St. Matthew Island. On reindeer and lichen

Today is all about reindeer. I stumbled upon this comic the other day and was delighted. I had seen it some time ago and thought it to be very neatly relevant to system dynamics. And had lost the link. Anyway, here is the link, go read it or the rest will make no damn sense.

Done?

OK, I’ll give you a minute.

Done? Good.

My interest in this is twofold. Firstly, this comic is a direct reflection of what World Dynamics is all about and secondly I’d very much like to put some numbers behind the story and the ecosystem structure should be for something like this to happen. Typically a case like this is used to illustrate a point of over-compensation: herd growth does not stop when the food runs out (as there are a number of calves underway) so the population grows beyond what the ecosystem can sustain.

I built a model. Actually I built several. And I did not get the behavior depicted in the diagram. The thing is that there are no right angles in nature. All the reindeer just didn’t eat happily to their hearts content one day and were utterly out of food the next. Also, lichen reproduces so slowly that we can assume the island can not sustain a single reindeer on just lichen growth alone. Therefore, lichen will run totally out at some point regardless of how the herd behaves (the consumption exceeds growth) and therefore the overcompensation concept does not apply: the model starts off in a point where it is already beyond the limit.

I inevitably ended up with a nice bell curve: the population grows to a point where the lichen starts having an effect on both fertility and longevity and its a nice steady decline to zero from there. as the food gets gradually scarcer. The important conclusion is that the result is symmetrical: exponential growth is followed by exponential decline.

Here’s the thing. Maybe what the people saw was _not_ the peak but rather the decline? If we assume that the island at some point had not 6 bot about 12 thousand reindeer, we can easily find a normal distribution curve that very closely fits the observation points. Which, of course, means that there was no dramatic cliff the population stumbled over. Don’t get me wrong, halving the population in a couple of years is dramatic as well but the diagram in the cartoon seems off. I’ll ponder over it for a while and see if I come up with an alternative solution but that’s that for the moment

Oh, and a notice: the next two weeks are going to be the peak of my thesis-writing so I might not get around to come up with stuff to post here – it takes considerable time and while superinteresting, I need to get the thesis done. Whatever I do, you should be enjoying system dynamics in action!

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