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

##### Lizzy Compton

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

- 1 year 8 months ago

#### Clone of Clone of Modelo da populacao de samambaias

##### Ilson Lopes de Oliveira

- 1 year 3 weeks ago

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

##### Hailey Smith

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

- 2 years 1 month ago

#### Clone of Plant, Deer and Wolf Population Dynamics

##### Bechara Assouad

- 8 months 4 weeks ago

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

##### Benjamin Nguyen

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.};

- 4 months 3 days ago

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

##### Rhys Almario

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

- 6 months 1 week ago

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

##### Parker Kain

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

- 1 year 8 months ago

#### Clone of lynx v. snowshoe hare

##### Hailey Smith

- 2 years 1 month ago

#### Clone of Mat375: 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.

- 1 year 8 months ago

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

##### Donna Odhiambo

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

- 1 year 8 months ago

#### Clone of Predator Prey

##### Kenneth C

A simulation illustrating simple predator prey dynamics. You have two populations.

- 4 months 3 days ago

#### Clone of Plant, Deer and Wolf Population Dynamics - ISD OWL

##### Sandra Chidiac

- 1 year 1 month ago

#### Clone of Plant, Deer and Wolf Population Dynamics G-IV Intro

##### Caden Spooner

- 2 years 5 months ago

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

##### Sarah Zeng

- 4 months 4 days ago

#### Clone of Modelo da populacao de samambaias

##### joD. Roger

- 1 year 1 month ago

#### Clone of Mat375: Isle Royale: Predator Prey Interactions

##### Allison Zembrodt

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.

- 1 year 8 months ago

#### Clone of Plant, Deer and Wolf Population Dynamics - ISD OWL

##### Sandra Chidiac

- 1 year 1 month ago

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

##### Leah Gillespie

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

- 1 year 7 months ago

#### Clone of Predator-Prey Model ("Lotka'Volterra")

##### Ethan Lee

**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 becomesdx/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.

PredatorsThe 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.

- 4 months 4 days ago

#### Clone of Plant, Deer and Wolf Population Dynamics - ISD OWL

##### Peter Morgan

- 1 year 6 months ago

#### Clone of Predator Prey

##### Melissa Richardson

A simulation illustrating simple predator prey dynamics. You have two populations.

- 2 years 1 month ago

#### Clone of lynx v. snowshoe hare

##### John Alonte

- 2 years 1 month ago

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

##### M Charnell

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

- 7 months 4 days ago

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

##### Hugo Baraer

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

- 1 year 11 months ago