Beyond Turing: The response of patterned ecosystems to environmental change

Siteur, Koen; Siero, Eric; Eppinga, Maarten B.; Rademacher, Jens D. M.; Doelman, Arjen; Rietkerk, Max

doi:10.1016/j.ecocom.2014.09.002

Cited by 130 publications

(240 citation statements)

References 44 publications

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“…For (1) on flat ground (no advection, c ¼ 0), the Busse balloon of 1D stable patterns is illustrated by the union of the two colored regions in Figure 1. 53 The extensions of these 1D patterns to 2D striped patterns, which are represented by the same single wavenumber, are only 2D stable in the dark-green (teal) region near the Turing bifurcation T. In Sec. III C, the nature and construction of these two types of Busse balloons will be considered.…”

Section: Introductionmentioning

confidence: 99%

“…31 For instance, what we refer to as slope driven advection c in (1) is influenced by the evaporation rate from the original model, which has been scaled to 1 in (1). 53 So, determining which values of c are realistic is non-trivial. This is resolved by choosing c over a wide range, giving an overview of the different possibilities.…”

Section: Introductionmentioning

confidence: 99%

“…For fixed c, we view the rainfall parameter a as the primary parameter to vary, as done in previous studies. 53 The choice of parameter values in (1) will correspond to choices in Ref. 53, which are themselves based on Ref.…”

Section: Introductionmentioning

confidence: 99%

“…53 The choice of parameter values in (1) will correspond to choices in Ref. 53, which are themselves based on Ref. 31.…”

Section: Introductionmentioning

confidence: 99%

“…This paper has been motivated by studies in one space dimension of a scaled phenomenological model for vegetation on possibly sloped planes in arid ecosystems. 53,60 One-dimensional patterns ideally represent striped patterns in two space dimensions by trivially extending them into a transversal direction. Such patterns are referred to as banded vegetation and have received considerable attention after reports of widespread observations.…”

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confidence: 99%

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Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

Siero¹,

Doelman²,

Eppinga³

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

124

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For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns. V C 2015 AIP Publishing LLC. This paper has been motivated by studies in one space dimension of a scaled phenomenological model for vegetation on possibly sloped planes in arid ecosystems. 53,60 One-dimensional patterns ideally represent striped patterns in two space dimensions by trivially extending them into a transversal direction. Such patterns are referred to as banded vegetation and have received considerable attention after reports of widespread observations. 8,58 Understanding the appearance and disappearance of vegetation bands may ultimately help prevent land degradation. The restriction to one space dimension may overestimate stability: patterns that are stable against 1D perturbations are not necessarily stable against all 2D perturbations. Natural questions to pose are:• Which of the 1D stable patterns extend to 2D stable striped patterns? • In case of destabilization by 2D perturbations, which mechanisms are responsible?In this paper, we answer these questions for the arid ecosystem model and determine the impact of slope induced advection of water. The influence of advection on striped pattern formation is studied in a more general setting. This approach provides a clear argumentation that is unobscured by model-specific details. Equally important, the results will be applicable to a wide range of models. Applicability to the arid ecosystem model is carefully checked though, assuring that the abstract requirements can in fact be met in practice.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…53 The choice of parameter values in (1) will correspond to choices in Ref. 53, which are themselves based on Ref. 31.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

Siero¹,

Doelman²,

Eppinga³

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

124

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Manipulating the strength of organism–environment feedback increases nonlinearity and apparent hysteresis of ecosystem response to environmental change

Garnier

Hulot

Petchey

2020

Ecology and Evolution

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Theory predicts that organism–environment feedbacks play a central role in how ecological communities respond to environmental change. Strong feedback causes greater nonlinearity between environmental change and ecosystem state, increases the likelihood of hysteresis in response to environmental change, and augments the possibility of alternative stable regimes. To illustrate these predictions and their dependence on a temporal scale, we simulated a minimal ecosystem model. To test the predictions, we manipulated the feedback strength between the metabolism and the dissolved oxygen concentration in an aquatic heterotrophic tri‐trophic community in microecosystems. The manipulation consisted of five levels, ranging from low to high feedback strength by altering the oxygen diffusivity: free gas exchange between the microcosm atmosphere and the external air (metabolism not strongly affecting environmental oxygen), with the regular addition of 200, 100, or 50 ml of air and no gas exchange. To test for nonlinearity and hysteresis in response to environmental change, all microecosystems experienced a gradual temperature increase from 15 to 25°C and then back to 15°C. We regularly measured the dissolved oxygen concentration, total biomass, and species abundance. Nonlinearity and hysteresis were higher in treatments with stronger organism–environment feedbacks. There was no evidence that stronger feedback increased the number of observed ecosystem states. These empirical results are in broad agreement with the theory that stronger feedback increases nonlinearity and hysteresis. They therefore represent one of the first direct empirical tests of the importance of feedback strength. However, we discuss several limitations of the study, which weaken confidence in this interpretation. Research demonstrating the causal effects of feedback strength on ecosystem responses to environmental change should be placed at the core of efforts to plan for sustainable ecosystems.

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

Caviedes‐Voullième

Hinz

2020

Ecohydrology

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The multiscale nature of ecohydrological processes and feedbacks implies that vegetation patterns arising in water‐limited systems are directly linked to water redistribution processes occurring at much shorter timescales than vegetation growth. This in turn suggests that the initially available water in the system can play a role in determining the trajectory of the system, together with the well‐known role of the rainfall gradient. This work explores the role of initial hydrological conditions on vegetation dynamics and vegetation patterns. To do so, the HilleRisLambers–Rietkerk model was solved with different rainfall amounts and a large range of initial hydrological conditions spanning from near‐equilibrium to far‐from‐equilibrium conditions. The resulting vegetation patterns and ecohydrological signatures were quantitatively studied. The results show that not only do initial hydrological conditions play a role in the ecohydrological dynamics but also they can play a dominating one even resulting in divergent vegetation patterns that exhibit convergent mean‐field properties, including a new set of hybrid patterns. Our results highlight the relevance of assessing both global ecological and hydrological signatures and quantitatively assessing patterns to describe and understand system dynamics and in particular to determine if the systems are transient or steady. Furthermore, our analysis shows that the trajectories the system follows during its transient stages cannot be neglected to understand complex dependencies of the long‐term steady state to environmental factors and drivers.

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Beyond Turing: The response of patterned ecosystems to environmental change

Cited by 130 publications

References 44 publications

Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

Striped pattern selection by advective reaction-diffusion systems: Resilience of banded vegetation on slopes

Manipulating the strength of organism–environment feedback increases nonlinearity and apparent hysteresis of ecosystem response to environmental change

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

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