Moose and Wolves
Prioiria copaifera (cativo) growth
Clone of Levels of transition needed to sustainability
This diagram attempts to summarize levels of self reinforcing destructive dynamics, authors that deal with them, and point of leverage for change.
The base of the crisis is a mechanistic rather than ecological worldview. This mechanistic worldview is based on outdated science that assumed the universe to be a large machine. In a machine there is an inside and an outside. The health of the inside is important for the machine, the outside not. In an ecological view everything is interconnected, there is no clear separation in the future of self and other. All parts influence the health of other parts. To retain health sensitivity and democracy are inherent. The sense of separation from other that keeps the mechanistic worldview dominant is duality. Being cut off from spiritual traditions due to a mechanistic view of science people need access to inter-spirituality to reconnect with the human traditions and tools around connectedness, inner discovery, and compassion. Many books on modern physics and biology deal with the system view implications. "The coming interspiritual age" deals with the need to connect spiritual traditions and science.
At the bottom for the dynamic is an individual a sense of disconnectedness leads to a dependency on spending and having rather than connecting. The connecting has become too painful and dealing with it unpopular in our culture. Joanna Macy deals with this in Active Hope.
This affluenza and disconnection is worsened by a market that floods one with advertisements aimed at creating needs and a sense of dissatisfaction with that one has.
National economies are structured around maximising GDP which means maximising consumption and financial capital movement. This is at the cost of local economies. These same local economies are needed for balanced happiness as well as for sustainability.
Generally institutions focus on maximising consumption rather than sustaining life support systems. David Korten covers this well.
Power and wealth is confused in this worldview. In striving for wealth only power is striven for in the form of money and monopoly.
Those at the head of large banks and corporations tend to be there because they exemplify this approach. They have few scruples about enforcing this approach onto everyone through wars and disaster capitalism. Naomi Klein and David Estulin documented this.
Power has become so centralized that we need this understanding to be widespread and include many of those in power. Progress of all of these levels are needed to show them and all that another way is possible.
Fish Populations and MPAs
Population dynamics with overshoot ("Seneca cliff"?)
Clone of Isle Royale: Predator Prey Interactions
Testing of Caribou Conservation Sub-Models v2
This model was developed by Rob Rempel and Jen Shuter at the Centre for Northern Forest Ecosystem Research, and was based in part on input from attendees of a modelling workshop ("Modelling the Caribou Questions") held at the 16th North American Caribou Workshop in Thunder Bay, Ontario, May 2016.
wolf ~ exponential growth
Clone of Spring and fall bloom
Simple model of the spring bloom in coastal temperate coastal waters. Nitrogen is assumed to be the limiting nutrient, so the model is based on N only. The model represents one liter of water. Dissolved inorganic nitrogen (DIN) accumulates in the water column during winter and has reached 250 µmol/L on March 1st where the model starts. At this time the light intensity have just reached the level necessary to initiate the bloom.
N uptake: Michaelis Menten kinetics with a maximum growth rate that doubles the population each day. Km=5µM.
Grazing: Michaelis Menten kinetics with a maximum daily uptake equal to the N in the population. Km=50µM.
Sloppy eating: 60% of the grazing is wasted to PON
Death: 5% of the zooplankton dies each day
Mineralization: 1% of the PON is mineralized to DIN each day
For the first 6 days the phytoplankton grows exponentially and depletes the DIN pool. The peak in phytoplankton is followed by a delayed peak in zooplankton due to its slower growth rate. Slowly the zooplankton graze down the spring bloom and the nitrogen is transformed to the pool of particulate dead organic nitrogen (PON). While this happens the phytoplankton is kept low by the still high zooplankton which allow the DIN pool to increase from day 25 to day 55. Eventually the phytoplankton escapes the top down control and we see a secondary bloom based on regenerated DIN.
Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.
We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.
I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20
I used RK-4 with step-size 0.1, from 1959 for 60 years.
The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W
equations I used in kill rate :
power model - 12*0.1251361120909615*([Moose]/[Wolves])^.44491970277839954*[Wolves]
Kill rate sqrt = 12*(0.0933207+.0873463*([Moose]/[Wolves])^.5)*[Wolves]
Holling Type III - ((0.986198*([Moose]/[Wolves])^2)/ (601.468 +([Moose]/[Wolves])^2))*[Wolves]*12
linear - 12*[Wolves]*(.400271+.00560299([Moose]/[Wolves]))
Day 22: Isle Royale: Predator/Prey Model for Moose and Wolves
Thanks Scott Fortmann-Roe.
I've created a Mathematica file that replicates the model, at
It allows one to experiment with adjusting the initial number of moose and wolves on the island.
I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at