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 W
Jobs Resources Strategy Engineering Technology Sea Economics Ocean Science Mortality Animals Demographics Rural Industrial Urban Services Labor Land Death Fish Population Growth Population Weather Politics Failure Climate Yield Regeneration Fertility Health Pollution Environment Plants Lifetime

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.

2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster
Guy Lakeman
52
This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.
Introductory Population Ecology

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

Bio 190: BIDE Model With Carrying Capacity
Todd Levine
10
This is a basic population estimator. Default values approximate recent data for the United States.
Population Demographics
This is a basic population estimator. Default values approximate recent data for the United States.
Population Projection (USA)
Gregory Fulkerson
100
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 int
Biology Chaos Population Education Ecology

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 and 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/dt = αx - 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.


Predator-Prey Model ("Lotka'Volterra")
Jacek Chmielewski
73
​Physical meaning of the equations 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
Population Education Chaos Ecology Biology
​Physical meaning of the equations
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/dt = αx - 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.


Prey&Predator
Tsogbadrakh Banzragch
194
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
SUSTAINABLE STABILITY DECAY Growth Population Model TURBULENCE Finance Economics Environment MATHS Mathematics Strategy Chaos Demographics Science Fractals BIFURCATION Engineering
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.
POPULATION LOGISTIC MAP (WITH FEEDBACK)
Guy Lakeman
9
国連が公表している人口の将来推計とOECDが公表している各種経済統計を参考にして、2100年までの人口・経済見通しを作成するためのダイナミクスモデル。 ①人口：年少(0-14歳)・再生産年齢人口(15-49歳)・生産年齢人口(15-64歳)・前期高齢者(65-74歳)・後期高齢者(75歳以上)にグループ分けし、出生数(再生産年齢人口×出生率)と死亡数(年代別死亡率×年代別人口の合計)を算出して総人口を推計 ②経済：2020年のGDPをストックとして、コブ＝ダグラス型関数に基づき労働力人口(15歳以上人口×労働参加率)と資本ストック(総固定資本形成)および全要素生産性の成長率をフ
Population Economy Social Security Japan
国連が公表している人口の将来推計とOECDが公表している各種経済統計を参考にして、2100年までの人口・経済見通しを作成するためのダイナミクスモデル。

①人口：年少(0-14歳)・再生産年齢人口(15-49歳)・生産年齢人口(15-64歳)・前期高齢者(65-74歳)・後期高齢者(75歳以上)にグループ分けし、出生数(再生産年齢人口×出生率)と死亡数(年代別死亡率×年代別人口の合計)を算出して総人口を推計

②経済：2020年のGDPをストックとして、コブ＝ダグラス型関数に基づき労働力人口(15歳以上人口×労働参加率)と資本ストック(総固定資本形成)および全要素生産性の成長率をフローとすることで将来のGDPを算出

③-1：就業者からの社会保険料と後期高齢者(75歳以上)からの保険料から総保険料を算出し、社会保障負担から差し引いた不足額は公費負担となる

③-2：国際比較の観点から国民経済計算体系(SNA)に従って、高齢・医療・遺族・障害・家族・雇用・失業・住居・その他の合計を社会保障負担とする

現状投影シナリオ：2020年から2100年までに制度や前提条件の極端な変更はなく、現状のトレンドが続くと想定される場合のシミュレーション結果
Japan, Population, Economy, Social Security Projection Model 2020-2100
University Open Data
4 months ago
The L ogistic 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  Rob
Population Environment Economics Fractals Chaos Mathematics

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

The Logistic Map
Guy Lakeman
25
Simulation of MTBF with controls F(t) = 1 - e ^ -λt  Where   • F(t) is the probability of failure   • λ is the failure rate in 1/time unit (1/h, for example)  • t is the observed service life (h, for example) The inverse curve is the trust time On the right the increase in failures brings its
TURBULENCE Demographics Fractals Physics Science Failure BIFURCATIONS Strategy Growth Risk Economics Navier Stokes Finance Engineering Biology Chaos Mathematics Environment Health Population MTBF
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period. 
BATHTUB MEAN TIME BETWEEN FAILURE (MTBF) RISK
Guy Lakeman
6
Primer ensayo de simulación, modelo sencillo de población de zorros y conejos. Mi modelo consiste en un modelo sencillo de la población de Zorros y conejos, donde la población de conejos se ve afectada  por la muerte de conejos, la cual es el producto  de la  tasa de muerte de los conejos  multiplic
Enviroment Population
Primer ensayo de simulación, modelo sencillo de población de zorros y conejos. Mi modelo consiste en un modelo sencillo de la población de Zorros y conejos, donde la población de conejos se ve afectada  por la muerte de conejos, la cual es el producto  de la  tasa de muerte de los conejos  multiplicado por la población de conejos, más  la población de zorros  multiplicada  por los conejos que se come cada zorro. También se tiene en cuenta que si no hay conejos suficientes  aumenta la  tasa de mortalidad de zorros.
Zorros y Conejos
Maria Isabel Diaz
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
Economics System Zoo Z602 Society Population
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.
Z602 Population with four age groups
Joe Van Steen
16
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
Drought Transport Silicene Graphene Resource Solar Nuclear Energy Food Agriculture Cyclone Tornado Typhoon Hurricane Loss Flood Animals Plants Fish Sea Ocean Yield Regeneration Pollution Lifetime Rural Industrial Urban Labor Jobs Land Resources Services Health Fertility Politics Economics Strategy Engineering Technology Science Mortality Death Failure Climate Weather Population Population Growth Demographics Environment

