HANDY Model of Societal Collapse from Ecological Economics Paper 

Clone of: 

This is a partial implementation of the 'Very Simple Ecosystem Model' (VSEM) from R package BayesianTools (Hartig et al. 2019). It simulates Gross and Net Primary Productivity based on a simple light-use efficiency model. Daily PAR values were generated in R using the BayesianTools function "VSEMcreatePAR()".

Food web based off of organisms within Yellowstone. For Bio 40

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

Simple model to illustrate Steele's equation for primary production of phytoplankton.

The equation is:

Ppot = Pmax I/Iopt exp(1-I/Iopt)

Where:

Ppot: Potential production (e.g. d-1, or mg C m-2 d-1)
Pmax: Maximum production (same units as Ppot)
I: Light energy at depth of interest (e.g. uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (same units as I)

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

The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst. 

Mathematically, the logistic map is written

where:

 is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation.
For approximate Continuous Behavior set 'R Base' to a small number like 0.125To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps

Combining electromobility and renewable energies since 2014.

http://www.amsterdamvehicle2grid.nl/

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.

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

all pictures sourced from google images

A simulation illustrating simple predator prey dynamics. You have two populations.

Our computer model details the change in allele frequency of resistant mosquitoes in Africa when the government began spraying DDT. The few mosquitoes that naturally survived the chemical sprays reproduced, and created a large population of resistant mosquitoes. When DDT was sprayed later to prevent the spread of malaria, the DDT was not as effective because of the large amount of DDT-resistant phenotypes in the population.

In 2012, the City of Vancouver created a sustainability strategy for staying on the leading edge of urban development called the “Greenest City: 2020 Action Plan (GCAP)” [1—Open in Pop-up]. In the report, the GCAP noted that its highest priority action was to encourage the use of electric vehicle transport in both public and private sectors. Since then, programs such as the Clean Energy Vehicle (CEV) program have been revamped to encourage consumers to choose the greener choice, often rewarding owners with up to $5000 in incentives for battery-powered vehicles and plug-in hybrids. However, the benefits of choosing electric cars are not all clear as several reports have found that hybrid electric vehicles (HEV), plug-in electric hybrid vehicles (PHEV), and battery electric cars (BEV) generate more carbon emissions during their production than current conventional vehicles [2]. I thought it would be interesting to study this sustainability issue through a systems model to determine how much impact it has on the environment compared to conventional vehicles. 

https://insightmaker.com/insight/159243/CO2-Emissions-by-Vehicle-Type-Gasoline-vs-Electric

Our model explores both carbon emissions of standard gasoline vehicles and electric vehicles from production to distribution in Canada specifically. Unfortunately, we were unable to find any statistics regarding the number of electric vehicles in production in Canada, so we have used the sales number as our production number estimate. For CO2 emission statistics, we made sure to carefully separate different types of electric vehicles as the production of the battery in battery electric vehicles have significantly more carbon emissions during production.

As expected, the carbon emissions from electric vehicles are much lower than those of gasoline vehicles after taking into account the lifecycle emissions from an average lifespan of 8 years on the road (which is the standard warranty length offered from most car companies). Some interesting things to note are that with our current rise in electric vehicle adoption, electric vehicles will dominate the roads in about 100 years. This transformation may be further accelerated by the large-scale initiatives offered by governmental organizations and increased awareness for sustainable practices. Furthermore, it was very surprising to find that electric vehicle carbon emissions will exceed that of gasoline vehicles after nearly 1000 years, but after further analysis, this makes sense as by then electric vehicles will greatly outnumber gasoline vehicles. This means that electric vehicles are not only the greener choice -- electric vehicles are by far the greenest choice as it will take nearly a thousand years before its emissions will be equal to that of its gasoline counterpart. In fact, it may even take longer than 1000 years for electric vehicles to emit more carbon emissions than gasoline vehicles if we continue looking for more sustainable methods for producing electricity and proactively choose renewable energy over fossil fuels.

Sources:

[1] https://vancouver.ca/files/cov/Greenest-city-action-plan.pdf—Open in Pop-up

[2] http://www.ccsenet.org/journal/index.php/jsd/article/view/64183

Statistics for number of gasoline and electric vehicle sales:

Gasoline Vehicles: https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=2010000201

Electric Vehicles: https://www.fleetcarma.com/electric-vehicle-sales-canada-2017/

This model uses simple functions (converters, cosine) to simulate the water balance inside a reservoir.

Forcings and feedbacks based on Tom Fiddaman, James Hansen and other feedback and cycle diagrams

A model of an infectious disease and control

The Streeter-Phelps oxygen dynamics model was originally developed in 1925, almost a century ago.

Play

You can explore the model by hitting the simulate button, and you can use the three sliders below to (i) switch the spill on or off (1 or 0); (ii) define the day when the spill occurs (0 to 15); and (iii) make the model use a constant water temperature (20oC) or a (pre-defined) variable one.

A variable temperature affects oxygen saturation, and therefore also the oxygen deficit and oxygen concentration.

Every model element shows an = sign when you hover over it, and if you click the sign you can view the underlying equation.

If you want to edit the model, you need to create an account in InsightMaker and then clone the model and adapt it to your needs.

Study

Below is a detailed explanation of the model concept.

The model calculates the oxygen deficit (D), defined as Cs-C, where Cs is the saturation concentration of dissolved oxygen (based on temperature, and salinity if applicable), and C is the dissolved oxygen concentration.

Since D = Cs-C, it follows that:
dD/dt = -dC/dt

The rate of change of oxygen concentration with time (dC/dt) depends on two factors, organic decomposition and aeration.

dC/dt = Ka.D - Kd.L

The first term on the right side of the equation is aeration (which adds oxygen to the water), calculated by means of the temperature-dependent aeration parameter Ka.

Ka is also a function of Kr, which depends on wind speed (U) and water depth (z).

The sink term represents oxygen consumption through mineralization (bacterial decomposition) of organic matter.

The organic load L decays in time (or in space, e.g. along a river) according to a first order equation, i.e. dL/dt = -Kd.L

This equation can be integrated to yield L = Lo.exp(Kd.t), where Kd is the decay constant.

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.