Patterned vegetation, tipping points, and the rate of climate change

Chen, Yuxin; Kolokolnikov, Théodore; Tzou, Justin C.; Chunyi, Gai

doi:10.1017/s0956792515000261

Cited by 33 publications

(56 citation statements)

References 59 publications

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“…In general, bistable dynamics makes a system especially prone to collapsing to an irreversible state as environmental conditions gradually worsen and a tipping point is reached (Dakos et al 2011, Kéfi et al 2014 through the phenomenon of hysteresis. Pattern formation has previously been suggested as a possible coping mechanism for systems close to degradation (Chen et al 2015). The analysis in this paper gives more insight into this previously reported phenomenon as we also find this to be the case in our model (Zaytseva et al 2018) where pattern formation allows the marsh edge to cope with harsher erosion through spatial variation.…”

Section: Discussionsupporting

confidence: 81%

“…This makes such systems especially prone to collapsing to an irreversible state as environmental conditions gradually worsen and a tipping point is reached (Dakos et al 2011, Kéfi et al 2014. Pattern formation has previously been suggested as a possible coping mechanism, allowing such systems to escape degradation past their tipping point (Chen et al 2015). Due to the reported degradation of tidal marsh habitats around the world, the study of pattern formation in these systems becomes particularly important and can provide more insight into the possible pattern forming mechanism and its implication for the system's resilience and adaptation to environmental changes.…”

Section: Introductionmentioning

confidence: 99%

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Model of pattern formation in marsh ecosystems with nonlocal interactions

2019

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Smooth cordgrass Spartina alterniflora is a grass species commonly found in tidal marshes. It is an ecosystem engineer, capable of modifying the structure of its surrounding environment through various feedbacks. The scale-dependent feedback between marsh grass and sediment volume is particularly of interest. Locally, the marsh vegetation attenuates hydrodynamic energy, enhancing sediment accretion and promoting further vegetation growth. In turn, the diverted water flow promotes the formation of erosion troughs over longer distances. This scaledependent feedback may explain the characteristic spatially varying marsh shoreline, commonly observed in nature. We propose a mathematical framework to model grass-sediment dynamics as a system of reaction-diffusion equations with an additional nonlocal term quantifying the short-range positive and long-range negative grass-sediment interactions. We use a Mexican-hat kernel function to model this scale-dependent feedback. We perform a steady state biharmonic approximation of our system and derive conditions for the emergence of spatial patterns, corresponding to a spatially varying marsh shoreline. We find that the emergence of such patterns depends on the spatial scale and strength of the scale-dependent feedback, specified by the width and amplitude of the Mexican-hat kernel function.

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Section: Discussionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Model of pattern formation in marsh ecosystems with nonlocal interactions

2019

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“…Recent studies suggest that ecosystems with spatially periodic patterns may exhibit rate dependent behaviour (Sherratt , Siteur et al , Chen et al ). Such patterns are ubiquitously observed in arid ecosystems (Deblauwe et al ), which are currently undergoing rapid climatic changes (Tebaldi et al , Siteur et al ).…”

Section: Identifying Real Rate Sensitive Ecosystemsmentioning

confidence: 99%

Ecosystems off track: rate‐induced critical transitions in ecological models

Siteur

Eppinga

Doelman

et al. 2016

Oikos

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Theory suggests that gradual environmental change may erode the resilience of ecosystems and increase their susceptibility to critical transitions. This notion has received a lot of attention in ecology in recent decades. An important question receiving far less attention is whether ecosystems can cope with the rapid environmental changes currently imposed. The importance of this question was recently highlighted by model studies showing that elevated rates of change may trigger critical transitions, whereas slow environmental change would not. This paper aims to provide a mechanistic understanding of these rate-induced critical transitions to facilitate identification of rate sensitive ecosystems. Analysis of rate sensitive ecological models is challenging, but we demonstrate how rate-induced transitions in an elementary model can still be understood. Our analyses reveal that rate-induced transitions 1) occur if the rate of environmental change is high compared to the response rate of ecosystems, 2) are driven by rates, rather than magnitudes, of change and 3) occur once a critical rate of change is exceeded. Disentangling rate-induced transitions from classical transitions in observations would be challenging. However, common features of rate-sensitive models suggest that ecosystems with coupled fast-slow dynamics, exhibiting repetitive catastrophic shifts or displaying periodic spatial patterns are more likely to be rate sensitive. Our findings are supported by experimental studies showing rate-dependent outcomes. Rate sensitivity of models suggests that the common definition of ecological resilience is not suitable for a subset of real ecosystems and that formulating limits to magnitudes of change may not always safeguard against ecosystem degradation.

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“…Reaction-diffusion PDE's are ubiquitous as models of pattern formation in a variety of biological and social systems. Some prominent examples include: animal skin patterns [1][2][3]; vortex lattices in Bose-Einstein condensates [4,5]; patterns in chemical reactions [6][7][8]; crime hot-spots in a model of residential burglaries [9][10][11][12]; and vegetation patches in arid environments [13][14][15][16] A common feature of many of these systems is the presence of localized patterns such as spots, stripes etc. There is a very large literature about the formation and stability of these patterns, especially within homogeneous environments.…”

Section: Introductionmentioning

confidence: 99%

“…Animal skin patterns are also highly dependent on the location within the animal, since the thickness, curvature and growth of the skin is nonuniform and has a large effect on the resulting patterns [26][27][28][29][30][31]. Similarly, the distribution of the vegetation patches is highly dependent on the amount of precipitation and slope gradients which vary in space and time [16,32,33].…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in a Reaction-Diffusion System with Space-Dependent Feed Rate

Kolokolnikov¹,

Wei²

2018

SIAM Rev.

Self Cite

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We consider a standard reaction-diffusion system (the Schnakenberg model) that generates localized spike patterns. Our goal is to characterize the distribution of spikes in space and their heights for any spatiallydependent feed rate A(x). In the limit of many spikes, this leads to a fully coupled nonlocal problem for spike locations and their heights. A key feature of the resulting problem is that it is necessary to estimate the difference between its continuum limit and the discrete algebraic system to derive the effective spike density. For a sufficiently large feed rate, we find that the effective spike density scales like A 2/3 (x) whereas the spike weights scale like A 1/3 (x). We derive asymptotic bounds for existence of N spikes. As the feed rate is increased, new spikes are created through self-replication whereas the spikes are destroyed as the feed rate is decreased. The thresholds for both spike creation and spike death are computed asymptotically. We also demonstrate the existnence of complex dynamics when the feed rate is sufficiently variable in space. For a certain parameter range which we characterize asymptotically, new spikes are continously created in the regions of high feed rate, travel towards regions of lower feed rate and are destroyed there. Such "creation-destruction loop" is only possible in the presence of the heterogenuity.

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Patterned vegetation, tipping points, and the rate of climate change

Cited by 33 publications

References 59 publications

Model of pattern formation in marsh ecosystems with nonlocal interactions

Model of pattern formation in marsh ecosystems with nonlocal interactions

Ecosystems off track: rate‐induced critical transitions in ecological models

Pattern Formation in a Reaction-Diffusion System with Space-Dependent Feed Rate

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