Linking spatial self-organization to community assembly and biodiversity

  1. Bidesh K Bera
  2. Omer Tzuk
  3. Jamie JR Bennett
  4. Ehud Meron  Is a corresponding author
  1. Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Israel
  2. Physics Department, Ben-Gurion University of the Negev, Israel
9 figures and 1 table


A schematic illustration of the three insights that the model study provides.

(A) Insight I: A drier climate shifts an original spatially uniform community of fast-growing plants, denoted by a green color, to a uniform community of stress-tolerant plants, denoted by blue color. Spatial patterning induced by the drier climate shifts the community back to fast growing plants. (B) Insight II: Once patterns have formed a yet drier climate has little effect on community structure – all patterned community states consist of fast-growing plants (green). This is because of further processes of spatial self-organization that increase the proportion of water-contributing bare-soil areas and compensate for the reduced precipitation. In one-dimensional (1d) patterns, these processes involve thinning of vegetation patches or transitions to longer wavelength patterns. In two-dimensional (2d) patterns, these processes involve morphological transitions from gap to stripe patterns and from stripe to spot patterns. (C) Insight III: Localized patterns in a bistability range of uniform and patterned community states significantly increase functional diversity, as they consist of both stress-tolerant (blue) and fast-growing (green) species. Such patterns can be formed by nonuniform biomass removal as an integral part of a provisioning ecosystem service.

Illustration of overland water flow toward vegetation patches (horizontal arrows), induced by differential infiltration: low in bare soil (short vertical arrows) and high in vegetation patches (long arrows).

Vegetation growth enhances the infiltration contrast and thus the overland water flow (green round arrow), while that flow further accelerates vegetation growth (blue round arrow). The two processes form a positive feedback loop that destabilizes uniform vegetation to form vegetation patterns, and acts to stabilize these patterns once formed.

Emergence of a community as a stationary solution of the model Equations (1).

(a) Competitive exclusion of species in the course of time T[y] when trait diffusion is not allowed (Dχ=0). (b) Asymptotic biomass distribution obtained with slow trait diffusion (Dχ=10-6). The distribution contains information about community-level properties such as community composition, quantified, among other metrics, by the position, χmax, of the most abundant functional group, and functional richness, quantified, among other metrics, by the distribution width, FR, at small biomass values representing the biomass density of a seedling. Parameter values: P=180 mm/y and as stated in Table 1.

Existence and stability ranges of various solutions of a model for a single functional group.

(a) A bifurcation diagram showing the L2-norm of the biomass density vs. precipitation for χ=1. The colors and corresponding labels denote the different solution branches: uniform vegetation (UV), periodic patterns at different wavelengths (PP), hybrid states consisting of pattern domains in otherwise uniform vegetation (HS), and bare soil (BS). Solid (dashed) lines represent stable (unstable) solutions. Example of spatial profiles of these solutions are shown in the insets on the right. (b) Instability thresholds of uniform vegetation, PT, and of bare soil, PB, as functions of χ.

Community reassembly in response to precipitation downshifts.

Left panels show biomass distributions in the trait (χ) – space (x) plane for the specified precipitation rates P1,P2,P3. Right panels show biomass profiles along the χ axis averaged over space. (a,b) A precipitation downshift from P=150 mm/y to 100 mm/y, starting with a uniform community, results in a uniform community shifted to more tolerant species (higher χ), and of lower functional richness (FR). (c) Further decrease to P=80 mm/y results in a patterned community that is shifted back to species investing in growth (lower χ), and has higher functional richness. The biomass distributions in black refer to the unstable uniform community.

The buffering effect of spatial patterning on community structure.

Shown is a partial bifurcation diagram depicting different forms of community assembly along the precipitation axis, as computed by integrating the model equations in time. Stable, spatially uniform communities, χ0(P) (solid dark-green line), shift to stress-tolerant species (higher χ), as precipitation decreases. When the Turing threshold, PT, is traversed, spatial self-organization shifts the community back to fast-growing species (lower χ), and keep it almost unaffected as the fairly horizontal solution branches, χk1(P) (light green line), representing periodic patterns of wavenumber k1, and χk2(P) (yellow line), representing patterns of lower wavenumber k2, indicate. The insets show biomass distributions in the (χ, x) plane for representative precipitation values. The unstable solution branch describing uniform vegetation (dashed line) was calculated by time integration of the spatially decoupled model.

Increased functional diversity of hybrid states and evenness control.

Left panels show biomass distributions of different hybrid states in the trait (χ) – space (x) plane. Right panels show biomass profiles along the χ axis averaged over space. The functional richness, FR, of all hybrid states is almost equal and higher than that of purely uniform or purely patterned states (compare with panel b in Figure 5), but their functional evenness, FE, differs – high for patterned and uniform domains of comparable sizes (b) and low for small (a) and large (c) pattern-domain sizes. Calculated for a precipitation rate P=P2=100 mm/y.

Author response image 1
Author response image 2


Table 1
Model paremeters, their descriptions, numerical values and units.
Λ0Growth rate at zero biomass0.032m2/(kgy)
ΓWater uptake rate20.0m2/(kgy)
fInfiltration contrast (f1 – high contrast)0.01-
AMaximal value of infiltration rate I40.0y-1
QReference biomass at which IA/2 for f10.06kg/m2
L0Evaporation rate in bare soil4.0y-1
REvaporation reduction due to shading10.0m2/kg
KiCapacity to capture lightvariablekg/m2
KminMinimal capacity to capture light0.1kg/m2
KmaxMaximal capacity to capture light0.6kg/m2
MiMortality ratevariabley-1
MminMinimal mortality rate0.5y-1
MmaxMaximal mortality rate0.9y-1
YiRelative contribution to infiltration ratevariable-
YminMinimal contribution to infiltration rate0.5-
YmaxMaximal contribution to infiltration rate1.5-
PPrecipitation ratevariablemm/y
χTradeoff parameter[0,1]-
NNumber of functional groups128-
DBBiomass dispersal rate1.0m2/y
DWSoil-water diffusion coefficient102m2/y
DHOverland-water diffusion coefficient104m2/y
DχTrait diffusion rate10-6y-1

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  1. Bidesh K Bera
  2. Omer Tzuk
  3. Jamie JR Bennett
  4. Ehud Meron
Linking spatial self-organization to community assembly and biodiversity
eLife 10:e73819.