World4 is a predictive model for world population. Population has grown hyper-exponentially in the last millenium, with the doubling time decreasing from 900 years  in 1000 CE to a minimum of ~35 years in 1963 CE. Technology is defined as that which decreases the death rate and/or increases the effective birth rate (i.e. by decreasing infant mortality). Technology grows exponentially, therefore population fits a hyper-exponential (exponent within an exponent). Models for the end of growth are explored using equations that express the ways humans are depleting Earth's biocapacity, the nature of resource depletion, and the relationship between natural resources and human carrying capacity. This simple model, containing just two closed systems, captures the subtle shifts in the population trajectory of the last 50 years. Specifically, hyperexponential growth has given way to subexponential growth. A peak is predicted for the time around 2028.  [Bystroff, C. (2021). Footprints to singularity: A global population model explains late 20th century slow-down and predicts peak within ten years. PloS one, 16(5), e0247214.]

Fertilizer inflow can cause lake eutrophication. In this simulation, we are studying what happens in a simple lake ecosystem.

Compost modelling

Simple model of the global economy, the global carbon cycle, and planetary energy balance.

This model describes the flow of energy from generation to consumption for neighborhoods in the metro Atlanta area. It also calculates the cost of energy production and the number of years it will take to recover that cost.

This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.

This diagram provides an accessible description of the key processes that influence the water quality within a lake.

From Jay Forrester 1971 Book World Dynamics, the earlier, simpler version of the World 3 Limits to Growth Model. adapted from Mark Heffernan's ithink version at Systemswiki.

An element of Perspectives: The Foundation of Understanding and Insights for Effective Action. Register at http://www.systemswiki.org/

This model shows the growth of two organisms competing for a limiting resource (space) .

Example of ​rIsk assessment on component of the building

Concepts are designed for Universatility and local variables without forcing a one size fits all model. 

Measurements in the course are designed to maintain a system perspective in all planning and measurement systems. 

This a simple and "totally accurate" model of the exponential human population.

Economic growth cannot go on forever, although politicians and most economist seem to think so. The activity involved in economic growth necessarily  generates entropy (disorder and environmental degradation). Entorpy in turn generates powerful negative feedback loops which will, as a response from nature, ensure that economic activity will eventually grind to a complete halt.  In these circumstances organised society cannot persist and will collapse. The negative feedback loops shown in this graph have already started to operate. The longer economic growth continues unabated, the more powerful these negative feedback loops will become. How long can economic growth continue before it is overwhelmed? It may not be very far in the future.

Primitives for Watershed modeling project. Click Clone Insight at the top right to make a copy that you can edit.

The converter in this file contains precipitation for Phoenix only.

this is the Australian food web of the water buffalo

A food web for Africa. :)

Thinking about biodiversity policy in the United States, specifically relating to the Endangered Species Act of 1973. I have focused on the impacts that governmental policy will have on the environment, rather than contributions from both the government and the private sector. I have also chosen to focus on the financial aspect of policy, keeping all other factors equal.

The simulation integrates or sums (INTEG) the Nj population, with a change of Delta N in each generation, starting with an initial value of 5.Nj+1 = Nj  + mu (1- Nj / Nmax ) Nj

Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died.

mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it.

F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model.

Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”.

Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

Clone of Pesticide Use in Central America for Lab work