Global Stability in Many-Species Systems

Goh, B. S.

doi:10.1086/283144

Cited by 290 publications

(161 citation statements)

References 6 publications

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“…To address the above question, here we recast the mathematical definition of structural 14 stability to that in which a system is more structurally stable, the larger the area of 15 parameter values leading to both a dynamically stable and feasible equilibrium (27)(28)(29). 16 This means that a highly structurally stable ecological system is more likely to be stable 17 and feasible by handling a wider range of conditions before the first species becomes 18 extinct.…”

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confidence: 99%

“…While it has been repeat-11 edly shown that this nested architecture may arise from a combination of life-history and 12 complementarity constraints among species (32)(33)(34)(35), the effect of this nested architecture 13 on community persistence continues to be a matter of strong debate. On the one hand, 14 it has been shown that a nested architecture can facilitate the maintenance of species 15 coexistence (6), exhibit a flexible response to environmental disturbances (7,8,36), and 16 maximize total abundance (12). On the other hand, it has also been suggested that this 17 nested architecture can minimize local stability (9), have a negative effect on community 18 persistence (10), and have a low resilience to perturbations (12).…”

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confidence: 99%

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On the structural stability of mutualistic systems

Rohr

Saavedra

Bascompte

2014

Science

490

759

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A structural approach to species interactions What determines the stability of ecological networks? Rohr et al. devised a conceptual approach to study interactions between species that emphasizes the role of network structure (see the Perspective by Pawar). Using the example of mutualistic networks of communities of plants and their pollinator species, they show how the structure of networks can determine the persistence of the interactions. Network structures and architectures observed in nature intrinsically match the most stable solution. This approach has promise for application to questions of ecological community stability under global change. Science , this issue 10.1126/science.1253497 ; see also p. 383

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mentioning

confidence: 99%

mentioning

confidence: 99%

On the structural stability of mutualistic systems

Rohr

Saavedra

Bascompte

2014

Science

490

759

View full text Add to dashboard Cite

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“…this conclusion is mathematically well known and is reported in many important references [Case and Gilpin (1974), Goh (1977), Case and Casten (1979), Abrams (1984bAbrams ( , 1986Abrams ( , 1987Abrams ( , 1998Abrams ( , 2001; all these references argued that intraspecific interference is common]. Although it is argued that spatial heterogeneity and dispersion can mediate the coexistence of an unlimited number of consumers on as few as a single resource (Tilman, 1994), intraspecific interference competition provides a powerful mechanism for species coexistence in more spatially homogeneous situations.…”

Section: Introductionmentioning

confidence: 78%

Biodiversity, Habitat Area, Resource Growth Rate and Interference Competition

Kuang

Fagan

Loladze

2003

Bulletin of Mathematical Biology

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For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers.

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“…Lyapunov functions of the form (2.3) have a long and venerable history. Volterra [57] first postulated the form of this function; however, Goh [17] used functions of this form to prove global asymptotic stability of the nontrivial equilibrium for a food chain with n species with a carrying capacity added to the prey equations. Under appropriate assumptions Harrison [19] showed that the entire positive orthant is in the domain of attraction of this nontrivial Downloaded 05/10/18 to 54.201.150.21.…”

Section: Globalmentioning

confidence: 99%

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

Previte¹,

Hoffman²

2013

SIAM Rev.

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Abstract. The dynamics of the classic planar two-species Lotka-Volterra predator-prey model are well understood. We introduce a scavenger species that scavenges the predator and is also a predator of the common prey. For this model, we analytically prove that all trajectories are bounded in forward time, and numerically demonstrate persistent bounded paired cascades of period-doubling orbits over a wide range of parameter values. Standard analytical and numerical techniques are used in the analysis of this model, making it an ideal pedagogical tool. We include exercises and an open-ended project to promote mastery of these techniques.

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Global Stability in Many-Species Systems

Cited by 290 publications

References 6 publications

On the structural stability of mutualistic systems

On the structural stability of mutualistic systems

Biodiversity, Habitat Area, Resource Growth Rate and Interference Competition

Period Doubling Cascades in a Predator-Prey Model with a Scavenger

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