​ This model is used in a world studies extended essay research. The research question is: In what ways would the water desalination method used in Singapore benefit   water-stressed and economically less developed countries, using Palestine as a case study.

It seems that I've made a mess of mine! But it's a mess with a purpose....

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

This model describes phosphorus cycling in a dune-lake system in the Northland region of New Zealand. It is based on stock and flow diagrams where each orange oval represents an input, while each blue box represents a stock. Each arrow represents a flow. Flows involve a loss from the stock at which they start and add to the stock at which they end.

Simple mass balance model for lakes, based on the Vollenweider equation:

dMw/dt = Min - sMw - Mout

The model was first used in the 1960s to determine the phosphorus concentration in lakes and reservoirs, for eutrophication assessment.

Simple model to illustrate oyster growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period.

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: 

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)
I: Light energy at depth of interest (uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (uE m-2 s-1)
S: Nutrient concentration (umol N L-1)
Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:
- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.
- Light limited by the concentration of phytoplankton.
- Temperature effect on phytoplankton and Oyster growth.

Modèle simple pour illustrer la croissance des huîtres sur la base de la production primaire de phytoplancton comme une variable d'état, forcé par la lumière et les éléments nutritifs, en cours d'exécution pour une période annuelle.

La croissance du phytoplancton sur la base de Steele et équations de Michaelis-Menten), où:

Production primaire = (([Pmax] * [I] / [Iopt] * exp (1 - [I] / [Iopt]) * [S]) / ([K] + [S]))

Pmax: production maximale (d-1)
I: L'énergie lumineuse en profondeur de l'intérêt (Ue m-2 s-1)
Iopt: L'énergie lumineuse à laquelle se produit Pmax (Ue m-2 s-1)
S: concentration des éléments nutritifs (N umol L-1)
KS: Demi constants de saturation en nutriments (N umol L-1).

D'autres développements:
- Les éléments nutritifs comme variable d'état dans le cycle de détritus de phytoplancton et d'huîtres de la biomasse.
- Lumière limitée par la concentration de phytoplancton.
- Effet de la température sur le phytoplancton et la croissance des huîtres.

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

 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 2011, 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.

THE BROKEN LINK BETWEEN SUPPLY AND DEMAND CREATES TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

Growth in supply and productivity is a summation of variables as is demand ... when the link between them is broken by catastrophic failure in a component the creation of unpredictable chaotic turbulence puts the controls ito a situation that will never return the system to its initial conditions as it is STIC system (Lorenz)

The chaotic turbulence is the result of the concept of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite working containers (villages communities)

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

 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 2011, 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.

This diagram provides a stylised description of important feedbacks within a shallow-lake system.

Testing for MSc

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 is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple mass balance model for lakes, based on the Vollenweider equation:

dMw/dt = Min - sMw - Mout

The model was first used in the 1960s to determine the phosphorus concentration in lakes and reservoirs, for eutrophication assessment.

​ This model is used in a world studies extended essay research. The research question is: In what ways would the water desalination method used in Singapore benefit   water-stressed and economically less developed countries, using Palestine as a case study.

Very simple model demonstrating growth of phytoplankton using Steele's equation for potential production and Michaelis-Menten equation for nutrient limitation.

Both light and nutrients (e.g. nitrogen) are modelled as forcing functions, and the model is "over-calibrated" for stability.

The phytoplankton model approximately reproduces the spring-summer diatom bloom and the (smaller) late summer dinoflagellate bloom.
 
Oyster growth is modelled only as a throughput from algae. Further developments would include filtration as a function of oyster biomass, oyster mortality, and other adjustments.

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 2011, 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.

As initially proposed by Pr. William M White of Cornell University:

FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION 
 BEWARE pushing increased growth blows the system!
(governments are trying to push growth on already unstable systems !)

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept and flawed strategy of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)

The body of research and studies generated on the Fryingpan River between the 1940s and the present supports the development of a conceptual model of ecosystem responses to hydrological regime behavior and streamflow management activities. This conceptual model should encourage conversations about system behavior and collective understanding among stakeholders regarding connections between specific hydrological regime characteristics affected by management of Ruedi Reservoir and the ecological or biological variables important to local communities. For the sake of simplicity, the model includes mostly unidirectional relationships—feedback loops are exploded to reveal intermediate connections between variables. This approach increases the number of variables represented in the system, perhaps increasing its complexity at first glance. However, the primary benefit to the end user is that the model becomes more readable and explicit in its representation of system behavior. 

 

The conceptual model presented here likely differs by degrees from those held by the various investigators who considered Fryingpan River processes over the previous 80 years. However, it affectively aggregates the ideas main presented by each of those individuals. This model focuses on hydrological and biological variables and does not incorporate the entire diversity of human uses and needs for water from the Fryingpan River (e.g. hydropower production for the City of Aspen, revenue generated in the Town of Basalt by angling activities, etc.).  Rather it attempts to illustrate how the conditional state of important ecosystem characteristics might respond to reservoir management activities that impact typical spring flows, peak flow timing and magnitude, summer flows, fall flows, and winter flows. 

Simple mass balance model for lakes, based on the Vollenweider equation:

dMw/dt = Min - sMw - Mout

The model was first used in the 1960s to determine the phosphorus concentration in lakes and reservoirs, for eutrophication assessment.