5: Steady States Models

MCED Chapter 5


Steady State Models of Ecological Systems: EcoPath Approach to Mass-Balanced System Descriptions


Matthias Wolff and Marc Taylor


We describe the fundamentals and applications of trophic models of ecological systems and show how a simple mass balance approach of the early 1980s was further developed into a very advanced complex software package, freely available on the internet (Ecopath with Ecosim, EwE, http://www.ecopath. org). Through its three decades of evolution, the approach became increasingly popular, with over three hundred Ecopath models being published to date. During its first 10–15 years, the approach was mainly used as a tool to integrate ecological and fisheries data to understand and visualize the trophic flow structure of ecosystems, thereby allowing for the meaningful comparisons between systems. Later (since the mid-1990s) it was increasingly used to explore ecosystem changes under the impact of management or climate impact scenarios. This evolution from a more descriptive mass-balance to a simulation modelling tool was enabled through fundamental changes in the mathematical architecture: the original version of Ecopath was based on linear algebra for input–output analysis to investigate the properties of steady state networks, while in the recent version, coupled differential equations are used for each of the defined system compartments. The new model architecture thus allows the magnitude of flows in and out of compartments to change over time, which makes simulations of changes possible. Foraging arena theory was also taken into account and prey biomass was allowed to vary in its availability (vulnerability) to predators. If the predators consumption is mainly determined by prey availability (bottom-up control, low vulnerability), predator biomass would greatly respond to changes in prey biomass, while under a situation of strong predator (top-down) control, changes in predator biomass would greatly impact its prey (high vulnerability). Since EwE also allows for specifying different resource use types (e.g. types of fisheries or other resource uses) and economic variables associated to them (operational costs, number of people employed etc.), different management regimes can also be explored in terms of their socio-economic outcome. If spatially explicit data on biomass distribution of model groups and dispersal rate values are available, the Ecospace module of the EwE package may be used to derive at a spatially explicit, dynamic trophic model able to simulate how the management of one part of the system area may affect other parts. The incorporation of these spatial dynamics is of particular interest in the exploration of management questions, such as in the size and placement of Marine Protected Areas (MPAs) (this application is not further described in this chapter).

Additional material

  • Exhaustive material on EwE, including a description of terms used (search index) and links to applications (models) and publications can be found in the internet under: www.ecopath.org
  • Input data matrix für ECOPATH-model (Inputparameter_Ecopath)

Summarising questions

  • What is the basic concept of the Ecopath mass balance approach and what are the elements of the first Ecopath master equation?

  • How are the groups (compartments) of a trophic model defined and what are the main input parameters required for each?

  • What are the fundamental differences in the mathematical architecture of Ecopath and Ecosim?

  • What are the main research applications for the EwE software?

Further Reading

    For beginners

  • Christensen, V. and Pauly, D. 1995. Fish Production, Catches and the Carrying capacity of the World Oceans. ICLARM Quarterly 18 (3):34-40

  • Polovina, J. 1984. Model of a Coral Reef Ecosystem I. The ECOPATH Model and Its Application to French Frigate Shoals Coral Reefs 3:1-11

  • Wolff, M. 2002. Concepts and approaches for marine ecosystem research with reference to the tropics. Rev. Biol.Trop. 50 (2): 395-414.

    For more advanced scientists

  • Christensen, V. and C.J. Walters. 2004. Ecopath with Ecosim: methods, capabilities and limitations. Ecological modeling 172: 109-139

  • Pauly, D., Christensen, V., and Walters, C. 2000. Ecopath, Ecosim, and Ecospace as tools for evaluating ecosystem impact of fisheries. – ICES Journal of Marine Science, 57: 697–706

  • Ulanowicz, R. E. 1986. Growth and Development: Ecosystems Phenomenology. Springer, New York, 203 pp.