Figure 2

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/CV_resist, and 1/CV_com, where CV_resist is the coefficient of variation in the change in abundance between samples, and CV_com 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. r_crit 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 (100K JPEG file)]

 

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