You need to stop using this phrase
Dear everyone who uses the term "carrying capacity" in debates about human population, as in "Australia's carrying capacity is probably a little less than 20 million...."
Stop it, please. I know your intentions are good, but you're talking out of your anus. Yes, really, even most of you professors of environmental science/biology etc who employ it in public policy debates, from what I've seen.
Now I'm a stupid crazy Cornucopian[1] on these issues, but fortunately you don't need to agree with my overall views to accept the argument I'm about to make...
What is a Carrying Capacity?
Essentially a carrying capacity is a number that derives from certain kinds of biological models of population growth. The first and simplest such model, which will do for the purposes of explaining the relevant concepts, is the logistic equation[2]:
dN/dt = rN[K-N]/K
In this equation K is the carrying capacity.
I know, Calculus is hard and boring, but this model isn't too hard to understand for non-maths people.
Its about predicting how the population of a given lifeform grows. It says the more lifeforms there are, the more lifeforms get born, which leads naturally to exponential growth[3]. However at a certain point, the ecosystem the lifeform lives in can't provide enough of some critical resource (energy, potassium, territory, etc) to sustain any more growth; so the population obtains a natural maximum value, our much beloved K.
While a massive oversimplification of most populations outside of bacteria on a petri-dish, its nonetheless a reasonably successful model; it predicts some things quite well, and is the basis of most of the more sophisitcated and accurate models that we have.
OK, so far so good.
Is the logistic model applicable at all to humans?
In a sense, yes. Based on what we know about physics, there are is an upper bound on the the amount of humans that can live in a given segment of space.
However, applying the model (or any of its variants) naievely to homo sapiens is useless, because basic biological models make simplified assumptions about living things that work reasonably for most organisms, but simply don't work for us. Its important to stress that I'm not saying that humans aren't subject to the basic laws of biology; I'm saying that our current understanding of the laws of biology are only an approximation, that break down especially badly in the case of humans, just as Newtonian physics breaks down for really small things, really fast things, and really heavy things.
So what's broken?
The model assumes that two important things are fixed: the environment, and the nature of the organism (technically, the species' phenotype).
Both of these assumptions are wrong. However they typically work well enough in practice. A lot of the time, the environment doesn't change very quickly relative to the growth of the organism whose population you're trying to predict. Sometimes there's a megavolcanic eruption or whatever and the environment does change rapidly, but no scientist who uses the Logistic Model would pretend it works in those scenarios.
Thanks largely to Darwin we understand that phenotypes also aren't fixed. Organisms make technological innovations, in the forms of experimental mutations to their genome, that are passed on via vertical and horizontal gene transfer. But, and this is a critical point so I will chuck in some emphasis, genetic evolution is generally slow when compared to the timescales of population growth.
Actually, to be honest, I gather biologists increasingly are of the opinion that both ecosystems and genes nearly always change fast enough to matter for any reasonable model of population in the real world. But the intuition, that the effect of population size dominates these other variables and so they can be approximated in our equations as a constant, is what most people mean (even if they don't realise it) when they talk about Carrying Capacities.
And humans...?Modern humans don't just challenge the assumptions of environmental change and evolution happening very slowly relative to population growth; they shatter them.
I shouldn't have to tell "we're overpopulated and the environment is dying" types that our environment is changing very rapidly due to our presence in it.
What a lot of people miss though is that the reason our physical environment is changing so fast is because we're causing it to, by virtue of evolving orders of magnitude faster than any other species in Earth's history.
The trick is that we no longer depend on genes alone to pass on our neat discoveries to our peers (horizontal transfer) and descendents (vertical transfer). We have what Richard Dawkins called memes. Before everyone changed the word to mean "amusing YouTube video", it was supposed to express the concept that the information contained in a human idea replicates, spreads, mutates, combines and evolves in a way that is related (but different) to a gene.
