Population | Insight Maker

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.

Clone of Prey&Predator

Ben Cope

A simplified population model with three age groups

Clone of Simple Population

Nesime Yıldırım

Influence of migration on the number of working-age population.

Clone of Clone of Clone of Radno sposobno stanovništvo

Antun

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.

Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

Tim Wille

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.

Clone of Prey&Predator

Ben Cope

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.

Clone of Prey&Predator

Muhammad Banendra

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.

Clone of Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

Gyula Dörgő

Shows the ecological impact of population.

Population Ecological Impact-Zimbabwe

Solomon Makoni

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.

Clone of Clone of Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

Urasa Kongdechakul

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.

Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

James McRae

This chart demonstrates the silo nature of the different sectors working in Refugee humanitarian assistance.

Refugee Humanitarian Assistance

Chelsea Poeppel

Module 2 model on Healthy Population model

CVD Disease Progression Model

Lee Robertson

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

Clone of Competition for Resources

Dennis Bao

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.

Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

ROSE LIAO

Just a little model put together for training purposes

Population with slider input model

Chris Skelly

This model has two main components. First is modelling the change in population composition as non-First Nations immigration increases with the opening of new mines in the region. The second is modelling the increasing income disparity between First Nations and non-First Nations as mining jobs are disproportionately gained by non-First Nations workers.

Clone of Northern Ontario Demographic and Income Trend Model

Denis

No stocking Aug 7 Lake Sturgeon with Growth Rate

Katherine L Bryant

Malthus Population Growth and Limits

Ashley Deibler

Clone of sample_ecology_capital

do stuff

Unconstrained exponential model to simulate population growth. There are three scenarios (Main, Big Population, High Growth) and four charts (Population, Growth, Population & Growth, Population vs Growth)

Population Growth

Pandega Abyan Zumarsyah

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.

Clone of 2014 Weather & Climate Extreme Loss of Arable Land and Ocean Fertility - The World3+ Model: Forecaster

Samson Tan

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.

Clone of Prey&Predator

Chloe

Migration Ratehttps://www.indexmundi.com/russia/net_migration_rate.html

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

Russia Population Growth

Adelaide S

Shows the ecological impact of population.

Clone of Population Ecological Impact-Sweden

Emily Roach

Population Models