Lecture 16 - March 02, 2009

1. Spatial models

models that we've seen before that have a spatial nature

• reserves as a strategy for population and harvest management
• island biogeography model for species
• watershed - runoff

topics in the text (Miller) that are spatial in nature

• habitat fragmentation (it's the specific features of the landscape, not the average)
• succession with zones of certain levels in the succession
• forest management strategies - rotational cutting
• urbanization and sprawl
• others?

 

2. Cells connected to each other

stella diagram for simple diffusion

• x --> z flux with a flux constant = 0.05 * (concentration difference)
• create this

more boxes - stella/2D-diffusion.stm

• 4 neighbors (NESW) or 8
• start by showing how it reaches equilibrium (100 + 50)/9 into each
• run with a constant input into one box, diffusion gradient away from that box

inhomogeneities in the diffusion path or flux between boxes can create differences

 

3. 2D- predator prey

one predator prey pair

then allow mixing/diffusion of the predator and prey into a nearby population

stella/2d-pred-prey

a bloom of algae followed by a bloom in a nearby basin

• basin 1 is the seed for the second bloom
• as the mixing increases -- the lines converge

4. Light and depth

stella/algae-with-depth

transmission of light per meter

1 box per meter

growth rates for each meter

using a MM type equation - could use tanh or other

5. water gradient on land

plants "up land" decrease water for plants

plants down stream actually form clumps that promote growth upstream of themselves

forms clumps (clump -- dry area -- clump) that move over time

descriptions

• Island Labrynth Pools - ilp.html
• Thiery 1995
• Rietkerk et al 2004

STELLA descriptive model (courses/stella/plants-clumps-ilp)

EXCEL CA format (algae/.../excel-simple-CA.xls)