Determine the population dynamics of a simple population model such as the example yield-density model shown to the right.

Step #2: Find N(1) from N(0)

Determine the starting value for the population, N(0)=5 in our example. Find N(1) by drawing a vertical line from the starting value along the x-axis to the point where it hits the functional response curve. Next draw a horizontal line from the intersection point to the y-axis. The value here is the value for N(1), approximately 17 in our example.

Step #3: The first trick

Instead of drawing a horizontal line to the y-axis we can draw a horizontal line to the point where it intersects the N(t+1)=N(t) line. A second line drawn parallel to the y-axis will intersect the x-axis at the point equal to the value of N(1).

Step #4: The second trick

Instead of drawing a vertical line from the N(t+1)=N(t) line to the x-axis, we can draw the line to its intersection point with the functional response curve. The y-value associated with the intersection point provides the value for the population size at time 2, N(2) is equal to approximately 6.6.

Step #5: Iterative solution

We can now iteratively apply the two tricks we have learned to determine the populations dynamics. (Note: The first 4 timesteps are indicated on the figure.)

Step #6: The Solution

With the information obtained through the cobwebbing process, we can look at the development of the population across several generations and determine the underlying dynamics that will be exhibited by the population.

The solution for the example shown here indicates that the population exhibits a behavior know as a damped oscillations. The population overshoots the equilibrium point at first, then undershoots the next timestep. Population size then gradually settles down to an equilibrium value (carrying capacity).