This is a basic model for use with our lab section.  The full BIDE options.
Population Introductory Ecology

This is a basic model for use with our lab section.  The full BIDE options.

Cēsis līdz 2020
inita
4
​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
Ecology Biology Population Chaos Education
​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
Mariane Kfoury
This is a basic model for use with our lab section.  The full BIDE options.
Ecology Population Introductory

This is a basic model for use with our lab section.  The full BIDE options.

Clone of Bio 101: Basic Population Model
ruta
Insight diagram
Training Population Public Health
Clone of 5-yr Age Grp Pop Model
ehsan taati
Insight diagram
Percent Infected Healthy Infected Recovery Population Infection
Disease Dynamics (ABM)
Krishna Vontedu
Shows the ecological impact of population.
Population Ecological Impacts
Shows the ecological impact of population.
Clone of Population Ecological Impact-Sweden
Emily Roach
​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
Chaos Population Ecology Education 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.


Clone of Prey&Predator
Jacobus van Antwerpen
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Value Market Tiger Population
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Clone of Tiger Population and Black Market Value
Taylor Nicole Koontz
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Market Tiger Value Population
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Clone of Tiger Population and Black Market Value
Mikayla Kelley
Here we model the population of Algeria 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
Population Growth
Here we model the population of Algeria 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 Algeria.
Population of Algeria (Developing) Over Time
Christopher Hartline
​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.


Clone of Prey&Predator
Jun UMEDA
​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
Biology Ecology Population Education Chaos
​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 - 3z MA
Bjarke Guldager Ardal
​Climate Sector Boundary Diagram By Guy Lakeman  Climate, Weather, Ecology, Economics, Population, Welfare, Energy, Policy, CO2, Carbon Cycle, GHG (green house gasses, combined effects) As general population is composed of 85% with an education level of a 12 grader or less (a 17 year old),
Economics Population Policy Ecology Weather Climate GHG CO2 Green House Gas Energy Carbon Welfare
​Climate Sector Boundary Diagram By Guy Lakeman
 Climate, Weather, Ecology, Economics, Population, Welfare, Energy, Policy, CO2, Carbon Cycle, GHG (green house gasses, combined effects)

As general population is composed of 85% with an education level of a 12 grader or less (a 17 year old), a simple block of components concerning the health of the planet needs to be broken down into simple blocks.
Perhaps this picture will show the basics on which to vote for a sustained healthy future
Democracy is only as good as the ability of the voters to FULLY understand the implications of the policies on which they vote., both context and the various perspectives.   National voting of unqualified voters on specific policy issues is the sign of corrupt manipulation.

Clone of Climate Sector Boundary Diagram of Guy Lakeman
Taylor Nicole Koontz
Shows a projection of birth and death rate over time, creating the elements of the demographic transition. This one is for Tanzania.
Death Population Demographic Transition Birth
Shows a projection of birth and death rate over time, creating the elements of the demographic transition. This one is for Tanzania.
Tanzania Population Projection 2045
Bailey Ganio
​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
Chaos Education Ecology Biology Population
​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
charbel khachan
​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
Ecology Biology Population Chaos Education
​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
reno marcello m
​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
Education Population Ecology Chaos 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.


Clone of Prey&Predator
Eric She
​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
Education Population Biology Ecology Chaos
​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
Nick May
​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
Biology Education Ecology Population Chaos
​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
Prakash
​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
Ecology Chaos Population Biology Education
​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
Chaos Biology Population Ecology Education
​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
Chiara Birk
Shows the ecological impact of population.
Ecological Impacts Population
Shows the ecological impact of population.
Population Ecological Impact-Ireland
Rachael Fikes-Maxson
​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
Biology Ecology Chaos Population Education
​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
Education Chaos Ecology Biology Population
​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
john nehme