Of Wolves And Sheep

In a recent post, I jokingly referred to consumers, publishers and advertisers as populations of predators and prey. The analogy reminded me of an area of mathematics known as system dynamics, which studies the behavior of complex systems over time.

One of the best-known system dynamics models is the predator-prey model, an example of population dynamics models.

The idea is simple: imagine a world in which only two species of animals exist: wolves and sheep. The wolves need other wolves to reproduce, and they must eat sheep to survive. The sheep need other sheep to reproduce, and in order to survive, they need to eat grass and to avoid being eaten by wolves.

For those who enjoy playing with computer models, there is a free computer simulation platform called NetLogo, where you can try a simple wolf-sheep model to test some of the things I describe.



One troubling aspect of predator-prey models is that, in many cases, they are unstable: Under most conditions the populations exhibit feast-to-famine swings, until at some point either the last wolf dies, leading to an explosion in the sheep population, or the wolves eat all the sheep and then they too become extinct, having annihilated their food supply.

Interestingly, it is possible to create some stability by adding other dynamics: for example, by limiting the amount of available grass and requiring time for the grass to regrow after it has been eaten. In other words, if the gluttony of the sheep is kept in check, then the ecosystem as a whole can become stable — or at least, there will still be fluctuations in the levels of sheep, wolf and grass, but under some conditions these fluctuations become stable.

The relationship of these examples to our daily lives should be clear, especially given the explosion in human population, coupled with our careless consumption of every resource on which we can get our hands.

But we needn’t look at the planetary level to observe these predator-prey dynamics. In fact, one could look at online publishing as another prime example of these oscillating population dynamics.

Twenty-five or so years ago, the Internet was like an immense field. Internet users, like our peaceful sheep, grazed on information: the digital equivalent of nutritious grass. As the population grew, farmers came along and created more fields, carefully planting and growing grass where more sheep would be enticed to graze.

In this particular story the wolves appeared not in the proverbial sheep’s clothing, but rather were invited to the party by farmers. “Don’t worry,” the wolves assured farmers, “a bit of predation will be good for keeping the population in check.”

The witless farmers believed the story, and watched in dismay as the wolves grew dramatically in numbers and began to attack the sheep without restraint, causing the flocks to flee to greener pastures. Alas, the wolves became increasingly ferocious, and even developed technology that allowed them to clone themselves and teleport, seemingly popping up out of nowhere wherever the terrified sheep stopped for a quick nibble of grass.

The end of this story hasn’t been written yet. Rumor has it that when the sheep began building fences to block the wolves, the farmer’s union intervened and threatened to sue the sheep, claiming they had no right to violate their implicit agreement to provide sustenance for all the farmers, who at this point had mostly given up growing grass and instead were being entirely supported by the wolves.

The moral of the story? The mathematics of predator-prey models has a certain inevitability to it: Unless greed is put in check, oscillations will continue until eventually one or more of these populations will drive themselves to extinction.
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