Diversity-Stability

 Natural ecosystems are diverse and mostly stable to perturbations:

Coral reef: O(10^4) coexisting species [Knowlton et al., 2010)]                                        Plankton: O(10^3) species  [Hutchinson, 1961)]

 Generalized Lotka-Volterra (GLV) equations,

describing competitive/cooperative growth of many species populations

Simulations indicate that starting from diverse initial conditions, only a small fraction of species survive and coexist:

Robert May, [Nature 238, 413 (1972)] argued for the diversity/stability tension based on eigenvalues of random matrices

G. Bunin, PRE 95, 042414 (2017):  

 Natural communities are likely not weakly interacting, and appear to lose diversity in artificial settings:

Next (Coexistence) Outline Growth & saturation Mean field analysis Extinction on a seascape Growth on a seascape Diversity vs Stability Coexistence on a seascape Phase behavior Summary