The dryland dynamics model is an agent-based simulation of spatial dynamics of vegetation in arid conditions. The environment is a grid of cells, representing a square piece of land. Each cell can either be degraded {-}, empty (unoccupied) {0} or vegetated {+}. The possible transitions are:
- degraded to empty: {-} to {0}
- empty to degraded: {0} to {-}
- empty to vegetated: {0} to {+}
- vegetated to empty: {+} to {0}
Launch an interactive server by Running run.py:
$ python run.py
Then open your browser to http://127.0.0.1:8521/ move sliders to set the parameters and press Reset, then Run.
To view and run the model analyses, use the Gather and plot Notebook.
The agent class is called Patch. Each Patch object is placed on the grid, and its condition is assigned at the model initialization based on user-specified parameters. Its transitions between different states are governed by the rates calculated at each step.
The additional extra agent class to recreate Fig.2 in Kefi et.al (2007). Instead of global parameters used in the original agent implementation, some parameters are calculated for each agent independently.
The EcoModel class is the model container. It is instantiated with parameters b - plant establishment probability of an empty site, m - mortality probability of a vegetated site and a set of additional parameters found in the accompanying config_file.json file.
This code defines and launches the in-browser visualization for the model. Each cell is a rectangle, with a color based on its condition. Vegetated sites are green, Empty sites are red, and Degraded sites are grey.
This file contains initial parameters for the model simulation.
| Parameter | Description |
|---|---|
| "height" | height of the model landscape |
| "width" | width of the model landscape |
| "delta" | fraction of seeds globally dispersed |
| "c" | includes germination probability and competitive effect from vegetated sites |
| "r" | regeneration probability of a degraded site without vegetation in its neighbourhood |
| "d" | degradation probability of empty sites |
| "f" | positive effect of a neighbouring vegetated site on a degraded site |
| "Empty sites density" | initial density of empty sites |
| "Degraded sites density" | initial density of degraded sites |
| "Use Torus" | set to 1 if Torus is used, otherwise set to 0 |
| "Use Flowlength" | set to 1 if Flowlength parameter is used , otherwise 0 |
| "alpha_feedback" | strengh of feedback between plant pattern and resource leakiness |
| "Patch size" | Length of a single patch in meters |
| "Theta" | angle of the slope in degrees |
| "Use infrequent rain" | set to 1 if there is periodicity of rain |
| "Rain period" | number of timesteps with rain |
| "No rain period" | number of timesteps without rain |
More detailed information on the parameters can be found in the accompanying literature.
Kefi, S., Rietkerk, M., Alados, C. L., Pueyo, Y., Papanastasis, V. P., ElAich, A., and De Ruiter, P. C. (2007a). Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature, 449(7159):213–217 - (https://www.nature.com/articles/nature06111)
Kefi, S., Rietkerk, M., van Baalen, M., and Loreau, M. (2007b). Local facilitation, bistability and transitions in arid ecosystems. Theoretical Population Biology, 71(3):367–379. - (https://www.sciencedirect.com/science/article/pii/S0040580906001250)
Mayor,A. G., Bautista, S., Small, E. E., Dixon, M., and Bellot, J. (2008). Measurement of the connectivity of runoff source areas as determined by vegetation pattern and topography: A tool for assessing potential water and soil losses in drylands. Water Resources Research, 44(10):1–13.
Mayor,A. G., K ́efi, S., Bautista, S., Rodr ́ıguez, F., Carten ́ı, F., and Rietkerk, M.(2013). Feedbacks between vegetation pattern and resource loss dramatically decrease ecosystem resilience and restoration potential in a simple dryland model. Landscape Ecology, 28(5):931–942
Rodriguez, F., Mayor, A. G., Rietkerk, M., and Bautista, S. (2017). A null model for assessing the cover-independent role of bare soil connectivity as indicator of dryland functioning and dynamics. Ecological indicators. - (https://www.sciencedirect.com/science/article/pii/S1470160X1730660X)