Evol Ecol Res 11: 667-675 (2009)     Full PDF if your library subscribes.

Stability and diversity in mathematical models of ecosystems

B.S. Goh

Department of Mathematics, Nanjing University, Nanjing, Jiangsu, China

Correspondence: B.S. Goh, Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, China.
e-mail: bsgoh82@gmail.com

ABSTRACT

Questions: Does diversity beget stability in ecosystems? What are the limits of mathematical modelling to understand this question? What is the dynamical behaviour of a model ecosystem that describes the effect of ‘not putting all one’s eggs into one basket’?

Methods: Mathematical models have been used to determine whether diversity begets stability in ecosystems. Experience of the use of mathematics in the management of fisheries helps us to understand the limits in using mathematics to describe biological populations and to answer this ecological question. I use some properties of dynamical systems in control theory to study the effects of ‘not putting all one’s eggs into one basket’ in a model ecosystem.

Conclusions: To better understand the issue of biodiversity and stability more research is required. First, there are many concepts of stability in model ecosystems and they do not define fully the stability of real ecosystems. Second, for a species with very high fecundity, for example the Asian silver carp, the Beverton-Holt approach does not even try to use mathematics to model the first stage of the dynamics of a year-class in the fish population. Thus, conclusions from an analysis of a model ecosystem may have limited applications to real ecosystems. I studied a linear model of a large ecosystem with many null interactions and showed that just a single disturbance can adversely affect each and every species or component of the model ecosystem. Thus to be invulnerable to continuous disturbances, an ecosystem requires subtle patterns of interactions among the species and between the species and the environment.

Keywords: biodiversity, decoupling, ecosystem stability, resilience, non-vulnerability.