Comment
The fractal biology of plague and the future of civilization
First online: 9 December 2020
William
E Rees
Professor
Emeritus, University of British Columbia
–––––––––––––––––––––––––––––––––––––––––––
DOI: 10.3197/jps.2020.5.1.15
Licensing: This article is Open Access (CC BY 4.0).
How to Cite:
Rees, W.E. 2016. 'The fractal biology of plague and the future of civilization'. The Journal of Population and Sustainability 5(1): 15–30.
https://doi.org/10.3197/jps.2020.5.1.15
–––––––––––––––––––––––––––––––––––––––––––
Abstract
At the time of writing, the
CoViD-19 pandemic was in its second wave with infections doubling every several
days to two weeks in many parts of the world. Such geometric (or exponential)
expansion is the hallmark of unconstrained population growth in all species
ranging from sub-microscopic viral particles through bacteria to whales and
humans; this suggests a kind of ‘fractal geometry’ in bio-reproductive
patterns. In nature, population outbreaks are invariably reversed by the
onset of both endogenous and exogenous negative feedback—reduced fecundity,
resource shortages, spatial competition, disease, etc., serve to restore the
reference population to below carrying capacity, sometimes by dramatic
collapse. H. sapiens is no exception — our species is nearing the peak of
a fossil-fueled ~200 year plague-like population
outbreak that is beginning to trigger serious manifestations of negative
feedback, including climate change and CoViD-19 itself. The human population
will decline dramatically; theoretically, we can choose between a chaotic
collapse imposed by nature or international cooperation to plan a managed,
equitable contraction of the human enterprise.
Keywords:
pandemics; CoViD-19; SARS-CoV-2; fractal geometric growth; overshoot; plague;
human population collapse.
Universal fundamentals of
population growth
Early
in the SARS-2-CoV pandemic (Feb to Mar 2020), CoVid-19 infection rates in
various European and Asian countries were doubling every two to ten days (see
Nunes-Vaz, 2020). The wide spread in doubling times
reflected the relative effectiveness of differing national control policies and
population behaviours. Many of these nations managed to reverse the trend
and ‘flatten the curve’, from several thousand to only a few hundred cases
daily, by late May or June, a situation that obtained through the summer
months. However, by early September 2020, the number of new daily
CoVid-19 cases was again on the uptick. People were spending more time indoors
at work, at play, at school, crowding together and more effectively
transmitting the virus. Infection rates were doubling every two weeks in
my home country, Canada, and doublings at an equivalent or even greater pace
were again the norm in countries that had previously had things under
control. The ‘second wave’ of the pandemic was taking serious hold and
threatening to become far more serious than the first (Figure 1).
Whenever
you hear reports of some entity doubling at a constant rate, think ‘exponential
growth’—or perhaps more accurately, geometricgrowth[1]. Exponential/geometric growth is
the expression of natural reproductive exuberance. Virtually every living
species is capable of expanding geometrically in a favourable, previously
unexploited environment as SARS-2-CoV demonstrates convincingly.
Reproductive
potential is perhaps the major form of positive feedback in every living system[2]. Inoculate a Petri dish of nutrient-rich
agar with bacteria at ideal temperature and the starter population may double
in as little as 12 minutes (although some species may take a few hours). Twelve
minutes later, the bacterial population will have doubled again and, after just
an hour, our little colony will have expanded by a factor of 32. So it is
with all living organisms—introduced to an ideal resource-rich environment, the
initial population will begin to grow geometrically. From the perspective of
SARS-2-CoV, today’s globally dense population of non-resistant humans is a
fertile Petri dish.
What
does differ among species is the generation time and hence the doubling rate.
As noted, it can be just a few minutes with bacteria (or viruses); house-mice
have a generation time of less than ten weeks and a pair may become 40
individuals in just five months; at 7-8%/year an unmolested population of
mature blue whales or elephants can double in less than ten years; the human
doubling time reached a minimum of about 33 years in the late 1960s when our
growth rate maxed out at 2.1%/year.
