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Science 6 July 2007:
Vol. 317. no. 5834, pp. 58 - 62
DOI: 10.1126/science.1133258
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Review
Stability and Diversity of Ecosystems
Anthony R. Ives1 and
Stephen R. Carpenter2
1 Department of Zoology, University of Wisconsin, Madison, WI 53706, USA. E-mail: arives{at}wisc.edu
2 Center for Limnology, University of Wisconsin, Madison, WI 53706, USA. E-mail: srcarpen{at}wisc.edu
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Fig. 1. Different types of stability, depending on the inherent dynamics of a system and the type of perturbation it experiences. (A) Alternative stable states, in which the initial densities of four species determine which species persist; pairs of alternatively persisting or nonpersisting species are shown with solid and dashed lines, respectively. (B) Nonpoint equilibria, illustrated by a stable and a chaotic attractor. (C) Pulse perturbations to systems with a stable equilibrium. The left panel shows the dynamics of a two-species system after a single pulse perturbation, with species densities shown by light and dashed lines, and combined densities shown by the heavy line. The right panel gives the same system with repeated (stochastic) pulse perturbations. (D) Press perturbations to systems with a stable equilibrium. The arrows trace the equilibrium densities of species i and j in a six-species ecosystem as the environment degrades (intrinsic rates of increase decline for all species). In the left panel, the equilibrium point collides with the unstable point at which species j goes extinct; in the right panel, the equilibrium point bifurcates into a stable nonpoint attractor. (E) Response of ecosystems to extinctions of the most common species (extinction marked by arrow). In the left panel, no other species went extinct; in the right panel, three additional species went extinct. (F) Response of ecosystems to invasion (invasion marked by arrow). In the left panel, the invading species persisted with the original six species; in the right panel, five of the original species went extinct. See fig. S2 for details.
[View Larger Version of this Image (84K GIF file)]
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Fig. 2. Stability of randomly constructed competitive communities versus diversity n, portrayed so that positive diversity-stability relationships have positive slopes. (A) For systems with alternative stable states, the average number of stable states and Holling's resilience, measured by the rate at which population densities are repelled from the unstable stationary point between stable states. (B) For systems with nonpoint attractors, the prevalence of cyclic (white region) versus chaotic (orange region) attractors, and the amplitude of fluctuations in combined species densities, measured by the minimum divided by the maximum density (dashed line). (C) For systems with stable equilibria, the characteristic return rate, 1/CVresist, and 1/CVcom, where CVresist is the coefficient of variation in the change in abundance between samples, and CVcom is the coefficient of variation of the community density through time. (D) The change in mean combined densities,   (with 95% inclusion bounds given by the orange region), when all species experience a press perturbation that decreases intrinsic rates of increase. rcrit measures the magnitude of the press perturbation before the stable equilibrium bifurcates, creating either a cyclic nonpoint attractor or an attractor with one species extinct. (E) For systems with a stable equilibrium, the numbers of secondary (2°) extinctions caused by removing the most common species, and compensation (calculated as the increase in combined abundances of surviving species immediately after extinction relative to the abundance of the species that went extinct). (F) For systems with a stable equilibrium, the number of attempts before an introduced species successfully invaded, and the numbers of secondary extinctions caused by the invader. (G) For randomly constructed communities, prevalence of stable points, alternative stable states, and nonstationary attractors. The dashed line gives the proportion of randomly constructed communities that were feasible (i.e., had an equilibrium point with positive densities of all species), which is a requirement for the three types of dynamics. For each level of diversity n, 10,000 random communities were constructed. See fig. S2 for details.
[View Larger Version of this Image (31K GIF file)]
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