Modeling Dryland Landscapes

Proceedings of the Royal Society B: Biological Sciences, 2010

Two major forms of vegetation patterns have been observed in drylands: nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The emergence of scale-free patterns has been attributed to global competition over a limiting resource, but the physical and ecological origin of this phenomenon is not understood. Using a spatially explicit mathematical model for vegetation dynamics in water-limited systems, we unravel a general mechanism for global competition: fast spatial distribution of the water resource relative to processes that exploit or absorb it. We study two possible realizations of this mechanism and identify physical and ecological conditions for scale-free patterns. We conclude by discussing the implications of this study for interpreting signals of imminent desertification.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013

Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern-formation theory suggests various scenarios for such dynamics; an abrupt global shift involving a fast collapse to bare soil, a gradual global shift involving the expansion and coalescence of bare-soil domains, and an incipient shift to a hybrid state consisting of stationary bare-soil domains in an otherwise periodic pattern. Using models of dryland vegetation we address the question which of these scenarios can be realized. We found that the models can be split into two groups: models that exhibit multiplicity of periodic-pattern and baresoil states, and models that exhibit, in addition, multiplicity of hybrid states. Furthermore, in all models we could not identify parameter regimes in which bare-soil domains expand into vegetated domains. The significance of these findings is that while models belonging to the first group can only exhibit abrupt shifts, model belonging to the second group can also exhibit gradual and incipient shifts. A discussion of open problems concludes the paper.

Dryland landscapes are mosaics of patches that differ in resource concentration, biomass production and species richness. Understanding their structure and dynamics often calls for the identification of key species that modulate the abiotic environment, redistribute resources and facilitate the growth of other species.

Recent theoretical studies have shown that spatial redistribution of surface water may explain the occurrence of patterns of alternating vegetated and degraded patches in semiarid grasslands. These results implied, however, that spatial redistribution processes cannot explain the collapse of production on coarser scales observed in these systems. We present a spatially explicit vegetation model to investigate possible mechanisms explaining irreversible vegetation collapse on coarse spatial scales. The model results indicate that the dynamics of vegetation on coarse scales are determined by the interaction of two spatial feedback processes. Loss of plant cover in a certain area results in increased availability of water in remaining vegetated patches through run-on of surface water, promoting within-patch plant production. Hence, spatial redistribution of surface water creates negative feedback between reduced plant cover and increased plant growth in remaining vegetation. Reduced plant cover, however, results in focusing of herbivore grazing in the remaining vegetation. Hence, redistribution of herbivores creates positive feedback between reduced plant cover and increased losses due to grazing in remaining vegetated patches, leading to collapse of the entire vegetation. This may explain irreversible vegetation shifts in semiarid grasslands on coarse spatial scales.

Journal of Geophysical Research, 2007

Abrupt transitions between large-scale grassland and desert in arid and semiarid regions have been observed in nature and reproduced by modeling studies. Observations also show the existence of nonuniform fine-scale vegetation patterns along the transition zone. This paper attempts to better understand these observations from two very different spatial scales. By explicitly introducing horizontal interaction terms into our previous dynamical grassland model, vegetation patterns with high diversities are found in the transition zone, and the system possesses an infinite number of equilibrium states in response to a given climatic forcing. The transition can be elucidated in two ways. In terms of the vegetation formations, the ecosystem undergoes the transition from uniform grassland to regular and irregular vegetation patterns, and then to pure desert as the moisture index (i.e., the ratio of precipitation over potential evaporation) decreases. In terms of biomass, the transition from grassland to desert goes through a narrow range of moisture index under which grassland is most fragile, as indicated by erratic vegetation patterns and large variation of average biomass. The existence of this range, however, has not been reported in previous modeling studies, and still needs to be validated using observational data.