Today’s
1.05%/year growth rate would double the current human population in 67 years
(by 2087) to 15.6 billion. Fortunately, this will not happen. The rate
continues its long decline; current estimates suggest that, conditions permitting, we might make 10.9 billion
by the end of the century and top out shortly thereafter (Roser,
2019).
Overshoot – triggering a
feedback
In
fact, conditions may not be ‘permitting’. Population estimates are usually
based on demographic data alone with no consideration of exogenous factors.
This is unrealistic. For living organisms, the fact
of their own existence ensures that no environment or habitat remains ideal for
long. As the subject population expands, it will invariably
use up any crucial resource in fixed supply. Even renewable resources can
be depleted once the population goes into ‘overshoot’, a situation in which
aggregate consumption exceeds food species’ recovery rates or waste
accumulation exceeds natural assimilative capacity. The rise and fall of
reindeer populations introduced to two previously unoccupied (by reindeer)
Pribilof Islands in the early 20thCentury
is a classic example (Figure 2). Collapse was attributed to overgrazed food
sources (primarily lichen) abetted by the stress of exceptionally cold winters
(Scheffer, 1951).
With
food shortages and pollution, survival and reproductive rates necessarily decline.
Meanwhile, other forms of ‘negative feedback’ may also set in—dense populations
make our subject species more attractive to predators; crowding and
malnutrition facilitate the spread of disease and parasites; there may be
intra-specific conflict over habitat in short supply. Invariably, growth ceases
and may be reversed, sometimes precipitously.
In
nature, the populations of density-dependent species are determined by push and
pull, the interplay of positive and negative feedback[3].Macroscopic organisms such as whales, elephants and
(pre-industrial) humans typically maintain a fluctuating unstable equilibrium
near their habitat’s average ‘carrying capacity’ (though perhaps not until
after a dramatic crash in the case of severe overshoot—see reindeer on St
George Island, Fig 2,). Microscopic organisms have evolved quite
different approaches to stress. Many species of bacteria (Bacillus, Clostridium, Desulfotomaculum, Sporosarcina,
Sporolactobacillus, and Oscillospira,
spp., for example) adapt to declining nutrient supply or other hostile
conditions by transforming into endospores, smaller, hardy, tough-walled
dormant cells that can survive conditions that would kill the active bacterium.
‘Sporulation’ thus protects the organism’s genetic material from extreme
environmental stress until the return of better times. Endospores may also be
readily transported by wind or water and will reactivate within minutes or
hours after being deposited in a new environment of favourable conditions.
Like
the CoViD-19 virus, various small mammal and insect populations exhibit
large-scale population outbreaks on an irregular basis enabled by temporarily
abundant food supplies, periods of favourable weather, increased survival
(e.g., from reduced predation) or some combination; other species have regular
repeating high-amplitude population cycles perhaps synchronized by the seasons
or, in the case of predators, by other natural cycles in prey species.
Again,
like the corona virus, outbreaks of non-human animal populations can seriously
harm people. The desert locust (Schistocerca gregaria), for example, may qualify as the world’s
most devastating agricultural pest. During the swarm phase of a locust
outbreak, the insects may multiply exponentially by 20-fold in just three
months to attain densities of 80 million per square kilometre. A swarm of 80
million can consume food equivalent to the needs of 35,000 people. In
2020, favourable conditions spawned locust outbreaks—the worst in decades—in
several African and Asian countries including Kenya, Ethiopia, Uganda, Somalia,
Eritrea, India, Pakistan, Iran, Yemen, Oman and Saudi Arabia (Njagi, 2020). Many of the affected regions are already
food-stressed.
