Simple Model of the Food Chain

This model is based off Meadows economic capital with reinforcing growth loop constrained by a renewable resource model.

This model describes the N isotope dynamics in a marine system where the shallowness of the chemocline prevents significant nitrification near the base of the photic zone.

This model simulates the growth of carp in an aquaculture pond, both with respect to production and environmental effects.

Both the anabolism and fasting catabolism functions contain elements of allometry, through the m and n exponents that reduce the ration per unit body weight as the animal grows bigger.

The 'S' term provides a growth adjustment with respect to the number of fish, so implicitly adds competition (for food, oxygen, space, etc).

 Carp are mainly cultivated in Asia and Europe, and contribute to the world food supply.

Aquaculture currently produces sixty million tonnes of fish and shellfish every year. In May 2013, aquaculture production overtook wild fisheries for human consumption.

This paradigm shift last occurred in the Neolithic period, ten thousand years ago, when agriculture displaced hunter-gatherers as a source of human food.

Aquaculture is here to stay, and wild fish capture (fishing) will never again exceed cultivation.

Recreational fishing will remain a human activity, just as hunting still is, after ten thousand years - but it won't be a major source of food from the seas.

The best way to preserve wild fish is not to fish them.

In Chile, 60% of its population are exposed to levels of Particulate Matter (PM) above international standards. Air Pollution is causing 4,000 premature deaths per year, including health costs over US$8 billion.

How the 4-H club became a marketing thingy for DuPont

The purpose of this deer management model is to explore the capacity of wildlife management actions to help us adapt to the effects of climate change.

A climate model

This model shows the growth of one type of organism as a function of the carrying capacity (i.e., logistic growth).

This model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

European Masters in System Dynamics 2016
New University of Lisbon, Portugal

 Model to represent oyster individual growth by simulating feeding and metabolism. Builds on the core model in three ways: (i) partitions metabolic costs into feeding and fasting catabolism; (ii) adds allometry to clearance rate; (iii) adds temperature dependence to clearance rate.

To calculate emission amount from mobile sources in particular from road traffic by vehicle age-cohort in DKI Jakarta - Indonesia

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

Bathtub SFD

Collapse of the economy, not just recession, is now very likely. To give just one possible cause, in the U.S. the fracking industry is in deep trouble. It is not only that most fracking companies have never achieved a free cash flow (made a profit) since the fracking boom started in 2008, but that  an already very weak  and unprofitable oil industry cannot cope with extremely low oil prices. The result will be the imminent collapse of the industry. However, when the fracking industry collapses in the US, so will the American economy – and by extension, probably, the rest of the world economy. To grasp a second and far more serious threat it is vital to understand the phenomenon of ‘Global Dimming’. Industrial activity not only produces greenhouse gases, but emits also sulphur dioxide which converts to reflective sulphate aerosols in the atmosphere. Sulphate aerosols act like little mirrors that reflect sunlight back into space, cooling the atmosphere. But when economic activity stops, these aerosols (unlike carbon dioxide) drop out of the atmosphere, adding perhaps as much as 1° C to global average temperatures. This can happen in a very short period time, and when it does mankind will be bereft of any means to mitigate the furious onslaught of an out-of-control and merciless climate. The data and the unrelenting dynamic of the viral pandemic paint bleak picture.  As events unfold in the next few months,  we may discover that it is too late to act,  that our reign on this planet has, indeed,  come to an abrupt end?  

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. To 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

This model implements the equations proposed by Ketchum in 1954. The rationale behind the concept is that only phytoplankton that grows above a certain rate will not be flushed out of an estuary.

For biological processes:

Pt  =  Po exp(kt)

Where Pt is the phytoplankton biomass at time t, Po is the initial biomass, and k is the growth rate.

For physical processes:

Pm  =  Po (1-r)^m

Where Pm is the phytoplankton biomass after m tidal cycles, and r is the exchange ratio (proportion of estuary water which does not return each tidal cycle).

By substitution, and replacing t by m in the first equation, we get:

Pm = Poexp(km).(1-r)^m

For phytoplankton to exist in an estuary, Pm = Po (at least), i.e. 1 / (1-r)^m = exp(km)
ln(1) - m.ln(1-r) = km
-m.ln(1-r) = km
k = -ln(1-r)

Ketchum (1954) Relation between circulation and planktonic populations in estuaries. Ecology 35: 191-200.

In 2005, Ferreira and co-workers showed that this balance has direct implications on biodiversity of estuarine phytoplankton, and discussed how this could be relevant for water management, in particular for the EU Water Framework Directive 60/2000/EC (Ecological Modelling, 187(4) 513-523).