ESR221 - Lecture 11

Lecture 11 - February 11, 2009

Today

build a metaphorical natural recycling system
examine the parts - review of components we've seen put together in a novel way
discuss the analogous human-build eco-commerce designs

1. Models we've seen

Resource limitation - MM flow control of the resource to new growth

Logistic

predator prey - multiplicative interaction term for efficiency of harvest of prey by predator

linear flow control - more in reservoir leads to faster loss rate

constant flow control - constant amount leaves reservoir each time unit (down to zero)

2. Describe and build a model on the board

four compartments

nutrient in soil

plant uptake (MM equation)

rabbit (eats plant with Pred/prey dynamics)

decomposers (get material from plants or rabbits)

decomposers seep nutrient to soil

draw on board

each component reaction

link together

short-term "logic"

what factors increase or decrease a compartment in the next interval (may be longer than a single computational time step)

example: high grasss and high rabbits --> high decomposers in the next interval

do these make sense?

3. This may be an overly simple description

assumptions

nutrient is conserved

only one limiting nutrient through all three biological compartments

but if you can't describe the behavior of this, how can you describe the behavior of busier models

4. Implementation in STELLA

could do this in Excel - need to state that nutrient can't < 0

stella/four-box

run under detritus to nutrients from 0.1 to 10

what are the patterns?

detritus domination

predatory/prey cycles

damped cycles

detritus(t) = detritus(t - dt) + (r_to_d + p_to_d - d_to_n) * dt
INIT detritus = 10

INFLOWS:
r_to_d = rabbits*rabbit_death_rate
p_to_d = plants*plant_death_rate
OUTFLOWS:
d_to_n = soil_rate
nutrients(t) = nutrients(t - dt) + (d_to_n - n_to_p) * dt
INIT nutrients = 10

INFLOWS:
d_to_n = soil_rate
OUTFLOWS:
n_to_p = max_plant_growth_rate*plants*nutrients/(nutrients+20)
plants(t) = plants(t - dt) + (n_to_p - p_to_r - p_to_d) * dt
INIT plants = 100

INFLOWS:
n_to_p = max_plant_growth_rate*plants*nutrients/(nutrients+20)
OUTFLOWS:
p_to_r = predation_efficiency*plants*rabbits
p_to_d = plants*plant_death_rate
rabbits(t) = rabbits(t - dt) + (p_to_r - r_to_d) * dt
INIT rabbits = 10

INFLOWS:
p_to_r = predation_efficiency*plants*rabbits
OUTFLOWS:
r_to_d = rabbits*rabbit_death_rate
max_plant_growth_rate = .1
plant_death_rate = .05
predation_efficiency = .001
rabbit_death_rate = .02
soil_rate = .5

5. Discuss the implications of these behaviors for human construction of eco-industrial systems

cyclic

limited rate of resource return