“…but real limits not seen are not limits repealed.”

*Overshoot, *William Catton

Homo Colossus is not long for this earth. With an appetite not even 10 earths could satisfy, soon this beast will starve to death. It will not be pretty, like a junkie cut off from their supply. We are talking here about the hard reality of ecological limits: consumption reduces the remaining stock of non-renewable resources. This is only common sense. The consequence is that there are limits to the number of non-renewable resources mankind will be capable of accessing as time proceeds.

Few subjects have suffered obfuscation by spin doctors more than the idea that there are limits to growth. The idea is so threatening to economics with its debt based fiat money that loud and pervasive voices work overtime to assure investors worldwide that there is really nothing amiss in the pursuit of unending growth on a finite planet. Our subject today is the role that limitations play in ecological science but due to the confusion deliberately propagated around it, the first task is to take some garbage out to the compost heap.

An argument could be made that modern science was born and continues to be a powerful means of inquiry through a proper appreciation of limits. The calculus provides the mathematical tools for many of the most fundamental theories across a wide swath of the sciences from physics to evolution, biology to ecology. With the mathematical tools of the calculus we are able to capture the rates at which things change. In a universe in which all things are constantly changing the value of such a tool is obvious. In the calculus the mind numbing subject of infinity is tamed. At the core of the calculus is the concept of, you guessed it, the limit. My favorite illustration of this limit concept is as an answer to Zeno’s paradox. In a race between a tortoise and a hare where the tortoise is given a head start, the paradox runs, the hare can never reach the finish line. Why? Because before the hare can reach the line he must go half way, but then he must go half way through the remaining distance again. And half way through that remaining distance, ad infinitum. This is a logical conundrum, a time bomb hiding in our maths. With the calculus we are able to prove the hare can indeed cross the finish line, to the great relief of racing fans everywhere, by saying the hare approaches the finish line *in the limit.*

The maths we all learned started with arithmetic where sets of static things provide most of the mental models needed for its comprehension. The operations of addition, subtraction, division and multiplication are often modeled with a set of colored blocks in classrooms around the world. Who doesn’t recall that proverbial set of apples our teachers went on and on about as we visualized giving and receiving some from our friends or slicing them into fractions? Most young students understand apple word problems fairly well. It is with the introduction of algebra that the first wave of math phobia strikes. Sure sometimes we want oranges instead of apples, but why call it X?

For many young people, who cannot help but notice that most of the really important issues of their lives concern ever changing qualities, the picture of relationships among static quantities algebra provides seems alien, of no consequence. I imagine the perennial complaint, ‘but how will I ever use any of this in my real life?’, was probably first spoken somewhere in ancient Persia right about the time algebra was invented. In my experience it is a shame really that so few make it across the algebra bridge into the calculus since it is in the calculus that all those fiddly and seemingly arbitrary rules found in maths begin to all fit together. It is also when one of the most important intellectual streams of our cultural inheritance is transmitted to an individual: our sciences.

Throughout our experience things are seen to be on trajectories that are inevitably thwarted. Enumerating a few examples reads like a who’s who of scientific discovery. Evolution – an animal species multiplies but it does not fill the whole earth with its offspring, something limits its reproduction potential. Dynamics – a body in straight line motion tends to stay in motion but on earth friction always slows it and other forces divert it from its path. Cosmology – there is an absolute speed limit in the universe, the speed of light as per the theory of relativity. Geology – there is a limit to the pressure that can build up between continental plates until earthquakes occur, there is a limit to the force the crust of the earth can suppress before a volcano erupts. I could go on but the point has been made; scientific knowledge is very often carved out of our ignorance by the recognition of the factors that limit processes. Each of these examples and many more are embodied in theories that have mathematical models at their heart, models built using the calculus.

This is the larger background required to honestly asses the role of limits in ecology. By no means do I believe everyone must understand the calculus to benefit from a mindful practice centered around ecology but it is important to recognize the role that mathematical models play in science generally so that when examining the theories and evidence in ecology sufficient understanding is brought to bear. At the risk of oversimplifying it could be said that when the sciences fit equations to data they have a small family of curves they can draw on to do the work. I tend to berate Descartes for his mind-body dualism so I would like to take this opportunity to thank him as well for the wonderful analytic geometry that opened up the vision of equations as curves.

Here for example is a graph of the mathematical model for the interaction of predator and prey as expressed in ecology’s famous, if simplified, Lotka – Volterra model. Consider a world consisting of rabbits and wolves. The rabbits multiply exuberantly while there are few wolves around but as the rabbit population increases the number of wolves that can survive on them also increases. More wolves, fewer rabbits, fewer rabbits, fewer wolves cycling back around to more rabbits, more wolves and so on:

In ecological field work researchers try to identify the differences that make a difference. The subject of limits is central to the ecological sciences for this is often how the environment induces its selection pressure. The ‘operationally significant’ factors that control the abundance and dispersion of a community stand out from the buzzing jungle of details where it is difficult to tell if one thing is more important than another or not. To get a handle on the survival characteristics of the species and environment interaction we ask what limits its growth? For a field of corn it could be the availability of phosphorous, for a Petri dish of yeast the nutrient sugars could be the limiting factor. Of all the many, many elements a biological community needs to survive and reproduce there are typically one or two that are in short supply. The limiting element acts as a brake on the growth potential of the biological community.