The
term ‘plague’ is usually reserved for the horrendous zoonotic infection caused
by Yersinia pestis, a bacterium usually carried
and transmitted to humans by small mammals and their fleas. (The resultant
‘Black Death’ or bubonic plague killed 75 -200 million people in Africa and
Eurasia during the 14th Century.) However, when swarms of
locusts infect large geographic areas or several countries, the outbreak is
also known as a plague. Even small mammal outbreaks can reach plague
proportions. Australia’s worst ever mouse plague caused $A96
million of damage in 1993 ($A184 million in 2020 dollars). The nearly
equivalent 2010/11 mouse plague affected three million hectares of crops in New
South Wales, as well as parts of Victoria and South Australia (CSIRO, 2020).
What
all the above data illustrate is that the population dynamics of
living species, from sub-macroscopic viruses to gargantuan whales, reflect a
universal fractal geometry: the same basic patterns are repeated in
all species, differing only in terms of vastly differing temporal and spatial
scales[4].
Implications for humans
How
might this reality enlighten H. sapiens beyond helping to understand the waves of
our current pandemic? To begin, humans are certainly not exempt from the
fundamentals of population dynamics. For at least 99.9% of anatomically modern H.sapiens’ evolutionary history (200,000-350,000
years) human populations, like those of other large mammals, fluctuated in the
vicinity of local carrying capacities[5].
Local constraints might have been relieved at times by trade and certainly the
(possibly reluctant) adoption of agriculture 8000-10,000 years ago enabled
larger populations, permanent settlements and division of labour—and hence advanced
‘civilization’. But for most of our species’ time on Earth—including most
of the agricultural era—humanity’s natural propensity to expand has been held
in check by negative feedback, e.g., food and other resource shortages,
disease, and inter-group conflict.
Circumstances
changed with the scientific/industrial revolution, particularly the
increasingly widespread use of fossil fuels. It took 200,000 – 350,000
years for human numbers to reach one billion early in the 19th Century,
but only 200 years (as little as 1/1750th as much time!) to balloon another
seven-fold by early in the 21st Century. Improvements in medicine, public
sanitation and population health contributed to this expansion, but coal, oil
and gas made it possible. Fossil fuels are the energetic means by which
humans extract, transport, and transform the prodigious quantities of food and
other material resources into the products needed to support our burgeoning
billions. More than any other factor, fossil fuels enabled H. sapiens to eliminate
or reduce normal negative feedbacks. Freed from historic constraints, our
species was at last able to exhibit its full potential for geometric growth
(Figure 3).
As
implied above, it is not just population that has bloomed. Since 1800,
propelled by a 28-fold increase in primary energy use, mostly fossil fuel, real
global GDP has increased over 100-fold. World average per capita income
(consumption) is up by a factor of 13, rising to 25-fold in the richest
countries (Roser, 2018). As Catton (1982)
famously observed, Earth is being asked to accept not only more people but ever
larger people.
There
is hidden irony in these data. Figure 3 shows clearly that only the most
recent ten or so of literally thousands of generations of humans have
experienced sufficient technological change and population growth in their
lifetimes to even notice it. In short, the period of spectacular
growth and change people today take be the norm (and wish to preserve)
represents the single most anomalous period in human evolutionary history!
Figure
3 also underscores humanity’s membership in the club of fractal population
dynamics. The recent accelerating surge in human numbers reflects classic
geometric growth—hyper-geometric, actually, since the growth-rate increased and
doubling time decreased throughout the boom period until ‘peak growth’ in the
1960’s. At peak, humanity’s numbers were doubling every 33 years.
(Compare the steepening human population growth curve with the geometric phases
of the CoViD-19 case count and reindeer populations in Figs 1 and 2
respectively.)
Meanwhile,
Earth was not getting any bigger.
