This is a first attempt to model I=PAT population growth. Impact on the renewables is equal to P*A*T. Footprint is limited by the amount of renewables left divided by the population. Death rate goes up if the Footprint goes down too far.
This is a first attempt to model I=PAT population growth. Impact on the renewables is equal to P*A*T. Footprint is limited by the amount of renewables left divided by the population. Death rate goes up if the Footprint goes down too far.
This simulation examines the caloric well of the world. World population is estimated to start at about 7.7 billion. Per capita estimates are from the International Energy Agency (IEA).
This simulation examines the caloric well of the world. World population is estimated to start at about 7.7 billion. Per capita estimates are from the International Energy Agency (IEA).
Einfaches Teilmodell für eine Bevölkerungsentwicklung. Geburten- und Sterberate sind einstellbare Parameter.
Einfaches Teilmodell für eine Bevölkerungsentwicklung. Geburten- und Sterberate sind einstellbare Parameter.
Verkoppelung der drei Teilmodelle zu einem Gesamtmodell, der "Miniwelt" im Umfang von Bossel. Eine Modifikation besteht darin, dass ein hohes Konsumniveau wieder zu einer Absenkung der Geburten führt.
Verkoppelung der drei Teilmodelle zu einem Gesamtmodell, der "Miniwelt" im Umfang von Bossel.
Eine Modifikation besteht darin, dass ein hohes Konsumniveau wieder zu einer Absenkung der Geburten führt.
 Simple one stock model of population increase with actual years using a converter

Simple one stock model of population increase with actual years using a converter

Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."  ​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for
Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."

​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for the elderly, pensions dynamics, etc.
Here we model the population of France given data between 1960 and 2013 from Worldbank.org. We used the crude birth rate and crude death rate for every 5 years since 1960 to 2005, and the rates every year from 2005 to 2013. To forecast, we used the slope of the net birth rate to calculate when the n
Here we model the population of France given data between 1960 and 2013 from Worldbank.org. We used the crude birth rate and crude death rate for every 5 years since 1960 to 2005, and the rates every year from 2005 to 2013. To forecast, we used the slope of the net birth rate to calculate when the net birth rate would be zero, and used this year for our birth and death rates to are equal to zero. We assumed no net movement of people into or out of France.
  Физический смысл уравнений    Модель Лотки-Вольтерры делает ряд предположений об окружающей среде и эволюции популяций хищников и жертв:         1. Хищная популяция всегда находит достаточно пищи.  2. Продовольственная обеспеченность популяции хищника полностью зависит от размера популяции жертвы.
Физический смысл уравнений
Модель Лотки-Вольтерры делает ряд предположений об окружающей среде и эволюции популяций хищников и жертв:

1. Хищная популяция всегда находит достаточно пищи.
2. Продовольственная обеспеченность популяции хищника полностью зависит от размера популяции жертвы.
3. Скорость изменения численности населения пропорциональна его численности.
4. В ходе этого процесса окружающая среда не меняется в пользу одного вида, и генетическая адаптация не имеет существенного значения.
5. Хищники обладают безграничным аппетитом.
Поскольку используются дифференциальные уравнения, решение является детерминированным и непрерывным. Это, в свою очередь, означает, что поколения как хищника, так и жертвы постоянно пересекаются.

Добыча
Когда умножается, уравнение добычи становится
dx/dt = αx - βxy
  Предполагается, что добыча имеет неограниченный запас пищи и размножается экспоненциально, если только она не подвержена хищничеству; этот экспоненциальный рост представлен в приведенном выше уравнении термином  αx. Предполагается, что скорость хищничества на добыче пропорциональна скорости, с которой встречаются хищники и добыча; это представлено выше в виде βxy.Если либо x, либо y равно нулю, то хищничества быть не может.
С помощью этих двух терминов приведенное выше уравнение можно интерпретировать следующим образом: изменение численности добычи определяется ее собственным ростом минус скорость, с которой она охотится.
ХищникиУравнение хищника становится

dy/dt =  - 

В этом уравнении,  представляет рост популяции хищника. (Обратите внимание на сходство со скоростью хищничества; однако используется другая константа, поскольку скорость роста популяции хищника не обязательно равна скорости, с которой он потребляет добычу).  представляет собой уровень потерь хищников вследствие естественной смерти или эмиграции; это приводит к экспоненциальному распаду в отсутствие добычи.


Следовательно, уравнение выражает изменение популяции хищников как рост, подпитываемый запасом пищи, минус естественная смерть.


 This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

Show relation of birth and death rate over time, creating the elements of the demographic transition. This one is for Italy. You can clone this insight for other nations, just plug in the new crude birth and death rates and find the starting population in 1960.
Show relation of birth and death rate over time, creating the elements of the demographic transition. This one is for Italy. You can clone this insight for other nations, just plug in the new crude birth and death rates and find the starting population in 1960.
 Acest model este adaptat după reprezentarea lui Harmut Bossel, în lucrarea  "System Zoo 3 Simulation Models, Economy, Society, Development."  Utilizarea modelului ne poate ajuta pentru a vizualiza evolutia populatiei pe grupe de varsta sau pentru a gestiona probleme cum ar fi ocuparea forței de mun
Acest model este adaptat după reprezentarea lui Harmut Bossel, în lucrarea  "System Zoo 3 Simulation Models, Economy, Society, Development."
Utilizarea modelului ne poate ajuta pentru a vizualiza evolutia populatiei pe grupe de varsta sau pentru a gestiona probleme cum ar fi ocuparea forței de muncă.
Migration Rate​https://www.indexmundi.com/russia/net_migration_rate.html    https://www.cia.gov/library/publications/the-world-factbook/fields/2112.html
Migration Rate​https://www.indexmundi.com/russia/net_migration_rate.html

https://www.cia.gov/library/publications/the-world-factbook/fields/2112.html

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. The equation for DeltaN is a version of  Nj+1 = Nj  + mu (1- Nj / Nmax ) Nj  the maximum population is set to be one million, and the growth rate constant mu
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.
The equation for DeltaN is a version of 
Nj+1 = Nj  + mu (1- Nj / Nmax ) Nj
the maximum population is set to be one million, and the growth rate constant mu = 3.
 
