1. 2.18.2009 A.R.F.M

2.  Chu et al Theories of Complexity (2003) chooses Lake Victoria as a case study. ◦ Heterogeneous agents ◦ Non-linear interactions between agents ◦ Net-like interconnectivity between agents ◦ The ability to form novel connections in the event of an agent or node’s extinction.

3.  The Lotka-Volterra expression of a single predator-prey dyad:  dx = r x x (K x – x – α xy y)  dtK x  dy = r y y (K y – y – α yx x)  dtK y  Where r x and r y are the inherent growth rates of the respective species, K x and K y are the environmental carrying capacity for each species, and α xy represents the predation effect that species X has on species Y.

6.  Two levels of complexity leads to systemic failure ◦ Baboons + Cheetahs alone causes species extinction (paradox of enrichment)  In the wolf / sheep scenario the system is stabilized by adding grass. An example of and addition of complexity into a system actually leading to increased stabilization.  For Lake Victoria, a representation of Salthe’s Basic Triadic Structure can be seen as the organisms in the lake, the lake as an ecosystem, and the external human factor.

7.  Give each agent set specific rules. Iterating these rules offers an alternative, non- equation based model of the situation.  For example: ◦ 1. Move cheetah agent randomly to an adjacent patch and decrease energy by [E1]. ◦ 2. If on the same patch as a baboon agent, then eat baboon (destroy that agent) and increase energy by [E2]. ◦ 3. If [Energy] < 0 then kill agent.

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