*(Clicking the above image will download a pdf file of a larger image.)*

In order to understand the complex world emerging around us, it is necessary to have a grasp of the ecological concept of “carrying capacity.” This post explains this crucial concept without letting the mathematics distract us from the important points.

In an ecology, you can learn a lot from a curve of the system dynamics (the second derivative of the population equations tells you about the relative rates of births and deaths in the population).

In describing an ecology, although we use words like “population” and “births” and “deaths” what we are *really* describing can be any complex adaptive system. The “population” is simply the parts that make up that system, and “births” and “deaths” simply refers to the entry and exit of those parts from the system.

So for example, we might be describing a Twitter ecology in which “population” refers to users with accounts, and “births” and “deaths” refer to those users coming online and going offline, i.e. participating and then not (within certain time frames). Since these concepts apply to the kinds of systems that we find in the emerging political, economic, and social environments, it is my hope that this brief explanation will help others.

There are six key elements on the graph above (from left to right):

- The Zero Threshold
- The Exinction Zone
- The Lower Threshold
- The Sustainable Zone
- The Upper Threshold
- The Overpopulation Zone

### The Zero Threshold

At zero, the curve is also at zero (i.e. on the horizontal x-axis), so the population neither rises nor declines. This is called a **stable** equilibrium because the population will never change again, i.e. there are no births, and no deaths.

### The Exinction Zone

In the extinction zone, the curve is below the x-axis, which means it is negative (-), therefore the population is shrinking. In this zone, the population is too small to support itself and it **decreases** to zero (without intervention from outside the system).

As an example, whales must be able to hear each other at sea in order to find each other and reproduce. If the whale population is spread too thinly to make contact with each other, then decline is inevitable.

### The Lower Threshold

The lower threshold is **not stable** because if the population ever reaches it, then the population will immediately move into the extinction zone, and decline. Above the lower threshold, the population has a chance at sustainability.

### The Sustainable Zone

In the sustainable zone, the curve is *above* the x-axis, so the population has enough resources (time, space, water, food, energy, etc.) and consequently **increases** until it reaches the upper threshold.

### The Upper Threshold

The upper threshold is **stable** because

*below*the upper threshold, the population will increase until it reaches the upper threshold*above*the upper threshold, the population will decrease until it reaches the upper threshold

### The Overpopulation Zone

In the overpopulation zone, the curve is again below the x-axis, which means the population exceeds the carrying capacity of its environment. Deaths exceed births, and the population **decreases** until it reaches the upper threshold.

*My sincere thanks goes out to Carl Simon of the University of Michigan Center for the Study of Complex Systems, who made all of this clear to me despite my mathematical shortcomings.*