Which
means, of course, that membership in the club will eventually bear a price. The
so-called ‘environmental crisis’ has little to do with the ‘environment’ and
everything to do with excess human demands on natural systems. For several
decades, H. sapiens has been in a state of ‘ecological
overshoot’—our species is exploiting even renewable resources faster than
species and ecosystems can regenerate and dumping (often toxic) waste at rates
well beyond nature’s assimilation and recycling capacities; think plunging
biodiversity, collapsing fish stocks, desertification, soil depletion, tropical
deforestation, ocean pollution, contamination of food supplies, rising
atmospheric greenhouse gas concentrations, resultant climate change, etc., etc.
By 2016, H.
sapiens was
68% in overshoot—i.e., acting as if Earth were 68% larger or more productive
than it is (GFN, 2020).
It is
worth noting that, initially, most of this damage could be traced to
consumption by the wealthiest 20% of humanity who have effectively appropriated
70-75% of Earth’s productive and waste assimilation capacities. However, there
is an upper limit to the amount any individual can consume. Today,
eco-degradation is being driven primarily by rising material demands and, more
importantly, by population growth in middle and low-income countries. The world
community must confront egregious inequality and population growth as separate
problems.
Clearly
overshoot cannot be sustained indefinitely (only economists think something can
grow forever). The endogenous positive feedback that dominated the geometric
phase of humanity’s population growth is already being countered by exogenous
negative feedback including the aforementioned ecosystems degradation and the
weakening of life-support functions. With overshoot, carrying capacity
declines in proportion to the loss of self-producing ‘natural capital’ and,
with it, the ability to support even existing populations. The world community
is literally financing its current population and material growth by
liquidating the biophysical resources and life-support functions upon which the
future of the human enterprise depends; the longer we remain in overshoot, the
more we compromise the ability of future generations to thrive (red curves in
Figure 4).
Keep
in mind, too, that degraded ecosystems are not the only source of negative
feedback on human exuberance. Food and other resource scarcities will intensify
geopolitical strife which, in turn, will be exacerbated by mass migrations of
people abandoning areas that have become uninhabitable because of climate
change or ecosystems collapse. Disease may once again emerge as a major
scourge—crowded human populations weakened by hunger and stress, no longer
protected by functional public health systems, present ideal conditions for the
spread of resurgent pathogens.
Or
new ones. Approximately 70% of the new diseases in humans in recent
decades, including CoViD-19, are zoonoses, ailments caused by pathogens
transmitted from animals (the SARS-2-CoV virus jumped to people from bats or
pangolins). CoViD-19, itself an exemplar of negative feedback, is at least the
sixth global health pandemic since the Great Influenza of 1918—and it may be a
harbinger of worse to come. A recent report notes that there are six to
eight hundred thousand unknown viruses in nature that could infect people as
humans encroach ever more insistently on wildlife habitats. “Future pandemics
will emerge more often, spread more rapidly, do more damage to the world
economy and kill more people than CoViD-19 unless there is a transformative
change in the global approach to dealing with infectious diseases…” (IPBES,
2020). Pandemics may originate from contact with animals, but their
emergence is driven by human activities.
And
what about our energy conundrum? Modern society is precariously suspended
on a gusher of fossil fuel—despite significant advances in so-called renewable
energy for electricity generation[6],
coal, oil and natural gas still provided 84% (492.3 exajoules) of the world’s
primary energy in 2019 (BP 2020). The problem is that, to avoid potentially
catastrophic climate change, the global economy must decarbonize by 2050. In
the absence of quantitatively similar renewable substitutes, this implies
significant energy (and food and other resource) shortages, shrinking GDP and a
major reset of societal priorities.
Even
the option of risking climate change by continued reliance on fossil fuel may
be closing. Economically viable sources of oil and gas require ever
greater levels of investment just to maintain supplies. Ironically, the
onslaught of CoViD-19 has so deflated demand for oil and gas that the resultant
glut has destroyed investment. Meanwhile, production has fallen precipitously,
and low prices have bankrupted dozens of companies. Some wonder whether
the industry can recover (e.g., Cho 2020) but the problem is much greater.
Society as we know it cannot survive the absence of abundant cheap energy.
