Lemming Population Flux Solved: Mass Suicide Not to Blame

quogmire writes "Australia's ABC reports that biologists from the Universities of Finland and Freiburg (Germany) have finally solved the question of lemming population fluctuations once thought to be caused by lemmings mass-suiciding by plunging off cliffs. 'Lemming populations, they say, surge spectacularly and fall just as quickly, thanks to the combined feasting of four predators: the stoat, arctic fox, snowy owl and a seabird called the long-tailed skua.' The original article (Login required) is published in Science."

Comments

Re:Carrying capacity

[Persecuted_Telemarke]

Actually, it depends pretty radically on which type of model you're considering.

For example, if you assume that the population is governed by a continuous-time model, i.e. by a differential equation, then it is not really possible for a population to exceed a carrying capacity, and then crash. What happens is that the population asymptotically approaches the carrying capacity, but can never go above it. I think it is reasonable to put humans in this case, as our growth rate is a smooth frunction of time (no breeding season, for example).

Aside note: for those who may not know, the term "carrying capacity" is a term used in population dynamics which sort of represents the available resources. In most models, what happens is that there is some amount of population which can be supported by the existing resources, and if the population is below that, it should grow, and above that, it should shrink. Most "reasonable" models of population dynamics have such a carrying capacity, and I can even state a theorem: if you have any model where the growth rate of a species depends on its size, AND it is true that this growth rate becomes negative for some sufficiently large value of the population, then you will have a carrying capacity. Furthermore, if nothing in the system changes, the population will approach this value and stay there forever.

Now, I'm not saying a crash is impossible, but you need a more complicated system. There are several ways to add complexity to the system. One way is to consider a predator-prey type of system, but of course humans have nothing which can really be called a predator. The only thing I can think of is some sort of disease, but this leads to a different model altogether (some sort of "epidemological model"), and these models rarely predict population crashes, as they have a different character, which is disease needs to be carried by disease-carrying individuals (ok, duh) but then these tend to die out. So the predator carries its own destruction around with it, in some sense, and it corrects itself.

Another postulate one can make, and I think this is somewhat reasonable, is that the carrying capacity of the earth might change radically in the future (and of course, radically downward would be the interesting case in this discussion). This could happen any number of ways. And if it turns out that the carrying capacity moves on some very quick timescale (much more rapid than the change in growth of the population), then we could see a "crash". For example, if it turned out that our ability to grow food took a big hit for some reason or another, then this could happen.

One last way to get population crashes is to consider the case of the discrete system. For example, this does apply to species which have a discrete (say, yearly) breeding system. The population does not change smoothly over time, but is simply a function of one year to the next. It is somewhat surprising, but true, that the dynamics of a population with a discrete model can be much more complicated than those with a continuous model. In fact, a discrete model can actually have what satisfies the mathematical definition of "chaos". Thus you can see any type of behaviour you might imagine, including crashes, but also including periodicity (say, a 17-year cycle for population values). I do not think it is reasonable to assume that humanity can be modeled by this sort of model, even in a coarse-grained sense, because we breed day in and day out all the time. This (and this is somewhat surprising) makes our population a much more stable quantity.