive were being drawn from internal sources, deteriorating the inhabited environments and harming the people who depended on them. This hypothesis gained credibility when I applied an observation from the previous version of the model relating to the populations of other species. I realized that the WWF's Living Planet Index could be used as a proxy for total environments (including what we occupy, inhabit, and haven't found yet), and used the relationship I discovered linking it to ecological footprint to track how it changed over time. The calculated number of maximum environments fell to the number of inhabited environments by 2008, which happens to be the year that the bottom fell out of the global economy.

If we did run out of additional environments in 2008, then our inhabited environments became the same as maximum environments; they became locked together. If the relationship between LPI and footprint remained in effect, then according to the worst and expected cases the number of environments dropped even further, then either recovered to the projected level of inhabited environments or something even stranger happened. If the recovery happened, then the LPI would either grow again as our total footprint dropped, or it would remain locked to our inhabited environments as they crashed to zero along with our population.

The "stranger" alternative is strange because it involves a breakdown of the relationship between happiness and inhabited environments. As inhabited environments decrease along with the LPI, the relationship to happiness implies that happiness will actually increase; but of course it doesn't, and no reasonable interpretation of reality would suppose that it did. It would be like having part of your house burn down, and being thrilled that you took up more of the remaining space.

The way I solved this apparent contradiction is by assuming that we would redistribute the remaining environments to effectively cushion the blow of having a bunch of them destroyed. Mathematically, this amounted to changing the statistical distribution of environments, either by adjusting its width (standard deviation) or its position (mean) relative to our population's distribution. Using some sophisticated trial-and-error, I calculated the best matches of the mean and standard deviation to the projected happiness and footprint, and sure enough they both changed.

One problem remained, however. The model showed that if LPI continued to fall, then by this year (2014) the ratio of the size of our population to the number of inhabited environments will exceed the maximum happiness value, which seems to be a hard limit. Interestingly, in the worst case, which was also the best curve fit to life expectancy, the ratio hovered very close to the limit until around 2020, when our total footprint decreased enough that LPI could increase again if left alone. I realized that given our desire to increase happiness, we wouldn't leave Nature alone; we would be inhabiting all the environments we could until there were no more left. So, I mathematically tied them together so the ratio of population to environments remained very close to the happiness limit beginning with when they might cross the limit. The number of environments was then a fixed multiple of our population size, and that was what I used to determine how we would manipulate the distribution of environments to be consistent with the projected happiness and footprint.

Using the statistical distributions had an additional benefit. It also allowed me to calculate how happiness would vary across our population over time. I could also use them to assess where the fatalities would come from as our population dropped from its peak. One obvious way to do this was to count the number of people whose happiness was below the minimum value I calculated from the best case maximum population using 1 Earth of resources. In such a group might be babies, but also extremely poor people who could die if they didn't improve their situation. I was inclined to believe that they were mostly the poor when I saw how their number changed over time.

Prior to 1990, the best fit to the data was an environments distribution perfectly aligned with ours; it was easy to see that minor variations in the mean could account for much of the variation in happiness that we saw (this was evident from actual happiness data I studied for a large fraction of the world's population). In 1990, the people below the minimum happiness threshold spiked to 146 million people, associated with movement of the mean. It dropped to zero until 2000, when it jumped to 959 million people with a movement of the mean that was about double the amount in 1990. It dropped to zero again, and in 2008 began to climb toward another spike in 2014 (in the worst case) or 2015 (in the expected case) of around 950 million people, again associated with movement of the mean.

I calculated these values for every year up to the 2022 peak projected in the expected case, then at the beginning of each decade afterwards, and the results clearly showed a volatility that hadn't existed before. There would always be a large, changing fraction of the population that was extremely poor, many of whom among the growing number of dying people. I couldn't help but interpret the displacement of the mean, which has been hiking upward since 2008, with the ideological shift that's become prevalent in politics and economics since then.

The best case is the outlier in the set of scenarios I chose to focus on. It is only "best" in terms of population growth. For it to work, we must effectively dispense with the rest of Nature, and soon. If the LPI decreased without us being able to stop it, then it would equal our population in 2016, and all species would crash to zero by 2052 as global temperatures (from the previous version of my model) reached an unlivable 4.6ºC above preindustrial levels – the mathematical embodiment of "short-term extinction." If we were able to continue growing our inhabited environments along with ourselves toward maximum happiness, we would need a massive new source of energy and materials that would essentially replace all of the natural resources we've depended on since we evolved, and then a lot more. By 2066, we would be using twice as many resources as we are in 2014; that would double by 2149, and double again by 2270. By 2821, the year before we get extremely close to the happiness limit, we would be consuming more than 46,000 times what we're consuming now.

The test of any hypothesis, and my model represents several, is the accuracy of the predictions it makes. Like its predecessors, this version is a thumbnail sketch of a set of a handful of extremely important variables, though I consider it the most detailed and robust of the group. Two of those variables, population and life expectancy, are constantly and directly measured. Other variables are intermittently measured (happiness and footprint). Related variables, such as temperature and LPI, are also measured; temperature on a regular basis, and LPI intermittently (updates for both have not yet been incorporated yet into the model). Proving the model is complicated by the fact that many trajectories of these variables are possible; I have, at best, bracketed those possibilities in my current presentation. As events unfold, I plan to provide ongoing analysis and incorporate changes to the model as necessary to conform with reality.

As indicated earlier, my main criteria for the model's success is the quality of guidance it can provide to make our future better, starting with improving our chances of survival. If accurate, it seems to have only provided better understanding of why we are doomed: simply, our collective pursuit of happiness drives us to use all the resources we can find.

The truly "best case," in my opinion, would be if we could somehow be fooled into thinking we were at the happiness limit without actually being at the limit of the world's resources, with just enough extra trickling in to maintain our inhabited environments, but not enough to trigger our pursuit of more. Ironically, if my interpretation of the worst case is accurate, we're currently facing the mirror image of that ideal: we've been fooled into experiencing a lower level of happiness while we're actually at the limit of our resources.

That said, if our goal is pure survival and we haven't already triggered self-amplifying global warming, we may still have the option of reducing our inhabited environments below the amount of maximum environments defined by the LPI, giving the rest of Nature a chance to grow back with minimal interference. That we will do so is extremely unlikely, especially since it will involve a considerable decrease in happiness and life expectancy, not to mention additional risks as we try to quickly dismantle complex infrastructure.


-- Bradley Jarvis

January 17, 2014

See also:

Population-Consumption v4 Main Page

Technical Description

Economics Overview

© Copyright 2014 Bradley Jarvis. All rights reserved.