Ecology, 2008

Spatially periodic vegetation patterns, forming gaps, bands, labyrinths, or spots, are characteristic of arid and semiarid landscapes. Self-organization models can explain this variety of structures within a unified conceptual framework. All these models are based on the interplay of positive and negative effects of plants on soil water, but they can be divided according to whether they assume the interactions to be mediated by water redistribution through runoff/diffusion or by plants' organs. We carried out a multi-proxy approach of the processes operating in a gapped pattern in southwest Niger dominated by a shrub species. Soil moisture within the root layer was monitored in time and space over one month of the rainy season. Soil water recharge displayed no spatial variation with respect to vegetation cover, but the stock half-life under cover was twice that of bare areas. A kernel of facilitation by the aboveground parts of shrubs was parameterized, and soil water half-life was significantly correlated to the cumulated facilitative effects of shrubs. The kernel range was found to be smaller than the canopy radius (81%). This effect of plants on soil water dynamics, probably through a reduction of evaporation by shading, is shown to be a better explanatory variable than potentially relevant soil and topography parameters. The root systems of five individuals of Combretum micranthum G. Don were excavated. Root density data were used as a proxy to parameterize a kernel function of interplant competition. The range of this kernel was larger than the canopy radius (125%). The facilitation-to-competition range ratio, reflecting the above-to-belowground ratio of plant lateral extent, was smaller than 1 (0.64), a result supporting models assuming that patterning may emerge from an adaptation of plant morphology to aridity and shallow soils by means of an extended lateral root system. Moreover, observed soil water gradients had directions opposite to those assumed by alternative mathematical models based on underground water diffusion. This study contributes to the growing awareness that combined facilitative and competitive plant interactions can induce landscape-scale patterns and shape the two-way feedback loops between environment and vegetation.

Austral Ecology, 2018

The Wiegand and Milton (1996) simulation model predicts that vegetation dynamics in arid shrublands are characterized by event-driven stochasticity (weather events), and demographic inertia (persistence of a species in a community) that lead to a lagged response in vegetation compositional change. Slow plant growth is one of the mechanisms driving slow vegetation change. We test this model at the same location (Tierberg Longterm Ecological Research site) on which the model was based. Three dwarf shrub species, differing in palatability, were tracked over 25 years (1988-2014) at two levels of the past herbivory (pre-1960) and three levels of the present herbivory (post-1988). In the period between 1960 and 1988, all sites were grazed at the recommended agricultural stocking rate. For each species, plant density and a number of size attributes (basal diameter, height, canopy area) were surveyed. Analyses using a two-way Analysis of Covariance (ANCOVA) took initial starting size into consideration. As the model predicted, event-driven stochasticity (rainfall) resulted in an increase in density of the smaller size classes following a single large recruitment event across all grazing regimes for the palatable and unpalatable species. Size-class distribution curve types remained unchanged illustrating that population demography remains unaffected for long periods and responses are slow (lagged response). Slow plant growth was evident in that there were no changes in height, canopy area, or density under present grazing regimes over the 25-year period. Palatable species had a reduced canopy area and density compared to unpalatable species. Our findings provide empirical evidence supporting the predictions of the Wiegand and Milton (1996) model, notably event-driven stochasticity, demographic inertia, and a lagged response in vegetation change in arid shrublands. In addition, our results support the model assumption of the significance of slow growth in long-lived plant species and the influence of grazing regime.

Ecography, 2011

Plant Ecology (formerly Vegetatio), 2004

Ecologists increasingly use spatial statistics to study vegetation patterns. Mostly, however, these techniques are applied in a purely descriptive fashion without a priori statements on the pattern characteristics expected. We formulated such a priori predictions in a study of spatial pattern in a semi-arid Karoo shrubland, South Africa. Both seed dispersal and root competition have been discussed as processes shaping the spatial structure of this community. If either of the two processes dominates pattern formation, patterns within and between shrub functional groups are expected to show distinct deviations from null models. We predicted the type and scale of these deviations and compared predicted to observed pattern characteristics. As predicted by the seed dispersal hypothesis, small-scale co-occurrence within and between groups of colonisers and successors was increased as compared to complete spatially random arrangement of shrubs. The root competition predictions, however, were not met as shrubs of similar rooting depth co-occurred more frequently than expected under random shrub arrangement. Since the distribution of rooting groups to the given shrub locations also failed to match the root competition predictions, there was little evidence for dominance of root competition in pattern formation. Although other processes may contribute to small-scale plant co-occurrence, the sufficient and most parsimonious explanation for the observed pattern is that its formation was dominated by seed dispersal. To characterise point patterns we applied both cumulative ͑uniand bivariate K-function͒ and local ͑pairand mark-correlation function͒ techniques. Based on our results we recommend that future studies of vegetation patterns include local characteristics as they independently describe a pattern at different scales and can be easily related to processes changing with interplant distance in a predictable fashion.