Stability and complexity of model ecosystems: Are large ecosystems more stable than small ones?

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 Downloadhandout (PDF, 212 KB) and DownloadR code (R, 8 KB) for the 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?

Advanced questions:

How does the ecosystem respond to the removal of a species? What is the average effect and what is the range of effects?
How does stability change if some interactions are predatory?
How does an ecosystem respond to the invasion of a new species?
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

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

Ives, R. A. & Carpenter, S. R. (2007). external pageStability and Diversity of Ecosystems. Science 317: 58-62. (a thorough review of the field).

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

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

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

Frank, K.T., et al. (2011). external pageTransient dynamics of an altered large marine ecosystem. Nature 477: 86-89.

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

Allesina, S. & Tang, S. (2012). external pageStability criteria for complex ecosystems. Nature 483: 205-208.

Cardinale, B. J., et al. (2012). external pageBiodiversity loss and its impact on humanity. Nature 486: 59–67.