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All the Bunnies in the Meadow Die

By   Follow Me on Twitter     Message B. Sidney Smith       (Page 1 of 8 pages)     Permalink    (# of views)   4 comments

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(This article is excerpted from the author's book, The Good American: A Situation Report for Citizens, available now from your favorite retailer, or on Amazon Kindle, or directly from the publisher, The Institute for Economic Democracy,

Take a pinch of the spores of a certain fungus and drop it into a gallon jug, one whose walls are coated with nutrient so the fungus can grow as fast as it likes. Suppose you do this one morning, and that exactly 4 days later you find that the fungus has filled the jar and is just beginning to overflow it. How full was the jug the morning of the 3rd day?

    1. Three-quarters full.
    2. Half full.
    3. One-quarter full.
    4. Mostly empty.

This question is one I pose to students in general math courses at the start of my standard lecture on modeling natural growth, a lecture with the deliberately provocative title of this chapter. I find that if the lecture isn't provocative students are unlikely to absorb the main point, because people tend to think of growth as something steady. Trees grow a few feet each year just as children grow by 5 to 7 pounds each year. Our lives grow with the steady accumulation of the years themselves.

Growth, we think, means adding a fixed amount for each fixed period of time. But most natural growth is nothing like that. In most kinds of natural growth it is not a fixed amount but a proportional amount that is added at regular intervals. This is why so many rates of growth, such as the growth of an investment or the growth of a population, are expressed in percentages-per-unit time.

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If natural growth matched our intuition, the jug would be three-quarters full the day before it overflows. But in fact the jug is still mostly empty the day before. The correct answer is D. One way of understanding how this could be so is to think in terms of doubling times. In natural growth the time it takes for whatever is growing to double in size is always the same regardless of how big or small it is. For the fungus to fill a gallon jug in 4 days starting from just a pinch means it has to double about once very 7 hours or so.1 So 7 hours before the jug overflows it is half full, and 7 hours before that it is one-quarter full, and 7 hours before that it is one-eighth full. Three times 7 is 21, so when we check the jug 24 hours before it overflows it is less than one-eighth full--mostly empty.

Now to make it vivid.

Suppose we start with 10 breeding pairs of bunnies living in a fenced meadow. There is no such thing as an infinite meadow: every meadow produces just so much food and water, and has just so much space. Suppose for the sake of the example that this is a large meadow that continuously produces enough food and water and contains enough space to support a thousand rabbits. Now the doubling time for populations of rabbits under ideal conditions is about 3 months, or 1 season, so they double their number 4 times per year. Thus after the first year our starting population of 20 rabbits has doubled 4 times, from 20 to 40, then to 80, then to 160, then to 320. So the second year starts with 320 rabbits. How many rabbits are there at the start of the third year?

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The correct answer is 0. At the start of the third year there are no rabbits in the meadow at all. Not only that, the meadow is gone too. This is because the rabbits' population went into overshoot. In the first three months of the second year their numbers doubled from 320 to 640 and everything was going along fine. By midyear they had doubled again, to 1,280, and were eating up the available food faster than the meadow was regrowing it. Things were getting crowded too, but there was no panic; all the rabbits were still getting enough to eat, even though all the fresh, green shoots were gone and everybody had to eat the tough, older leaves and stems. But by the autumn the population had doubled again, to 2,560--far more than the meadow could support. Having eaten all the leaves, the rabbits ate the stems down to the ground. As they began to starve, in desperation they dug up the roots and ate those. In the end they ate each other. When the last rabbit died from starvation, it died in a desert.

This is a horrifying outcome, and fortunately nature has ways of preventing it. Coyotes, to begin with. Also, when food supplies become stressed the strongest and luckiest survive while others, weakened by hunger, succumb to predators and disease. In the real world populations of rabbits and of all animals fluctuate, sometimes wildly, from year to year, but over time tend to remain in rough balance.

Humans are an altogether different kind of animal. There is nothing to play the role of coyotes for us--we are the top of the food chain. We don't have to depend any longer on natural processes alone for our food, because with machinery and fertilizers and science we can extract from Mother Nature far more than she would give on her own. Disease too, while not conquered, is nothing like the scourge it once was. With the aid of technology we can fit vast numbers of us into comparatively small spaces. There are few natural forces left to constrain our numbers, and because of this our rate of population growth increased dramatically in the 20th century while our doubling time decreased from half a millennium to half a century.2

Humans are a different kind of animal, but not so different that the laws of mathematics don't apply to us. We live in a finite meadow, called the Earth. There is no other to which we might go. With all our knowledge and all our technology, there is still an absolute limit to how much this meadow can provide. We are not as prolific as rabbits, but our population is 7 billion and growing; our current doubling time is about 65 years.3

And we are in overshoot. It is not a question of if we will overshoot our environment, and it is not a question of when. We are in overshoot--right now. Sometime in the 1970s came the first year when the ecological footprint of humanity became so large that the impact on the planet was no longer sustainable.4 Now, some 30 to 40 years later, we use up about 150% of the planet's yearly supply of resources every year.5 In effect, if we apply the rabbits-in-the-meadow analogy, we are at the point of eating the stems.

There are several aspects that must be considered in measuring the degree and effects of human overshoot. They include the availability of food and water, disposal of waste, energy, biodiversity, and climate change. Each of these affects all the others.

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Predictions of mass starvation owing to overpopulation have been made for 200 years, but have not come to pass.6 This is because our capacity to produce food has increased far beyond what was predicted. In the last 45 years in particular food production globally has more than doubled, keeping pace with the growth in population, even though the amount of land used for agriculture has scarcely increased at all.7 This "green revolution," as it is called, is the result of four factors: Increased irrigation from underground aquifers, the increased use of manufactured fertilizers and pesticides, the use of machinery to more efficiently plant, harvest, process, and distribute food, and the development of higher-yielding, more disease and insect-resistant crops.8 9 However, currently a billion people, 1 in 6, does not get sufficient nutrition, and an additional billion people are at risk.10 Moreover, in order to keep pace with the population food production would have to double again in the next 35 years,11 and this can't happen. Instead, food production is going to decline soon, and before long decline drastically.

One reason is that three of the four factors that made the green revolution possible cannot be sustained.

First, water. The United States' Great Plains, often called the breadbasket of the nation, produces enough grain for the country to be the world's biggest exporter of food.12 However, this is possible in large part because of irrigation with water pumped from the Ogallala aquifer, an immense underground body of fresh water that stretches from South Dakota to Texas. Because of the geology and weather patterns of this region the aquifer is not replenished, and it is being used up so fast that in many areas water can no longer be pumped from it. It will be largely unusable for agriculture within 25 years.13 This situation is mirrored across the globe, as aquifers that have driven increased food production in Europe, Asia, India, Africa, Australia, and the Middle East are drying up.14 There is no replacement for water. As these aquifers run dry, food production will decline sharply.

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B. Sidney Smith is a recovering math professor, gardener, and creative loafer living near Appomattox, Virginia. His autobio, curriculum vitae, favorite recipes, and much more besides can be found on his website,

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