Stability and complexity of model ecosystems

Level 2 module

Basic problem:
Are large ecosystems inherently more stable than small ones? Robert May addressed in 1970s the stability of ecosystems using mathematical models. In this module we want to address how complexity (i.e. number of interacting species and the connectivity between species) affects stability of model ecosystems.

General approach:
We will not follow Robert May’s original approach, but will instead simulate multi-species Lotka-Volterra systems to study how ecosystem stability is related to size.

What can be learned?
Concepts:
• Nonlinear biological networks
• Ecosystem stability and how it can be defined
• Biodiversity and stability
• Connectivity of a network and its effect on stability
• Keystone species
• Path dependency
Methods:
• Numerical simulation of (large) systems of ordinary differential equations

Starting point:
• Download accompanying reader and R code for n-species Lotka-Volterra Model.

Interesting questions that you can investigate:

• How does ecosystem stability depend on size (i.e. the number of species)?
• How does stability depend on the connectivity of the ecosystem?
• What are useful measures of ecosystem stability?
• Does the coexistence of a set of species depend on the order in which they were introduced into an ecosystem?
• More advanced questions:
o How does the ecosystem respond to the removal of a species? What is the average effect and what is the range of effects?
o How does stability change if some interactions are predatory?
o How does an ecosystem respond to the invasion of a new species?
o Are ”evolved” ecosystems more stable than random ones?

Glossary:
• Connectivity: The number of species with which a given species interacts.
• Path dependency: Refers to the question of whether the coexistence of a set of species depends on the order in which they were introduced into the ecosystem.
• Keystone species: A species whose removal has particularly strong effect on the ecosystem (just as taking away the keystone from an arch leads to the collapse of the arch).

Literature & Weblinks:

• R.M. May, Will a large complex system be stable?, Nature 238: 413-414, 1972
• R.M. May, Stability and complexity in model ecosystems, 1973, Princeton University Press
• S. Pimm, The complexity and stability of ecosystems, Nature, 1984, 307, 321-326
• D. Tilman, J.A. Downing, Biodiversity and stability in grasslands, Nature 367: 363-5, 1994
• R.D. Holt, Ecology: Asymmetry and stability, Nature 442: 252-3, 2006

Here is a paper showing that competition can indeed be a strong selection force:

• R. Calsbeek, R.M. Cox, Experimentally assessing the relative importance of predation and competition as agents of selection, Nature 465: 613-616, 2010

And another paper with a case study on how a real complex ecosystem reacts to severe perturbation:

• K.T. Frank et al., Transient dynamics of an altered large marine ecosystem, Nature 477: 86-89, 2011
  

And 30 years after the original paper by May, the saga still continues (with predatory interactions and else):

• Allesina, S. and Tang, S. (2012). Stability criteria for complex ecosystems. Nature 483: 205-208.
  

• Homepage Bob May
• Homepage Stuart Pimm
• Homepage Tony Ives
• Homepage David Tilman