The stability of a feasible random ecosystem

Roberts, A.

doi:10.1038/251607a0

Cited by 165 publications

(153 citation statements)

References 3 publications

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“…However, the matrix that must be studied to determine the internal stability of a fixed point is the community matrixΛ, which has a complicated relationship to the interaction matrix M and should not be expected to have a simple element distribution. In fact, for some bilinear population dynamics models there is numerical evidence that most feasible fixed points are also internally stable [32,35]. However, the relations between connectivity and stability have not yet been fully clarified and are still being discussed [36,37].…”

Section: A N -Species Fixed Pointsmentioning

confidence: 99%

Punctuated equilibria and1/fnoise in a biological coevolution model with individual-based dynamics

2003

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We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies interactions, while genetic variation is provided through a low mutation rate. Both selection and mutation act on individual organisms. Consistent with some current theories of macroevolutionary dynamics, the model displays intermittent, statistically selfsimilar behavior with punctuated equilibria. The probability density for the lifetimes of ecological communities is well approximated by a power law with exponent near −2, and the corresponding power spectral densities show 1/f noise (flicker noise) over several decades. The long-lived communities (quasi-steady states) consist of a relatively small number of mutualistically interacting species, and they are surrounded by a "protection zone" of closely related genotypes that have a very low probability of invading the resident community. The extent of the protection zone affects the stability of the community in a way analogous to the height of the free-energy barrier surrounding a metastable state in a physical system. Measures of biological diversity are on average stationary with no discernible trends, even over our very long simulation runs of approximately 3.4 × 10 7 generations.

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Section: A N -Species Fixed Pointsmentioning

confidence: 99%

Punctuated equilibria and1/fnoise in a biological coevolution model with individual-based dynamics

2003

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“…We discuss the applicability of our 4 framework to other types of interspecific interactions in complex ecological systems. 5 Structural stability of mutualistic systems 6 Mutualistic networks are formed by the mutually-beneficial interactions between flower-7 ing plants and their pollinators or seed dispersers (31). Importantly, these mutualistic 8 networks have been shown to share a nested architectural pattern (32).…”

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confidence: 99%

On the structural stability of mutualistic systems

Rohr

Saavedra

Bascompte

2014

Science

482

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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“…S i = 100 and D = 1 [equation (2)] plus R = 1 and B = 0.01 [equation (3)]). This allows us to analyse the stability of "attainable" [and hence stable and feasible (Roberts, 1974)] equilibrium points. In fact, it is not the percentage of stable equilibrium points in which we should be interested, but the likelihood that at least one (n-D) equilibrium is stable.…”

Section: (S/d = R/b)mentioning

confidence: 99%

Stability of symmetric idiotypic networks—A critique of Hoffmann's analysis

Boer¹,

Hogeweg²

1989

Bulletin of Mathematical Biology

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Hoffmann (1982) analysed a very simple model of suppressive idiotypic immune networks and showed that idiotypic interactions are stabilizing. He concluded that immune networks provide a counterexample to the general analysis of large dynamic systems (Gardner and Ashby, 1970;May, 1972). The latter is often verbalized as: an increase in size and/or connectivity decreases the system stability. We here analyse this apparent contradiction by extending the Hoffmann model (with a decay term), and comparing it to an ecological model that was used as a paradigm in the general analysis. Our analysis confirms that the neighbourhood stability of such idiotypic networks increases with connectivity and/or size. However, the contradiction is one of interpretation, and is not due to exceptional properties of immune networks. The contradiction is caused by the awkward normalization used in the general analysis.

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The stability of a feasible random ecosystem

Cited by 165 publications

References 3 publications

Punctuated equilibria and1/fnoise in a biological coevolution model with individual-based dynamics

Punctuated equilibria and1/fnoise in a biological coevolution model with individual-based dynamics

On the structural stability of mutualistic systems

Stability of symmetric idiotypic networks—A critique of Hoffmann's analysis

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