Where do we go from here?
A
bacterial culture can quickly overwhelm and deplete its Petri dish; the
SARS-2-CoV virus will continue to ravage the human population until herd
immunity or a successful vaccine cuts it off. This is the way of living things,
including humans—our species has expanded over the entire planet and is well on
the way to depleting resources essential to its own survival. Earth is to H.
sapiens as
Petri dish is to Bacillus sp.
The
analogy, or rather ‘homology’, goes quirkily further. When the
bacterium’s medium turns hostile, its cells sporulate; the resultant endospores
wait in dormant state to be wafted to a more favourable environment. How
does this adaptation differ functionally from NASA’s inquiries into using
suspended animation to facilitate human interstellar travel (Bagelley, 2017) or plans to colonize Mars to ensure that
humans survive a war-ravaged or eco-degraded Earth (Solon 2018; McFall-Johnsen
and Mosher 2020)?
Whether H.sapiens will ever reach some Earth-like planet
‘x’ light-years away or even successfully colonize Mars, may be entirely moot.
In the best of circumstances, serious interplanetary exploration, even within
the solar system, would be decades in the future and these are hardly the best
of circumstances. The ‘Anthropocene’ is quickly becoming dominated by negative
feedback induced by the already excessive scale of the human enterprise.
Not
that this makes much difference to decision-makers. Despite cumulative evidence
of potential disaster, the world’s major governments, international development
organizations, the corporate sector and probably the majority of even
well-educated citizens are fully committed to maintaining the global cultural
narrative of perpetual economic growth abetted by continuous technological
progress. It seems that few people comprehend the physical implications
of humanity’s material addiction. When something is growing geometrically
(e.g., plague-like) with a constant doubling period, the quantity attained at
the end of any doubling period is greater than the sum of the quantities at the
end of all previous doublings (e.g., 128 > ∑(64 + 32 + 16 + 8 +
4 + 2+ 1))[7].
More or less on geometric projection, the global material footprint
rose from 43 billion tonnes/year in 1990 to 92 billion in
2017— an increase 113%. Similarly, half the fossil fuels ever
used were burned in just the past 30 years (90% has been consumed since 1943).
Consider, then, that with population growing at 1.0%/year and incomes in
developing countries increasing even faster, the global economy will more than
double again the next 30 years (i.e., >2.0% /year). Since much of that
income growth will be in countries where people have yet to satisfy basic needs
let alone luxury wants, we can expect parallel growth in economic energy and
material throughput—the material footprint is projected to expand another 106%
to 190 tonnes/year by 2060 (UN 2019).
All
this on a planet already 68% in overshoot; unable to control soil and landscape
degradation; beginning to reel from climate change; witnessing a 68% drop in
the populations of hundreds of regularly monitored vertebrate species
world-wide since 1970; etc., etc. What is the likely impact of imposing
an energy, material, and waste load on the ecosphere in just the next 30 years
potentially greater than the sum of the loads imposed by all previous doublings
since the beginning of the 19th Century?
The
time has come to face biophysical reality. Contemporary data and trends suggest
that global society is nearing the end of an unprecedented—and likely one-off—human
population outbreak (Fig 1) affecting the entire planet[8].
Distasteful as it may seem to human exceptionalists,
we can justifiably describe H. sapiens seeming dominance as a form of global
plague, a description that would surely apply if we were discussing any other
species (Rees, 2020).
On
our present course, the likely outcome for global society is systems collapse
as we run up against serious climate effects, resource shortages, and
increasing geopolitical conflict in coming decades. Compare the
‘overshoot’ simulation in Figure 4 (red curves) with the real-world boom-bust
collapse of the St Paul Island reindeer herd as it depleted its food resources (Fig.
2).
