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wolf ~ boom and bust

K Phu
This model is to be used with Mr. Roderick's AP biology activity on population growth. See for a copy of the activity worksheet.
Use the sliders below to quickly change the initial values of components of the model.

Ecology Computer Modeling

  • 4 years 2 months ago

Isle Royale: Predator/Prey Model for Moose and Wolves, with Total Population

Andrew E Long
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at
Thanks Scott Fortmann-Roe.

I've added in an adjustment to handle population.

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

woStart} =

Environment Ecology Populations Math Modeling

  • 1 year 4 months ago

A More Realistic Model of Isle Royale: Predator Prey Interactions

Andrew E Long
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.

A decent match to the data is made with
Wolf Death Rate = 0.15
Wolf Birth Rate Factor = 0.0203
Moose Death Rate Factor = 1.08
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 MBR*M*(1-M/K)
Moose death flow is MDRF*Sqrt(M*W)
Wolf birth flow is WBRF*Sqrt(M*W)
Wolf death flow is WDR*W

Environment Ecology Populations Midterm

  • 1 year 4 months ago

Selection under logistic population dynamics

Barry McMullin
Logistic population dynamics with selection: Two species, able to exploit one resource, which is available at  a fixed, finite, flow (not a depleting stock). At low populations, growth is exponential. As long as total population below total carrying capacity, growth in total population continues, stabilizing at carrying capacity. Similar stabilization "from above" (if, e.g., carrying capacity dynamically falls to some lower level). "Smooth" stabilization (formally logistic) in either case. But selection between species if respective carrying capacities are different (regardless of intrinsic growth rates?); or, if equal carrying capacities, then selection based on intrinsic growth rates (but much slower?).


  • 11 months 2 weeks ago

Clone of Levels of transition needed to sustainability

Challenges in sustainability are multilevel.
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.

Environment Power Capitalism Exploitation Affluenza Sustainability Crisis Ecology Transition The Great Turning

  • 5 years 4 months ago

Dystopia: simple energy system model

Barry McMullin
Basic idea is to model demand with endogenous growth (but "satiation" becomes possible - eventually - at some notional "sufficiency" level); and supply then attempts to track demand with some time lag (~5-50 years - characteristic of commissioning/decommissioning large scale energy infrastructure). But supply also produces pollution, which accoumulates. We can specify a notional constraint/limit; approaching this should trumpdemand and forces supply to zero. In this version we'll only have one source. so no substitution is possible. We expect to see a fairly sudden supply crash. Of course, "demand" will still carry merrily on its way up anyway, but the interpretation of the consequently growing supply shortfall will be left to the eye of the beholder. NB: this version doesn't automatically succeed in limiting P to P_max. It forces dS/dt to zero as A*(P/ P_max) reaches 1; and then as that value exceeds 1, dS/dt is forced negative. But this dynamics has no way to "undo" any overshoot of P over P_max (which would require S itself to become negative: "negative emissions"). Need to manual find/choose a big enough value of A to limit P effectively.

Energy Environment Ecology

  • 11 months 2 weeks ago