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 MODEL IS ZONE SPECIFIC AS GLOBAL WEATHER IS NOT HOMOGENEOUS BUT A COLLECTION OF HEAT BUMBPS DEPENDENT ON POPULATION SIZE OF URBAN HEAT ISLANDS AND MASSED CONURBATIONS AND AGGLOMERATIONS 

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.

2017 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility by Guy Lakeman - The World3+ Model: Forecaster
Guy Lakeman
24
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 th
Strategy Weather Environment MTBF BIFURCATIONS Growth Economics Finance Mathematics Population Demographics Science Navier Stokes Physics Engineering TURBULENCE Chaos Fractals Biology Health
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)

FORCED GROWTH INTO TURBULENCE
Guy Lakeman
4
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Population Market Value Tiger
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Tiger Population and Black Market Value
Taner Durusu
16
OVERSHOOT GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION The existing global capitalistic growth paradigm is totally flawed 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 Dunb
Health Environment Economics Finance Mathematics Physics Biology Fractals Chaos TURBULENCE Engineering Navier Stokes Science Demographics Population Growth Strategy Weather
OVERSHOOT GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION

The existing global capitalistic growth paradigm is totally flawed

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 limited size working capacity containers (villages communities)

OVERSHOOT GROWTH INTO TURBULENCE
Guy Lakeman
6
Simple BIDE model
Education Ecology Population
Simple BIDE model
Population - BIDE
Todd Levine
3
From NAP Toward Quality Measures for Population Health and the Leading Health Indicators  Report  with detailed Maternal  Infant and Child Health Example Fig.3-5. Compare with WHO NCD Framework picture and IHI Whole system measures 2.0 (Added Nov 2016) See CLD conversion insight
Regional Child Prevention Program Health Framework Capability Social Performance Population Health System
From NAP Toward Quality Measures for Population Health and the Leading Health Indicators Report with detailed Maternal  Infant and Child Health Example Fig.3-5. Compare with WHO NCD Framework picture and IHI Whole system measures 2.0 (Added Nov 2016) See CLD conversion insight

Health Outcome Logic Model
Geoff McDonnell
3 6 months ago
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 int
Population Biology Ecology Education Chaos

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 and 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/dt = αx - 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.


Bio103 Predator-Prey Model ("Lotka'Volterra")
John Petersen
102
A system dynamics model of a predator-prey lifecycle relationship
Foxes Population Interdpendence Environment Rabbits Predator Prey
A system dynamics model of a predator-prey lifecycle relationship




Predator-Prey relationship
Richard Craig
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
Community Population Ecology Yellowstone
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
YellowstoneEcoClassModel
Esther
6
Exploring the conditions of permanent coexistence, rather than gradual disappearance of disadvantaged competitors. ​Z506 p32-35 System Zoo 3 by Hartmut Bossel.
Health Care Social Psychology Self System Zoo Competition Population

Exploring the conditions of permanent coexistence, rather than gradual disappearance of disadvantaged competitors. ​Z506 p32-35 System Zoo 3 by Hartmut Bossel.

Competition for Resources
Geoff McDonnell
3
Insight diagram
Births Feedback Loop Postive Population
Exercise 3
Jacinda Maassen
Flows between acute hospital and aged care for older people. See  IM-1012  for a simpler version
Population Aged Care Patient Flow Hospital Health Care Policy

Flows between acute hospital and aged care for older people. See IM-1012 for a simpler version

Aged Care and Hospital Flows
Geoff McDonnell
4
THE 2018 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 R
Death Strategy Engineering Technology Science Mortality Energy Failure Climate Economics Weather Politics Fertility Population Population Growth Demographics Environment Health Services Resources Land Jobs Labor Urban Industrial Rural Lifetime Pollution Regeneration Yield Ocean Sea Fish Plants Animals Flood Drought Loss Hurricane Typhoon Tornado Cyclone Agriculture Transport Silicene Graphene Resource Solar Food Nuclear

THE 2018 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.

2018 OVERPOPULATION LEADS TO POLLUTION based on Weather & Climate Extreme Loss of Arable Land and Ocean Fertility by Guy Lakeman - The World3+ Model: Forecaster
Guy Lakeman
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