#### BirthRateDeathRateAndR

##### Todd Levine

- 7 months 2 weeks ago

#### Modelo da populacao de samambaias

##### Ismael Costa

- 1 year 8 months ago

#### Predator Prey Interactions

##### Katherine Scalise

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

- 4 years 3 days ago

#### projekt OSA - Systém výroby elektrické energie

##### Ladislav

- 4 years 1 month ago

#### Overexploitation from Critical Transitions

##### Geoff McDonnell ★

The dynamics of the food population as a function of growth and consumption. Notation matches the Appendix of Marten Scheffer's 2009 Book Critical Transitions in Nature and Society p332-4 http://bit.ly/yrd3GN

- 7 years 8 months ago

#### Cēsis līdz 2020

##### inita

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

- 4 years 5 months ago

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

##### Andrew E Long

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.

- 2 years 4 months ago

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

##### Robert Bilyk

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

- 3 years 6 months ago

#### Allee Effect from Critical Transitions

##### Geoff McDonnell ★

Addition of Allee effect to Logistic Growth Insight 1540. From the Appendix of Marten Scheffer's 2009 Book Critical Transitions in Nature and Society p332 http://bit.ly/yrd3GN. The Allee affect describes a threshold density (smaller than the carrying capacity K) below which populations go into free fall extinction.

- 7 years 8 months ago

#### Algae, Tadpole and Dragonfly Population Dynamics

##### Laryssa Faith Laurignano

- 3 years 5 months ago

#### WKCTC Bio121: Modeling Predator and Prey

##### Todd Levine

A simulation illustrating simple predator prey dynamics. You have two populations, one of which preys on the other. Each population is affected by a birth and death rate. The birth rate of the predators depend on their efficiency at harvesting prey items, while the death rate of the prey depends on how many are caught by the predator.

- 1 year 6 months ago

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

##### Andrew E Long

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

- 2 years 3 months ago

#### Jacob Englert MAT 375 Midterm: Model of Isle Royale: Predator Prey Interactions

##### Jacob Englert

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

- 2 years 3 months ago

#### Kangaroo population control

##### Essi

- 2 years 11 months ago

#### Senina

##### Senina Anastassiya

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

- 5 years 11 months ago

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

##### Sean R Westley

**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.

- 9 months 2 weeks ago

#### Logistic Growth: One and Two Stocks

##### Theodore Pavlic

- 3 years 5 months ago

#### Cēsu iedzīvotāju skaita izmaiņas

##### ruta

Rūta Grasberga

- 5 years 2 months ago

#### Day 22: Isle Royale: Predator/Prey Model for Moose and Wolves

##### Jacob Englert

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.};

- 2 years 4 months ago

#### Munz 2009 Zombies 2 - tested

##### Todd Levine

- 7 years 8 months ago

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

##### Yves

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

- 6 years 4 months ago

#### Nick's Fern Population Model

##### A Man Has No Name

- 3 years 4 months ago

#### Competition model/Georgiette Oduro-Boateng

##### Georgiette Oduro-Boateng

- 5 years 8 months ago

#### Isle Royale Revised: Predator Prey Interactions

##### Walter M. Stroup

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

- 5 years 8 months ago