The modeling approach
The severe implications of desertification have accelerated the investigation of the desert biome. These studies seek to clarify the processes underlying this phenomenon, to discover ways of rehabilitating regions undergoing desertification, and to better manage water and soil resources in order to prevent its spread. Investigating the desert biome requires knowledge of the interrelationships between three component systems: organisms (plants, animals), resources (water, nutrients, solar radiation), and landscape (soil type, topography).
Recent studies at the Blaustein Institutes for Desert Research have centered on understanding these interrelationships in vegetative systems growing in water-limited regions. The scientists, led by Prof. Ehud Meron and Prof. Moshe Shachak, divided their work-plan into three stages:
1. Construction of a conceptual model based on observations and experimental data that defines the biome components - organisms, resources, and landscape - and their interrelationships;
2. Building of a mathematical model that enables determination of how these interrelationships affect the appearance of vegetation patterns, similar to those shown in Figs. 2 a,b; and
3. Solution of the mathematical equations underlying the model and applying these solutions to understanding the appearance of desertification.
a) b)
Figure 2. a) Air photograph of vegetation bands on a sloped region near Niamey, Niger. The bands develop in the direction perpendicular to the slope and are tens of meters wide. From Catena, ©1999, with permission of Elsevier Science. b) Labyrinth-like pattern in Paspalum vaginatum grass on a level lawn in Ganei Omer, northern Negev. Width of green growth is about 15 cm.
The mathematical model developed by the researchers enables simulation of the vegetation patterns generated under various environmental conditions and of situations that could lead to the appearance of desertification.
Predictions generated by the model
Two major predictions arise from the mathematical model:
1. Vegetation patterns along a precipitation gradient
The model describes the types and order of vegetation patterns appearing on flat and sloped ground as precipitation levels drop:
On flat ground: |
Uniform vegetation > Vegetation with holes > bands (labyrinth) > spots > bare soil (see Fig. 3 and Animation 1). |
On sloped ground: |
Uniform vegetation > bands (perpendicular to the slope direction) > broken bands > bare soil. |
Uniform |
Holes |
Labyrinth |
Spots |
Bare |
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Figure 3. Vegetation states on flat ground along the rainfall gradient. Precipitation decreases from left to right. Click on a state picture to see a model simulation showing how the state develops from a bare soil when seeds are dispersed.
The vegetation patterns result from instabilities induced by the positive feedback between vegetation and water. Vegetation in areas where the biomass is slightly greater than in a neighboring area will be more successful in absorbing water. As a result, the difference in biomass of the two regions will increase, further expanding the gap in the ability of the regions to take up water, thereby increasing the gap in biomass. This cycle continues until the neighboring region dries out completely.
2. Coexistence of stable vegetation patterns
The model predicts the possibility of finding different stable patterns at the same level of precipitation: the preferred pattern will depend upon the initial distribution of the vegetation and water, as demonstrated in Animation 1. The coexistence of different stable patterns is, again, a result of the positive feedback between vegetation and precipitation. While small plants have difficulty surviving under dry conditions, thereby perpetuating a bare soil state, larger plants with well-developed roots can capture sufficient water from their surroundings and endure, thereby stabilizing the vegetative pattern. Along the rainfall gradient, one may find precipitation ranges where additional pairs of stable states coexist, such as spots and bands, bands and holes, and holes and uniform vegetation.
Mathematical model versus field observations
Most of the patterns discussed above were observed in various regions of the world (Valentin et al. 1999; von Hardenberg et al., 2001; Rietkerk et al., 2003). These are generally stationary patterns, representing long-term behavior. Over shorter time spans, however, system behavior can be dynamic and more strongly dependent on the initial distribution of the vegetation and water. Even in these situations, there is agreement between predicted patterns and patterns observed in nature, as shown in Fig. 4.
Figure 4. (a) Solutions of the mathematical model demonstrating rings (center), which is the intermediate state between spots (left) and labyrinth-arranged stripes (right). (b) Rings of bluegrass (Poa bulbosa) as found in Yatir Forest. Their diameter is about 15 cm.
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