In 1840 Justus Liebig expounded this principal that the availability of a limiting resource controls an environment’s carrying capacity. It is known as Liebig’s law of the minimum. Fertilizer is our solution to this limit problem in our crop growing efforts. Fertilizer is designed to provide just those elements that are in short supply so the harvest can produce its maximum yield.

In addition to the limit brought by the minimum critical factor ecology recognizes a second family of limitations. This “law” of the limits of tolerance was included in the work of V.E. Shelford in 1913. This is the set of limits around what living things and their environments find tolerable. Not only too little can be a limiting factor but also too much. Life is very sensitive to numerous boundaries which it cannot violate and remain viable. Temperature, salinity, and toxicity are a few of the better known. Mammals, an example particularly relevant to ourselves, exist within a narrow band of temperatures, maintain internal PH levels and must consistently remove waste products running the gamut from dead cells to fecal matter.

There are a few details worth pointing out. Organisms might have a wide range of tolerance for some factors but very narrow for others; I can drink a wide range of water volumes in a day and survive but can’t eat too many strychnine cookies. When conditions are not optimal in one factor the limits of tolerance in other factors may become reduced; a meadow low in nitrogen needs more water to fend off drought. The period of reproduction is generally the most sensitive to limits; the seeds, eggs, embryos, and larvae cannot withstand the more extreme conditions an adult of the species could. Each of these details is worth some contemplation to tease out how they play out in both natural and human history as well as how they might contribute to the overall shape of the future.

No one knows when the limit to the giantism of Homo Colossus is going to be found. Will it be next year, five years from now, fifty, one hundred? No one knows which crucial element will not meet its supply without a viable substitute or which might move the habitat beyond our limits of tolerance. The way to investigate the issue, as we learned looking at the calculus, is to examine the rates at which resources are being used, pollutions are being produced and populations are growing. An uncomfortably large family of candidates confronts the researcher. Most of my readers will already be familiar with many of them and sites like Desdemona Despair gather news about them daily. Still, just to assure we are on the same page here; it is estimated the U.S. loss of topsoil is 10 times faster than it can be replaced, global arable land loss is 30 to 35 times the historical rate, species loss is estimated at 1,000 to 10,000 times the background rate, ocean acidifcation is increasing at the fastest rate in 300 million years, etc. Note that some of these are minimum limits (lack of required topsoil) and others deal with tolerances (how much pollution can the oceans take).

It was in the late 1960s that a team at MIT decided to use these tools to examine the overall shape of the future of industrial civilization. *They dissected Homo Colossus*. They created a model of the modern, industrial world that would be simple enough to be tractable yet complete enough to have some chance at capturing the essential factors of the real world outside the laboratory doors. For this model they chose the following to be the central families of variables: agricultural output, industrial production, human population, pollution and resource depletion.

In October of 1972 the reading public was introduced to the results of a computer simulation created by this crack team of computer scientists at MIT. Opening the cover of *Limits to Growth*, the 207 page mass market paperback, the publisher’s blurb rang a historic wake-up call worth quoting in full:

“Will this be the world that your grandchildren will thank you for? A world where industrial production has shrunk to zero. Where population has suffered catastrophic decline. Where air, sea, and land are polluted beyond redemption. Where civilization is a distant memory. This is the world that the computer forecasts. What is even more alarming, the collapse will not come gradually, but with awesome suddenness, with no way of stopping it.”

It was in the 1970s that there was the first general recognition that the resource limits of a finite planet will not sustain modern, petroleum based, industrialized civilization. The standard run simulation in *Limits to Growth* had the crunch time coming about forty years into the future, just about now. At the time it was published other news worthy events were seen as confirming how serious our plight was. In that decade there would be reports of collapsed fisheries, an oil embargo that produced gas lines and choked the economies of the overdeveloped world even while population pressures brought ghettos and slums of the inner city to the boiling point. Things have not improved since then; on the contrary and we have come a long way since the 70s. Homo Colossus stalks the very boundaries of peaking resources everywhere; fresh water, lithium, uranium, copper, platinum, grain harvest, oil, phosphorus…

Australian physicist Graham Turner working for the Melbourne Sustainable Society Institute performed an updated comparison of the *Limits to Growth* study with historical data in ‘Is Global Collapse Imminent?‘ National Geographic in April of 2012 published an update to the *Limits to Growth* graphic based on Dr. Turner’s work thereby sharing it with the world at large. Take a look. The first graphic is from the paper, the second National Geographic.

“…the myth of limitlessness had at last become obsolete.”

*Overshoot, *William Catton

This is most unwelcome news. Next week we will take a look at the plethora of cargo cults and cornucopianisms it has created.