Structural Instability of Food Webs and Food-Web Models and Their Implications for Management

Rossberg, Axel G.; Caskenette, Amanda; Bersier, Louis–Félix

doi:10.1017/9781316871867.024

Cited by 7 publications

(10 citation statements)

References 22 publications

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“…Note that there exist other approaches to address stability of complex systems. In particular, recent studies show that in the context of ecology structural stability, linked to the existence (feasibility) of stationary points and referring to their sensitivity to changes in the ecological parameters, should be primarily looked at [29][30][31][32][33]. Although this paper mainly focuses on linear stability, we will show at the end of the paper that our result on system stability also applies to structural stability.…”

Section: Introductionmentioning

confidence: 90%

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

2022

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We analyze the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modeling the stability of fixed points in large systems defined on complex networks, such as ecosystems consisting of a large number of species that interact through a food web. We develop an exact theory for the spectral distribution and the leading eigenvalue of the corresponding sparse Jacobian matrices. This theory reveals that the nature of local interactions has a strong influence on a system's stability. We show that, in general, linear dynamical systems defined on random graphs with a prescribed degree distribution of unbounded support are unstable if they are large enough, implying a tradeoff between stability and diversity. Remarkably, in contrast to the generic case, antagonistic systems that contain only interactions of the predator-prey type can be stable in the infinite size limit. This feature for antagonistic systems is accompanied by a peculiar oscillatory behavior of the dynamical response of the system after a perturbation, when the mean degree of the graph is small enough. Moreover, for antagonistic systems we also find that there exist a dynamical phase transition and critical mean degree above which the response becomes nonoscillatory.

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Section: Introductionmentioning

confidence: 90%

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

2022

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“…which they are structurally unstable [48]. By combining resilience, structural stability and persistence, we show that there exists parameter ranges for which a system can be resilient but structurally unstable, an observation that introduces a previously overlooked phase in parameter space.…”

Section: Discussionmentioning

confidence: 89%

“…It has been argued that all real systems self-organize to structural instability [48]. The rationale behind this is that there can always be immigration, adaptation or speciation until the point where additional species will cause others to go extinct.…”

Section: Discussionmentioning

confidence: 99%

Predicting collapse of complex ecological systems: quantifying the stability–complexity continuum

Pettersson

Savage

Jacobi

2020

J. R. Soc. Interface.

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Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

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“…Ecological structural instability has been shown to play a critical role in the regulation of biodiversity, setting hard limits to the number of species that can coexist 24 , a mechanism found to operate at both local and metacommunity scales 23 . Empirical observation of many of the emergent phenomena associated with ecological structural instability provides strong indirect evidence for the prevalence of structural instability in nature 23,31 . Our understanding of the impact of structurally unstable diversity regulation on temporal community-level properties, however, remains incomplete 32 .…”

Section: Resultsmentioning

confidence: 99%

Intrinsic ecological dynamics drive biodiversity turnover in model metacommunities

O’Sullivan

Terry

Rossberg

2020

Preprint

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1 Turnover of species composition through time is frequently observed in nature. 2 Often explained by changes in abiotic conditions or regional species pools, 3 compositional turnover is employed as an indicator of external stress in nat-4 ural ecosystems. Theoretically, the possibility of turnover driven by intrinsic 5 ecological dynamics-species interactions, dispersal-is also known, but what 6 role such autonomous turnover plays in nature remains unclear. Expanding 7 the boundaries of metacommunity modelling, we show that in large meta-8 communities immigration pressure from neighbouring locales robustly drives 9 continuous turnover in local composition-without environmental change or 10 regional invasions. That ecological communities may turn over autonomously 11 challenges assumptions implicit in assessment and management tools, and sug-12 gests that natural compositional change should be incorporated in ecological 13 status assessments based on ancestral baselines. 14 Main Text: 15 Change in species composition through time, called community turnover, is observed in most 16 ecosystems (1-3). Potential drivers include changes in the abiotic environment (4-6), random 17 population fluctuations due to demographic stochasticity (7), and autonomous population dy-18 namics driven by species interactions and dispersal (8, 9). While there exist well-developed 19 bodies of theory describing community turnover due to environmental change (10, 11) and 20 demographic stochasticity (12), our understanding of autonomous compositional change is un-21 derdeveloped. In particular, it remains unclear to what extent observed spatio-temporal patterns 22 in biodiversity may be due to autonomous ecological dynamics. 23If it were known that intrinsic ecological dynamics alone cannot account for observed com-24 2 positional turnover, then abiotic environmental change would be the most plausible explanation 25 (turnover by demographic stochasticity alone is predicted to be orders of magnitude slower than 26 observed (1)). In the current phase of rapid anthropogenic environmental change, any altera-27 tion in the composition of an ecological community should then be interpreted as a potential 28 indicator of stress (13)(14)(15) and the degree of compositional change compared to past baselines 29 a valid measure of anthropogenic impact. 30If, on the other hand, temporal community turnover is a natural phenomenon that can arise 31 independently of changes in the abiotic environment, then observed shifts in the composition 32 of ecological communities would not necessarily imply the presence of external pressures. 33Intrinsic dynamics may even permit ecosystems to adapt and absorb environmental change 34 without impacting ecosystem functioning. Assessments, projections and mitigation strategies 35 would then need to account for such autonomous compositional turnover. 36 So, can communities of many interacting species turn over autonomously? If so, what is 37 the driving mechanism? And does the resulting turnover reproduce patt...

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Structural Instability of Food Webs and Food-Web Models and Their Implications for Management

Cited by 7 publications

References 22 publications

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

Predicting collapse of complex ecological systems: quantifying the stability–complexity continuum

Intrinsic ecological dynamics drive biodiversity turnover in model metacommunities

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