Ecosystems’ responses to changing environmental conditions can be modulated by spatial self-organization. A prominent example of this can be found in drylands, where formation of vegetation patterns attenuates the magnitude of degradation events in response to decreasing rainfall. In model studies, the pattern wavelength responds to changing conditions, which is reflected by a rather gradual decline in biomass in response to decreasing rainfall. Although these models are spatially explicit, they have adopted a mean-field approach to grazing. By taking into account spatial variability when modelling grazing, we find that (over)grazing can lead to a dramatic shift in biomass, so that degradation occurs at rainfall rates that would otherwise still maintain a relatively productive ecosystem. Moreover, grazing increases the resilience of degraded ecosystem states. Consequently, restoration of degraded ecosystems could benefit from the introduction of temporary small-scale exclosures, to escape from the basin of attraction of degraded states.

GNU Octave/MATLAB model implementationThis file can be used to compute model runs as in Figure 2 from the publication.extKAmNat.mModel RunsData from model runs in Figure 2 and 3. Each of the five variables, umatFigxxxx, corresponds to a panel in Figure 2 or 3. Use imagesc(umatFigxxxx(:,:,2)) to see the vegetation component (as in the panels) and deduce the correspondence, and imagesc(umatFigxxxx(:,:,1)) for the water component of the Klausmeier model.ModelRunsAmNat.mat