This is the defining feature of humans as organisms. It sets us apart from other animals. There are of course some quite striking examples of similarities between human intelligence and the intelligence found in other animals - the agriculture of Ants, the tool use of Chimpanzees, the puzzle solving of Octopuses - but none of them can be said to have culture.
They can't learn how to make a hand-axe or a fibre optic cable from a diagram. They can't change how they think about their co-species members by reading a Bible or a Tao Te Ching. They don't write songs or novels or advertisements or newspapers, they don't make speeches or status updates or scultputres or blog posts.
The speed of evolution of all these other species is limited to the speed at which genetic mutations appear, can be tested for fitness by nature, and can be spread amongst a population. This is normally such a glaically slow pace that it took until Darwin for us to even realise that it happens.
In contrast, consider a tiny little bit of memetic information, a Martin Luther King Jr quote [4]. Look at how quickly, with ze power of teh interwebs, it was accidentally mutated, spread, and then the faultiness of the mutation was identified and counteracted.
OK, enough ranting about memes
The point is that:
dN/dt = rn[K-N]/K
is, to use the technical term, an idiotic model to apply to humans. Thanks to memes that store their information in your brain and your iPhone instead of your genome, our species is not only changing fast enough to effect our population growth (and in a nice little feedback loop the size of our population in turn effects the speed of memetic evolution), we, and as a result our environment, are actually changing faster than our population is growing. Contrast for instance the rate of change of per GDP over human history with the rate of change of population.
Now there are naturally still constraints, and there are still going to be constants of various descriptions in whatever the correct model of human population growth is, including one that might resemble a carrying capacity: maybe something like
(dN/dt) = rN[K-N][C-M(N,T)]/CK
where M(N,T) is total memetic information [i.e. our collective cultural knowledge] as a function of population size and time. But the constant CK here is a very, very different beast from the K that models a limit on the amount of available grass for a cow to eat.
And furthermore you may think we're going to rapidly evolve to a dead end where we nuke or pollute one another out of existence (eventually N -> 0), or to a triumphant program of galactic colonisation (eventually N -> Lots), or any one of a million scenarios in between. And that's fine, we can disagree about that, its kinda hard to say at this point who is right, since we don't have any other memetic species to study for clues. Scientific reasoning is sadly of little help in understanding unique data points.
In conclusion
If you continue to try to treat N as the only variable in our own population equation, and approximate all other relevant factors with a constant K, and if you further try to guess what that K looks like based on a vague intuition formed from other, non-memetic species, you're going to end up looking very, very silly. Some otherwise quite respectable biologists[5] keep making this mistake, because scientists love to take a model that works for the phenomena they've studied, apply it to a superficially similar but actually far more complex phenomenon, and then act puzzled when it doesn't seem to work so well. That's ok; learning why the models don't carry over, and updating them, is what science is all about.
But please don't try to tell me Australia can only "biologically sustain" 20 million people, as opposed to 10,000 people, or 10 billion people. You made the number up, based purely on the remarkable coincidence that we happen to have a little over 20 million living here right now. Its fictious; it has no basis in scientific reality.
And, if you try and use your bullshit number to justify preventing people fleeing corruption, poverty, war and genocide from moving here, I reserve the right to first mock you as clueless, and second attack you for using terrible reasoning to inflict a moral outrage.
So yeah, STFU with the "carrying capacity" phrase already.
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EDIT: Fixed some tyops, tidied wording in a couple of sentences slighly, clarified the language concerning what changes in genetic evolution (species wide phenotype, not individual organisms.)
Footnotes, because I'm old fashioned, and wanted you to read my argument in full before following the links.
[1] http://en.wikipedia.org/wiki/Cornucopian
[2] http://mathworld.wolfram.com/LogisticEquation.html
[3] http://en.wikipedia.org/wiki/Exponential_growth
[4] http://www.theatlantic.com/national/archive/2011/05/anatomy-of-a-fake-quotation/238257/