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

##### Matthew Gall

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

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

- 3 years 3 months ago

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

##### Matthew Gall

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

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

- 3 years 3 months ago

#### Clone of Clone of Isle Royale: Predator Prey Interactions

##### nancy aziz

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.

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

- 5 years 8 months ago

#### Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Eliecer Alvarado Rodriguez

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.

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

- 6 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Lena Kamp

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.

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

- 5 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Jonas Korn

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

- 5 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Omotunde Kasali

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

- 5 years 7 months ago

#### Clone of Clone of Isle Royale: Predator Prey Interactions

##### sow

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

- 5 years 5 months ago

#### Clone of Key Concepts in Systems Thinking : Predator Prey Interactions

##### Kevin Crowthers

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

- 2 years 6 months ago

#### Clone of Isle Royale: Predator Prey Interactions

##### Evgeny Gaponov

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

- 6 years 11 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Pia Scholz

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

- 5 years 7 months ago

#### Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Jana Koltzau

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

- 6 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### ninel ninel

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

- 5 years 7 months ago

#### Clone of Isle Royale: Predator Prey Interactions

##### Evgeniy

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

- 6 years 11 months ago

#### Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### DerTheo

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

- 6 years 7 months ago

#### Clone of Isle Royale: Predator Prey Interactions

##### a;sdlkgj

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

- 5 years 3 months ago

#### Clone of Isle Royale: Predator Prey Interactions

##### Nicholas Head

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

- 7 years 1 week ago

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

##### Matthew Gall

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

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

- 3 years 3 months ago

#### Clone of Isle Royale: Predator/Prey Model for Moose and Wolves

##### Benjamin Nguyen

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at

https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions

Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker.nb

It allows one to experiment with adjusting the initial number of moose and wolves on the island.

I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-BestFit.nb

{WolfBirthRateFactorStart,

WolfDeathRateStart,

MooseBirthRateStart,

MooseDeathRateFactorStart,

moStart,

woStart} =

{0.000267409,

0.239821,

0.269755,

0.0113679,

591,

23.};

https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions

Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker.nb

It allows one to experiment with adjusting the initial number of moose and wolves on the island.

I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-BestFit.nb

{WolfBirthRateFactorStart,

WolfDeathRateStart,

MooseBirthRateStart,

MooseDeathRateFactorStart,

moStart,

woStart} =

{0.000267409,

0.239821,

0.269755,

0.0113679,

591,

23.};

- 1 year 11 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Paulina von Magnus

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

- 5 years 7 months ago

#### Clone of MAT 375 Midterm file: Model of Isle Royale: Predator Prey Interactions

##### Terra Ficke

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.

Thanks to Jacob Englert for the model if-then-else structure.

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

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.

Thanks to Jacob Englert for the model if-then-else structure.

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

- 3 years 3 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Sabrina Gerdes

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

- 5 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Chris S.

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

- 5 years 7 months ago

#### Clone of Clone of (3) Copy of "Isle Royale: Predator Prey Interactions"

##### Eva Brinkmann

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

- 5 years 7 months ago