Ecology | Insight Maker

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

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions

Austin Hardesty

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

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 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

Alice Harter

This model is to be used with Mr. Roderick's AP biology activity on population growth. See steveroderick.net for a copy of the activity worksheet.

Use the sliders below to quickly change the initial values of components of the model.

Clone of wolf ~ boom and bust

Albert El-hage

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

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

Clone of Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions

Leah Gillespie

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

Clone of Bio 190: BIDE Model With Carrying Capacity

Andre Henderson

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

Clone of Bio 190: BIDE Model With Carrying Capacity

Todd Levine

Clone of wolf ~ logistic growth

Rayla da Cunha Ferreira

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

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

Clone of Bio 190: BIDE Model With Carrying Capacity

ella ah

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.

Clone of Bio 101: Basic Population Model

ruta

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

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions

Donna Odhiambo

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

Clone of Clone of Bio 190: BIDE Model With Carrying Capacity

Heidi Ballew

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

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

Clone of Bio 190: BIDE Model With Carrying Capacity

ella ah

The model simulates the comparison between mountain biking industry and forestry/logging in Derby Tasmania.

How the model works

On the left-hand side, Derby Mountain biking, tourists visit the mountain according to reviews and recommendation of mountain scenery and entertainment activities. The number of people who hire bikes and who choose to dine on the mountain are limited by bike availability. Both bike hiring and biker dining contribute to tourist revenue in Derby. On the right-hand side, forest trees grow at certain rates, but are negatively affected by timber demand. Timber logging generate revenue, which depends on sale price and associated cost.

Interesting insights

Although forestry contributes more revenue in a certain time, it seems that Derby Mountain bike generate more tourist revenue from dining services and bike hiring in a long term.

Simulation of Derby Mountain biking versus logging

Yuanyuan Zhao

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

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions

Alyssa Farmer

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

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

Clone of Isle Royale: Predator Prey Interactions

Robert L. Brown

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

Chris-Daniel Krempels

This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.

CURSO MAR 25 - Grama, Cervo e Lobo - Presa Predador - modelo da internet

Guilherme Caloba

17 2 weeks ago

STEM-SM combines a simple ecosystem model (modified version of VSEM; Hartig et al. 2019) with a soil moisture model (Guswa et al. (2002) leaky bucket model). Outputs from the soil moisture model influence ecosystem dynamics in three ways.

(1) The ratio of actual transpiration to maximum evapotranspiration (T/ETmax) modifies gross primary productivity (GPP).

(2) Degree of saturation of the soil (Sd) modifies the rate of soil heterotrophic respiration.

(3) Water limitation of GPP (by T/ETmax) and of soil nutrient availability (approximated by Sd) combine with leaf area limitation (approximated by fraction of incident photosynthetically-active radiation that is absorbed) to modify the allocation of net primary productivity to aboveground and belowground parts of the vegetation.

Ecosystem dynamics in turn influence flows of water in to and out of the soil moisture stock. The size of the aboveground biomass stock determines fractional vegetation cover, which modifies interception, soil evaporation and transpiration by plants.

References:

Guswa, A.J., Celia, M.A., Rodriguez-Iturbe, I. (2002) Models of soil moisture dynamics in ecohydrology: a comparative study. Water Resources Research 38, 5-1 - 5-15.

Hartig, F., Minunno, F., and Paul, S. (2019). BayesianTools: General-Purpose MCMC and SMC Samplers and Tools for Bayesian Statistics. R package version 0.1.7. https://CRAN.R-project.org/package=BayesianTools

Clone of Simple Terrestrial Ecosystem Model - Soil Moisture (STEM-SM)

duoer

6 months ago

Ecology Models