Using wavelength and slope to infer the historical origin of semiarid vegetation bands

Abstract

Landscape-scale patterns of vegetation occur worldwide at interfaces between semiarid and arid climates. They are important as potential indicators of climate change and imminent regime shifts and are widely thought to arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. Recent field studies have found an inverse correlation between pattern wavelength and slope, in apparent contradiction with the predictions of mathematical models. Here I show that this “contradiction” is based on a flawed approach to calculating the wavelength in models. When pattern generation is considered in detail, the theory is fully consistent with empirical results. For realistic parameters, degradation of uniform vegetation generates patterns whose wavelength increases with slope, whereas colonization of bare ground gives the opposite trend. Therefore, the empirical finding of an inverse relationship can be used, in conjunction with climate records, to infer the historical origin of the patterns. Specifically, for the African Sahel my results suggest that banded vegetation originated by the colonization of bare ground during circa 1760–1790 or since circa 1850.

Spatial self-organisation enables species coexistence in a model for savanna ecosystems

“…In particular, Deblauwe et al [22] were able to estimate the uphill movement of vegetation stripes by comparing recent satellite images with those taken by spy satellites in the 1960's, but this relied on the clear contrast between vegetation and bare ground -changes in vegetation type within savannas are much more difficult to detect. Data on precipitation (both current and historical [77]) and on elevation (and hence slope) [83] are also available. But these are insufficient to provide an effective empirical test of model (2.2).…”

Advection and Autocatalysis as Organizing Principles for Banded Vegetation Patterns

“…For most parameter values, those wavenumbers can be predicted from a linear analysis [39,15]. We did not perform a systematic study here of this selection mechanism, but refer to [35] for a scenario where wavenumber selection in the presence of invasion can possibly yield information on the origin of banded patterns.…”

“…A technically complementary analysis focuses on separation of spatial scales as a means of systematically building and understanding spatial patterns, exploiting for instance disparities in spatio-temporal scales for water transport versus biomass evolution; see for instance [33,38]. In a different direction, the actual formation process of banded patterns may well have a crucial role in the selection of banded patterns: colonization through spreading rather than emergence after a spontaneous and uniform change in the environment can produce quite different resulting patterns; see for instance [35,36].…”

From nonequilibrium initial conditions to steady dryland vegetation patterns: How trajectories matter

“…Mathematically, initial conditions are the required, known, and prescribed initial states. In natural systems, initial conditions may be impossible to identify or retrieve (Sherratt, ), although systems that have experienced large natural or anthropogenic disturbances—e.g., overgrazing, mining, agriculture, fires, and volcanic eruptions—may allow to identify characteristic initial conditions prior to a (natural or assisted) restoration process. Initial states in such cases may strongly constrain or determine the long‐term state of complex natural systems (Perron & Fagherazzi, ; Maurer & Gerke, ).…”

“…Ecological succession has been explained through modelling ecohydrological interactions (Pueyo et al, ). Importantly, patterns have been shown to be history dependent (Sherratt, ; ; Siteur et al, ), and steady patterns can be used to infer the historical origin of the system (Sherratt, ). Additionally, the so‐called hybrid patterns (Meron, ; Zelnik, Meron, & Bel, )—that is, stable patterns characterized by anomalies in pattern periodicity—have been identified arising from different system trajectories and also strongly affect the response trajectory of the system to perturbations.…”