Forget
about interstellar space travel or even colonizing dead-cold Mars. Humans
should be focused on regenerating ecosystems and life-support functions on
Earth, the planet on which we evolved, which continues to sustain us and for
which we are best adapted. Despite damage wrought by H. sapiens, Earth remains infinitely more
hospitable than the red planet; why would anyone think that efforts to
terraform Mars is more likely to pay off than restoring the earth?
Epilogue – the choice before us
CoViD-19
may well exemplify the biological universal to expand that H.sapiens shares with all other life-forms. But
humans have other unique qualities that we have yet to exercise fully in
addressing overshoot. Our species is blessed with high intelligence, the capacity
to reason logically from the evidence, and the ability to plan ahead in ways
that could dramatically alter our future prospects. It helps that we also
possess a unique appreciation of our own vulnerability and mortality, no doubt
heightened by the current pandemic.
The
scientific evidence tells us that some form of contraction of the human enterprise is a material necessity if we
are to maintain the functional integrity of the ecosphere. It
seems we have a choice: either allow nature to take its course and suffer the
ugly consequences of a chaotic implosion or rise to our true potential by
executing a controlled down-sizing of the human enterprise. The overall goal
must be ‘one-planet living’ which means learning to thrive more equitably on
Earth well within the carrying capacity of the ecosphere (Moore and Rees,
2013). When dealing with the human plague, this is the real meaning of
‘flattening the curve’ (Fig. 4).
The
question is: how can the self-proclaimed most-intelligent-species-on-Earth
organize socially, politically, and economically to implement a process to
ensure an orderly and equitable contraction? Could there be a more riveting
intellectual and practical challenge? Indeed, this, more than fear, is
proving to be the real motivation for some of our best minds in dealing with
our (un)sustainability crisis (see, for example the degrowth initiative at
https://www.degrowth.info/en/what-is-degrowth/). If the global community
does not rise fully to engage its fate, humanity proclaims itself to have no
more practical intelligence or conscious moral agency when it comes to ensuring
its own survival than does the CoViD-19 virus.
Notes
[1] Some mathematicians make no
distinction between ‘exponential’ and ‘geometric’ growth. Others argue that an exponential distribution involves
raising each number in a series by the same power to get the next number (e.g.
2, 4, 16, 256…), while geometric growth is defined more generally as involving
performing a constant operation on a sequence of numbers (e.g., 2, 4, 8, 16…).
[2] ‘Positive
feedback’ implies a process that is deviation-accelerating; ‘negative feedback’
is deviation-correcting.
[3] Density
dependent species are those subject to negative feedback triggered by their own
growing populations. Negative feedback can be endogenous (e.g., reduced
fecundity, infanticide) or exogenous (resource shortages, increased predation).
[4] In
theoretical mathematics, fractals are infinitely iterating, similar,
detailed mathematical constructs having fractal dimensions at all
scales. A fractal dimension is a ratio giving a statistical index
of complexity comparing how detail in a particular fractal pattern changes
with the scale of measurement. By analogy, the population
dynamics of species from viruses to whales display self-similar, iterative,
detailed properties (fecundity, growth rates, geometric potential, etc.) that
vary among species only in terms of temporal and spatial scale.
[5] Carrying capacity (CC) refers to
the average maximum population of a species – the maximum fluctuates with
exogenous conditions – that can be supported by a given habitat more or less
indefinitely without permanent damage to that habitat. With humans, CC
varies inversely with average material standard of living (consumption).
[6] Wind
turbines and solar PV panels are not truly renewable, merely replaceable, and
their production involves mining, refining and manufacturing processes
dependent on fossil fuel. Indeed, many key direct uses of fossil
fuels—high-heat manufacturing, inter-urban, air and marine transportation,
agriculture—are not readily electrifiable.
[7] Alternatively,
with geometric growth, the quantity consumed during the latest doubling period
is greater than the sum of quantities consumed in all previous doubling
periods.
[8] “One
off” because, with all readily accessible resources used up, survivors would
likely be unable to resurrect a technologically advanced global civilization.
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