Clicking on the picture above will open an interactive animation showing how different initial vegetation distributions change with time when experiencing a fixed level of precipitation. The animated simulations have been obtained by numerically solving a mathematical model of vegetation growth on a computer (Hardenberg et al., 2001). For further information on vegetation patterns press here.
Operating the animation
The three frames represent different initial distributions of vegetation: (a) bare soil (no vegetation),(b) a single vegetation spot, (c) uniform vegetation. To view the time evolution of any of these initial states under a given level of precipitation, proceed as follows:
Click a desired precipitation level on the bottom bar (the chosen value will appear in orange).
Choose the frame of the desired initial state and press the big arrow at the bottom of the frame.
You can follow the time evolution in slow forward or backward motion by repeatedly clicking the little arrows at the bottom of the frame.
Learning from the animation
A. How do vegetation states change along a rainfall gradient?
Run the simulations in one of the three frames, starting at the lowest precipitation value (40 mm/year) and incrementing it up to 520 mm/year. Repeat this process in the other two frames. Are there any similarities between the sequences of vegetation states obtained with the different initial conditions?
B. Coexistence of stable states
Run all three initial state frames (a) at precipitation values of 40, 160, 320, and 520 mm/year, and (b) at precipitation values 120 and 480 mm/year. Are the final patterns dependent on the initial states?
Understanding your observations:
The mathematical model of vegetation growth predicts five pure vegetation states in uniform planar systems. The states, obtained at increasing precipitation values, are: bare soil, spots, stripes, holes and uniform vegetation. The five states can be identified in the simulations (learning item A) although some of them show mixed states such as spots and stripes (frames (a) and (c) at 240 mm/year) or stripes and holes (frames (a) and (c) at 360 mm/year).
In addition, the model predicts precipitation ranges where two different pure states can coexist. For example, at 120 mm/year both bare soil (frame (a)) and spots (frame (c)) coexist as stable states. At 480 mm/year both uniform vegetation (frame (c)) and holes (frame (b)) are stable states. The coexistence of stable states allows for a variety of patterns that mix the two states in space. The mixed state obtained at 240 mm/year is a result of coexistence of stable spots and stable stripes. The mixed state obtained at 360 mm/year is a result of coexisting stripes and holes. Coexistence of stable states implies vulnerability to desertification.
