TL;DR: It is proposed that patch-size distributions may be a warning signal for the onset of desertification in arid ecosystems with different grazing pressures, using both field data and a modelling approach.
Abstract: Arid ecosystems cover about 40% of Earth's land area and are home to over two billion people, yet they remain vulnerable to climate change and human actions. Using numerical simulations, and data from Mediterranean ecosystems in Spain, Morocco and Greece, Kefi et al. show that patch-size distribution of vegetation follows a power law. As grazing pressure increases, patch size deviates from the power law close to the transition to desert conditions. So patch-size distribution may be a useful early warning of desertification. The cover shows an arid landscape (top) in the El Planeron nature reserve in Belchite, Spain, and the lower panels show degradation in this landscape. In a separate paper, Scanlon et al. use satellite imagery to show that the size distribution of tree clusters in the Kalahari basin also follows a scale-free power law. This can be explained by positive feedback associated with preferential environments near existing trees. In News & Views Ricard Sole discusses both papers. COVER IMAGE Sonia & Michael Kefi/ Yolanda Pueyo/ Santiago Begueria Portugues This paper describes and models the effect of grazing on vegetation patchiness in three arid Mediterranean ecosystems. The patch size distribution of the vegetation in these ecosystems follows a power law, which can be explained by invoking local positive interactions among plants. Deviations from power laws occur when grazing pressure is high, and may be a harbinger of imminent desertification. Humans and climate affect ecosystems and their services1, which may involve continuous and discontinuous transitions from one stable state to another2. Discontinuous transitions are abrupt, irreversible and among the most catastrophic changes of ecosystems identified1. For terrestrial ecosystems, it has been hypothesized that vegetation patchiness could be used as a signature of imminent transitions3,4. Here, we analyse how vegetation patchiness changes in arid ecosystems with different grazing pressures, using both field data and a modelling approach. In the modelling approach, we extrapolated our analysis to even higher grazing pressures to investigate the vegetation patchiness when desertification is imminent. In three arid Mediterranean ecosystems in Spain, Greece and Morocco, we found that the patch-size distribution of the vegetation follows a power law. Using a stochastic cellular automaton model, we show that local positive interactions among plants can explain such power-law distributions. Furthermore, with increasing grazing pressure, the field data revealed consistent deviations from power laws. Increased grazing pressure leads to similar deviations in the model. When grazing was further increased in the model, we found that these deviations always and only occurred close to transition to desert, independent of the type of transition, and regardless of the vegetation cover. Therefore, we propose that patch-size distributions may be a warning signal for the onset of desertification.
TL;DR: A simple model of plant and water dynamics based on ecologically realistic assumptions and with reasonable parameter values captures both the regular and irregular patterns of vegetation in semiarid regions.
Abstract: Vegetation in many semiarid regions is strikingly patterned, forming regular stripes on hillsides and irregular mosaics on flat ground. A simple model of plant and water dynamics based on ecologically realistic assumptions and with reasonable parameter values captures both of these types of patterns. The regular patterns result from a Turing-like instability; the irregular patterns arise when the ecological dynamics amplify slight small-scale topographic variability. Because of the close agreement between observations and these theoretical results, this system provides a clear example of how nonlinear mechanisms can be important in determining the spatial structure of plant communities.
TL;DR: The results show that self-organized vegetation patterns observed in arid ecosystems might all be the result of spatial self-organization, caused by one single mechanism: water infiltrates faster into vegetated ground than into bare soil, leading to net displacement of surface water to vegetated patches.
Abstract: Scientists are still searching for possible unifying mechanisms
to explain this range of spatial patterns (Tongway
and Ludwig 2001), and an important question of this research
is whether this range is the result of preexisting
environmental heterogeneity, the result of spatial selforganization,
or both (Klausmeier 1999; Couteron and
Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg
et al. 2001). Here, we contribute to the ongoing debate
about vegetation pattern formation in arid ecosystems
by presenting novel, spatially explicit model analyses and
results, extending on the work of HilleRisLambers et al.
(2001). Our results show that these different vegetation
patterns observed in arid ecosystems might all be the result
of spatial self-organization, caused by one single mechanism:
water infiltrates faster into vegetated ground than
into bare soil, leading to net displacement of surface water
to vegetated patches. This model differs from earlier model
results (Klausmeier 1999; Couteron and Lejeune 2001;
HilleRisLambers et al. 2001; Von Hardenberg et al. 2001) primarily in two ways: it is fully mechanistic, and it treats
the lateral flow of water above and below the soil as separate,
not independent, variables. Although the current
model greatly simplifies the biophysics of arid systems, it
can reproduce the whole range of distinctive vegetation
patterns as observed in arid ecosystems, indicating that
the proposed mechanism might be generally applicable.
We further show that self-organized vegetation patterns
can persist far into regions of high aridity, where plants
would become extinct if homogeneously distributed,
pointing to the importance of this mechanism for maintaining
productivity of arid ecosystems (Noy-Meir 1973).
Our analyses are based on the model first developed in
HilleRisLambers et al. (2001)
TL;DR: A new model for vegetation patterns is introduced that predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns and predicts wide precipitation ranges where different stable states coexist.
Abstract: A new model for vegetation patterns is introduced. The model reproduces a wide range of patterns observed in water-limited regions, including drifting bands, spots, and labyrinths. It predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns. It also predicts wide precipitation ranges where different stable states coexist. Using these predictions we propose a novel explanation of desertification phenomena and a new approach to classifying aridity.
TL;DR: In this article, a spatially explicit model con- sisting of partial differential equations using a method for demonstrating pattern formation (Turing analysis) was proposed. And the model revealed that pattern formation can occur in semi-arid areas given only the positive feedback between plant density and local water infiltration coupled with the spatial redistribution of runoff water.
Abstract: Hypotheses about the origin of vegetation pattern formation in semi-arid areas around the world almost all include a common feature of semi-arid areas: the presence of a positive feedback between plant density and water infiltration We investigate whether this positive feedback and the spatial redistribution of runoff water are sufficient to explain vegetation pattern formation For this purpose, we analyze a spatially explicit model con- sisting of partial differential equations using a method for demonstrating pattern formation (Turing analysis) Our analysis reveals that pattern formation can occur in semi-arid areas given only the positive feedback between plant density and local water infiltration coupled with the spatial redistribution of runoff water Thus, slope and underlying heterogeneity are not essential conditions Other factors in the model, such as herbivory, plant dispersal, rainfall, and drought tolerance of plants, appear to determine under what conditions pattern formation is likely but are not the primary factors that generate the patterns The model is in agreement with field observations and indicates the conditions for which vegetation pattern formation can be expected in arid and semi-arid grazing systems