VIGRE Research Group
Structure and Dynamics of Ecological Networks

Group Picture
Organizer: Caner Kazanci and Malcolm Adams.
Schedule: Tuesday 3:30-4:30pm, Room 326 (Boyd).
Content: Syllabus is here.
This group continues in Spring 2010. Here is the website.

Overview

Ecosystems are often modeled using weighted digraphs, representing flow of energy or nutrients among compartments. Depending on the model, what a compartment represents may range from accumulated organic matter in a lake to hundreds of species living in a specific area. Flows among compartments may represent feeding, uptake, excretion, etc. Flow currency may be energy, biomass, or a specific element such as C, N or P.

There are various methods to study ecosystem models. A common way to simulate these systems is to form a set of differential equations where the solution represents the state of each identity changing in time. Another way to analyze these systems is by formulating system-wide organizational properties, which provide insights as to how the environmental inputs are shared among identities, how much energy or matter cycling occurs within the system, or how strong are any two identities in the system related to each other. Obviously, such analysis is essential in understanding how a specific ecological system functions, how it can be sustained, or manipulated.

We will study basic ecosystem models (their organization, effects of network structure on dynamics, residence time of nutrients within the system, relations among compartments) using recent mathematical ideas and developments. Some questions we will try to answer are "What are the utility relations between compartments in an ecosystem?", "What is the average time a C atom emmitted by a passing by car will stay on plants located by the road, and where will it eventually end up?", "How can we quantify the health of an ecosystem?"

Projects

Decomposition of general ecological networks - David, Louis, Qianqian and Zandra

Ecological networks are often represented as weighted digraphs, and can be fairly complicated. Decomposing a complicated ecosystem into sub networks for easier analysis is often tempting. However, essential ecosystem behavior may be lost by breaking connections. For simpler models, we can identify flow sub-networks (fluxes) without breaking connections. We will investigate the uniqueness and existence properties of this decomposition; and try to create an algorithm that can decompose any ecological network into its sub flow networks.

Decomposition of cycling index - Alex, Stacy and Whitney

In relation to the decomposition problem above, we investigate if the cycling property of the full network can be represented by the cycling properties of the decomposed flow sub networks.

Ecological network decomposition from an algebraic graph theory point of view. - Cindy, Matt and Michael

We study the same decomposition problem using algebraic graph theory of weighted digraphs.

Decomposition of Indirect Effects - Emmanuel and Grant

In relation to the decomposition problem above, we investigate if the indirect effects within the full network can be represented by the indirect effects within the decomposed flow sub networks.

Presentation schedule

  • 9/29 - Bernard C. Patten - Ecological Utility Analysis.
  • 10/6 - Cycling index group presentation - Ulanowicz (1983) paper on cycling index.
  • 10/13 - Caner Kazanci - Network Particle Tracking.
  • 10/20 - Group Presentations - Cycling bases.
  • 10/27 - Group Presentations - Functional decomposition.
  • 11/03 - Group Presentations - Functional decomposition using Network Particle Tracking.
  • 11/10 - Group Presentations - Cycling Index and Indirect effects.

Documents & Materials

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