Three Models of Algal Processes

date = May 10, 2004

Project Overview

This set of papers describes an approach for studying natural complex processes that involve algae. The processes at each scale are described from three very different viewpoints. These multiple views are brought together for a better understanding of the whole picture. The three views are:

1 - Rich description: Construct a complete description of the processes, actors and linkages. Besides a complete objective description of the system, this should include value-laden terms and statements about how we know what we know about the system.

In the 3 models approach a rich description will look like a text narrative of the composition, borders and behaviors of the system. The value laden statements may include the desirability of particular outcomes or the these statements may comment on the quality of the data.

2 - Structure: One image of the structure of the interactions of the system can be built from a network of nodes and linkages. The response of each node to all possible states of linked-nodes can be characterized. This description focuses on the network logic structure. An important consideration for analysis of the model structure is that the states of the nodes can change rapidly or slowly. This will be illustrated in the model output.

In the 3 models approach a structural model will be expressed as an NK-Boolean model. This model will identify basins of attraction that result just from the logic structure.

3. - Dynamic behavior: A dynamic model can be constructed that simulates the behavior of the real system. This model is built from flow rates, storages and information connections that control flow.

In the 3 models approach, a constrained systems model will be constructed using STELLA simulation software.

These three views are not supposed to converge into one view. Each view has some information that overlaps with the other two, but also some aspects that are unique. For example, the value-laden statements contained in the rich description can be very useful when this approach is applied to management decisions in natural water. Most people prefer a eutrophic and diverse algal community to a hyper-eutrophic community dominated by "scum". Human activities that lead to hyper-eutrophication can not be evaluated in the context of a ecosystem network or a dynamic systems model, but the preferred outcomes are clearly indicated in the rich description.

A simple example: Regime change in shallow urban lakes.

The first example will demonstrate the process of assessing the system using the three views. This example includes descriptions of how each model is constructed and identify the salient features of each view. Subsequent models will not contain this detail, but rather skip right to presenting the three views and analysis.

Other examples:

	time scale
Down regulation of photosynthesis rate	seconds to minutes
Inhibition of AFA by humics	days to weeks
Mixotrophy in Waldo Lake	days to a season
Regime of clarity of Waldo Lake	seasons to decades

 

Connections between scales

Each of these natural complex systems is regulated at multiple time scales simultaneously. According to Ashby's Law, there is a required level of complexity in the regulation of complex systems. I will describe how the interaction between fast and slow processes serves both to help develop the required level of complexity in the embedded regulation and how the fast and slow processes are linked to other scales of response and structure in the system. The interaction between the fast/slow components is necessary for the system to self-organize structures that dissipate the energy flow.

Application of the 3 models approach

This framework, with multiple views, can be applied to lake management issues such as preserving or restoring healthy lake communities. This section describes several attempts at such application.

References