Welcome to the age of diminishing returns

Monday, April 23, 2012

The story of Rabbit Island



This post had started as a review of the book "Too Smart for Our Own Good" by Craig Dilworth. After having worked on it for a while, however, I found that I could add nothing to the excellent review already written by George Mobus. So, I thought that I could rather express my feelings in terms of a little story. If you have studied population dynamics, you'll recognize that what I wrote is a fictionalized version of the Lotka-Volterra model of foxes and rabbits interaction. I think it is the bottom line of Dilworth's thesis: humans are smart at inventing technological toys just as foxes are smart at catching rabbits. The results, however, are not necessarily good. It doesn't matter if you are a fox or a human being: you are too smart for your own good. (Image above from Jokeroo)






The Story of Rabbit Island
by Ugo Bardi

It is said that foxes came to the Island long, long ago. Some say that the first fox couple arrived on a raft from a place beyond the horizon. Others say, instead, that foxes were created here by the Fox-God, and others still that they had always been here, from the day when the Gods raised the Island out of the waters of the infinite Ocean.

Wherever they came from, the first fox couple found the Island rich in grass, trees, water, and many, many rabbits. And the foxes were smart and strong and they grew by chasing rabbits and killing them in great numbers. Many young foxes were born and that was -  some foxes said -  the way things had to be.

In time, foxes grew even more in numbers and some foxes started saying that rabbits had become difficult to find. A story is told of an old fox, that many saw as wiser than most, who gathered the whole fox folk and spoke to them. "Fellow foxes," the old fox said, "we have been growing so much in numbers that soon there won't be enough rabbits to feed our youngsters; and they will starve. We shouldn't kill so many rabbits as we have been doing so far, and we shouldn't have such large litters, either."

But some foxes said that there was no such a thing as too much killing of rabbits. They said that there were still plenty of rabbits around; it was just a question of looking harder. If some young foxes were starving, they said, it was because they had become lazy. They had to be taught how to run faster and to be smarter. In this way, foxes would still be able to catch as many rabbits as they needed. And they laughed at the old fox and they returned to chasing rabbits.

And then, the Great Die-Off came. I have been telling this story many times and it still scares me, even though I am the oldest rabbit of the Island. But I have to tell to you this story, young rabbits. I have heard it from my father, who heard it from his father, who heard it from the father of his father, and so on in a chain that arrives to one of the few rabbits who survived the Great Die-Off. And, believe me, young rabbits, it was a terrible time, for the Island was full of foxes. Rabbits died in large numbers and there was no way for them to escape. It is said that just a few of them could hide in the darkest places of the forest; in thornbushes and in mazes of tree roots, praying the Rabbit-God that they could be spared from the fury of the foxes.

And the Rabbit-God must have heard their prayers because they were not found by the foxes. After some time, they dared to come out of their hideouts and they found that there was no fox to be seen alive anywhere on the island; only their bones were left; strewn all over the plains. Once, there were many, many more of these bones, but you may have had a chance, young rabbits, to see some of the few that remain.

So, this story has a happy ending. After the Great Die Off was over, we rabbits had the Island all for ourselves. And we have had good grass to eat and good times to grow and multiply, which some say is what the Rabbit God told us to do. Yet, sometimes I think that this story may not have such a happy ending after all.

You know that there are now many, many rabbits living in the island; so many that fields seem at times to be white and brown rather than green. And that cannot be good. Some of the wise rabbits have been telling us that we shouldn't let our numbers grow so much, because grass can't regrow fast enough to feed so many of us. But others have said that grass is not the problem. Young rabbits have become lazy, they say, and they only complain so much because they can't always find grass at paw length. That's not the way a good rabbit should be: they must learn to find their food, even at the cost of walking far away, where there is still plenty of grass.

It may be that there is still enough grass for all of us, somewhere, although I doubt it. But what makes me afraid the most is what I have been hearing lately. You may have heard the same rumors: that some rabbits have disappeared and nothing was heard of them any more - not even their bones could be found. And you may have heard of some who have been telling of grey shapes they saw hiding in the forest. And, at nightfall, some have been telling of bright, yellow eyes looking at them from the darkness. Could it be, God forbid, that the foxes are back?

If that is true, nobody can say if some foxes had survived the Great Die-Off, or if some of them came again on a raft from beyond the horizon. The only thing I can tell is that perhaps we should not have grown in numbers so much, because rabbits make good food for foxes and some old rabbit folks had alerted us about that; long ago, but nobody listened to them. And now it is too late. I am an old rabbit now, so I won't see what the future has in store; but you will, young rabbits. So, it is time for you to go to sleep. Sleep well and don't look at the forest. 


4 comments:

  1. Nice. :)

    In these Lotka–Volterra systems, each fox is the same, as is rabbit, so the size of a species population is the best way to aggregate their impact (on the rabbits or grass respectively).

    This isn't the same for humans though. Population doesn't tell us very much as an individual's consumption varies by significantly more than an order of magnitude. For example, considering oil consumption (a fair proxy for total consumption), the US consumes 22 barrels per person, per year, Germany 11, Mexico 6.5 and India 1. The carrying capacity, the triggering of our Great Die-Off, depends not so much on the population size but on the consumption distribution.

    Halve US consumption down to Germany's and enough capacity in the system is freed up to support another 3.4bn 'Indians' or 530 million 'Mexicans'.

    This report from Christian Aid, which I haven't read in any detail yet, states "The wealthiest 20 per cent of the world’s population account for 80 per cent of consumption of global resources." http://www.christianaid.org.uk/images/constrained-world.pdf

    It would be nice to see a simple L-V extended to include mega-greedy foxes and rabbits. Such a system might teach us that behaviour/consumption is more important than population.

    ReplyDelete
  2. Yes, you can also differentiate individuals - it is another kind of simulation called "agent based modeling". It is fun; the simulation in Netlogo includes a 2D output on which you see each fox and each rabbit running around. I had done some work in this field some years ago. About your point, what happens is that the "rich foxes" tend to survive for longer than the "poor foxes"; actually the wealth distribution becomes more and more uneven. I think it is a very realistic result!!!

    ReplyDelete
  3. Thank you Ugo, this is a very relevant and "up close" interpretation of the classic "foxes and rabbits" simulation/system. Makes it personal. I suppose when we see these simulations we understand the implications for humans but we don't understand them at the grass roots level, or maybe we don't want to. There are grim scenarios that would trouble us too much, better to know the implications abstractly and use that to take action. But sometimes we do need to look at what it will mean at the individual level. Of course the problem with the "Foxes and rabbits" scenario is that there is insufficient biological diversity to prevent boom/bust cycles. However, although rabbits reproduce oil doesn't.

    ReplyDelete
  4. Ugo, yeah, I always knew that "Greeks are lazy"!!

    Chris, by "mega-greedy" you mean "mega-successful"? :-)

    Alex

    ReplyDelete