Nj: is the “number of items” in our current generation.

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 equation is a form of what is known as the logistic map or equation. It is a map because it "maps'' the population in one year into the population of the next year. It is "logistic'' in the military sense of supplying a population with its needs. It a nonlinear equation because it contains a term proportional to Nj^2 and not just Nj. The logistic map equation is also an example of discrete mathematics. It is discrete because the time variable j assumes just integer values, and consequently the variables Nj+1 and Nj do not change continuously into each other, as would a function N(t). In addition to the variables Nj and j, the equation also contains the two parameters mu, the growth rate, and Nmax, the maximum population. You can think of these as "constants'' whose values are determined from external sources and remain fixed as one year of items gets mapped into the next year. However, as part of viewing the computer as a laboratory in which to experiment, and as part of the scientific process, you should vary the parameters in order to explore how the model reacts to changes in them.
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
   THE 2017 MODEL (BY GUY LAKEMAN) EMPHASIZES THE PEAK IN POLLUTION BEING CREATED BY OVERPOPULATION WITH THE CARRYING CAPACITY OF ARABLE LAND NOW BEING 1.5 TIMES OVER A SUSTAINABLE FUTURE (PASSED IN 1990) AND NOW INCREASING IN LOSS OF HUMAN SUSTAINABILITY DUE TO SEA RISE AND EXTREME GLOBAL WATER REL

THE 2017 MODEL (BY GUY LAKEMAN) EMPHASIZES THE PEAK IN POLLUTION BEING CREATED BY OVERPOPULATION WITH THE CARRYING CAPACITY OF ARABLE LAND NOW BEING 1.5 TIMES OVER A SUSTAINABLE FUTURE (PASSED IN 1990) AND NOW INCREASING IN LOSS OF HUMAN SUSTAINABILITY DUE TO SEA RISE AND EXTREME GLOBAL WATER RELOCATION IN WEATHER CHANGES IN FLOODS AND DROUGHTS AND EXTENDED TROPICAL AND HORSE LATTITUDE CYCLONE ACTIVITY AROUND HADLEY CELLS

The World3 model is a detailed simulation of human population growth from 1900 into the future. It includes many environmental and demographic factors.

THIS MODEL BY GUY LAKEMAN, FROM METRICS OBTAINED USING A MORE COMPREHENSIVE VENSIM SOFTWARE MODEL, SHOWS CURRENT CONDITIONS CREATED BY THE LATEST WEATHER EXTREMES AND LOSS OF ARABLE LAND BY THE  ALBEDO EFECT MELTING THE POLAR CAPS TOGETHER WITH NORTHERN JETSTREAM SHIFT NORTHWARDS, AND A NECESSITY TO ACT BEFORE THERE IS HUGE SUFFERING.
BY SETTING THE NEW ECOLOGICAL POLICIES TO 2015 WE CAN SEE THAT SOME POPULATIONS CAN BE SAVED BUT CITIES WILL SUFFER MOST. 
CURRENT MARKET SATURATION PLATEAU OF SOLID PRODUCTS AND BEHAVIORAL SINK FACTORS ARE ALSO ADDED

Use the sliders to experiment with the initial amount of non-renewable resources to see how these affect the simulation. Does increasing the amount of non-renewable resources (which could occur through the development of better exploration technologies) improve our future? Also, experiment with the start date of a low birth-rate, environmentally focused policy.

Show relation of birth and death rate over time, creating the elements of the demographic transition. This one is for Morocco.
Show relation of birth and death rate over time, creating the elements of the demographic transition. This one is for Morocco.
    Clone of Bio103 Predator-Prey Model ("Lotka'Volterra")  Tags:  Education ,  Chaos ,  Ecology ,  Biology ,  Population   Thanks to Insight Author:  John Petersen       Edits by Andy Long     Everything that follows the dashes was created by John Petersen (or at least came from his Insight model).

Clone of Bio103 Predator-Prey Model ("Lotka'Volterra")
Thanks to Insight Author: John Petersen

Edits by Andy Long

Everything that follows the dashes was created by John Petersen (or at least came from his Insight model). I just wanted to make a few comments.

We are looking at Hare and Lynx, of course. Clone this insight, and change the names.

Then read the text below, to get acquainted with one of the most important and well-known examples of a simple system of differential equations in all of mathematics.

http://www.nku.edu/~longa/classes/mat375/mathematica/Lotka-Volterra.nb
------------------------------------------------------------

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system. 

For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system. 

The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined. 

Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed. 

Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.

The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.
2. The food supply of the predator population depends entirely on the size of the prey population.
3. The rate of change of population is proportional to its size.
4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.
5. Predators have limitless appetite.

As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey
When multiplied out, the prey equation becomes
dx/dtαx - βxy
 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.