Reactivity and stability of large ecosystems

Tang, Si; Allesina, Stefano

doi:10.3389/fevo.2014.00021

Cited by 72 publications

(74 citation statements)

References 41 publications

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“…To that end, we also investigate the transient stability of the system. It can be shown (29,30) that the reactivity λ H can be computed as the maximum real part of the eigenvalues of the matrix H = ðJ + J T Þ=2. If MaxðReðλÞÞ < 0 and MaxðReðλ H ÞÞ > 0, then the equilibrium point is stable but the system is said to be reactive.…”

Section: Significancementioning

confidence: 99%

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Resilience and reactivity of global food security

Suweis¹,

Carr

Maritan³

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

202

149

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be more prone to instability than self-sufficient countries from group A (Fig. 3 C and D). This result suggests that food insecurity is increasing worldwide and trade-dependent countries are particularly vulnerable to food crises" should instead appear as "countries from groups A and B appear to be more prone to instability (Fig. 3 C and D). These results suggest that long-term food insecurity is increasing worldwide and also affecting selfsufficient (group A) countries. Trade-dependent countries are particularly vulnerable to food crises (Fig. 3D)." These errors do not affect the conclusions of the article.www.pnas.org/cgi

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Section: Significancementioning

confidence: 99%

“…If MaxðReðλÞÞ < 0 and MaxðReðλ H ÞÞ > 0, then the equilibrium point is stable but the system is said to be reactive. We note that, if λðtÞ → 0, then λ H ðt 0 Þ → 0 for t 0 < t and thus reactivity can also be used to develop an early warning signal for systems approaching instability (17,30).…”

Section: Significancementioning

confidence: 99%

Resilience and reactivity of global food security

Suweis¹,

Carr

Maritan³

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

202

149

View full text Add to dashboard Cite

show abstract

“…The motivation for ongoing studies on critical slowing down indicators, among many other warning signals, is to identify their potential as well as their limitations (26) and develop a toolbox of indicators. Investigations into other properties [e.g., resistance (49), reactivity (50,51), invasiveness, etc.] and their relations will help us address a fundamental question: how to measure the "stability" of a system (52,53).…”

Section: Discussionmentioning

confidence: 99%

Relation between stability and resilience determines the performance of early warning signals under different environmental drivers

Dai

Korolev

Gore

2015

Proc. Natl. Acad. Sci. U.S.A.

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Shifting patterns of temporal fluctuations have been found to signal critical transitions in a variety of systems, from ecological communities to human physiology. However, failure of these early warning signals in some systems calls for a better understanding of their limitations. In particular, little is known about the generality of early warning signals in different deteriorating environments. In this study, we characterized how multiple environmental drivers influence the dynamics of laboratory yeast populations, which was previously shown to display alternative stable states [Dai et al., Science, 2012]. We observed that both the coefficient of variation and autocorrelation increased before population collapse in two slowly deteriorating environments, one with a rising death rate and the other one with decreasing nutrient availability. We compared the performance of early warning signals across multiple environments as "indicators for loss of resilience." We find that the varying performance is determined by how a system responds to changes in a specific driver, which can be captured by a relation between stability (recovery rate) and resilience (size of the basin of attraction). Furthermore, we demonstrate that the positive correlation between stability and resilience, as the essential assumption of indicators based on critical slowing down, can break down in this system when multiple environmental drivers are changed simultaneously. Our results suggest that the stability-resilience relation needs to be better understood for the application of early warning signals in different scenarios.early warning signals | population collapse | environmental drivers | stability-resilience relation

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“…This matrix has many useful properties in addition to determining local stability. For instance, a stable equilibrium is reactive [3,4] if perturbations, before damping, are initially amplified in a transient manner. Reactivity is measured by the leading eigenvalue of the Hermitian part of the community matrix, with positive values signalling reactive systems.…”

Section: Introductionmentioning

confidence: 99%

Predicting global community properties from uncertain estimates of interaction strengths

Barabás

Allesina

2015

J. R. Soc. Interface.

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The community matrix measures the direct effect of species on each other in an ecological community. It can be used to determine whether a system is stable (returns to equilibrium after small perturbations of the population abundances), reactive (perturbations are initially amplified before damping out), and to determine the response of any individual species to perturbations of environmental parameters. However, several studies show that small errors in estimating the entries of the community matrix translate into large errors in predicting individual species responses. Here, we ask whether there are properties of complex communities one can still predict using only a crude, order-of-magnitude estimate of the community matrix entries. Using empirical data, randomly generated community matrices, and those generated by the Allometric Trophic Network model, we show that the stability and reactivity properties of systems can be predicted with good accuracy. We also provide theoretical insight into when and why our crude approximations are expected to yield an accurate description of communities. Our results indicate that even rough estimates of interaction strengths can be useful for assessing global properties of large systems.

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Reactivity and stability of large ecosystems

Cited by 72 publications

References 41 publications

Resilience and reactivity of global food security

Resilience and reactivity of global food security

Relation between stability and resilience determines the performance of early warning signals under different environmental drivers

Predicting global community properties from uncertain estimates of interaction strengths

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