#### Lab 2 Part 3

##### Kaitlynne Thornton

- 1 year 6 months ago

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

##### Aleksandr

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

- 6 years 1 month ago

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

##### Fran

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

- 6 years 1 month ago

#### Clone of Bio103 Predator-Prey Model ("Lotka'Volterra")

##### Celil Ekici

**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.

- 2 years 9 months ago

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

##### CreateRandom

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

- 5 years 11 months ago

#### Clone of Northern Ontario Demographic and Income Trend Model

##### Denis

This model has two main components. First is modelling the change in population composition as non-First Nations immigration increases with the opening of new mines in the region. The second is modelling the increasing income disparity between First Nations and non-First Nations as mining jobs are disproportionately gained by non-First Nations workers.

- 7 years 3 months ago

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

##### janinak

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

- 5 years 9 months ago

#### 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.

- 5 years 9 months ago

#### Clone of wolf ~ logistic growth

##### Andrew Carlson

- 5 years 3 months ago

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

##### Svyatoslav Solopchenko

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

- 6 years 1 month ago

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

##### Kristaps Cjaputa

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

##### Victoria Sukhopluyeva

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

- 6 years 1 month ago

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

##### Matthew Gall

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 4 months ago

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

##### Marat Jilikbaev

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

- 6 years 1 month ago

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

##### alikhatab

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

- 6 years 10 months ago

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

##### Paulo Eduardo Sampaio

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

- 6 years 1 month ago

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

##### Rolando Jaime Acosta Nunez

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

- 4 years 8 months ago

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

##### Denis

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

- 6 years 1 month ago

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

##### kerinasu

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

- 7 years 9 months ago

#### Clone of Midterm - Linear Model

##### Maria E Ruwe

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 4 months ago

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

##### Carl Wu

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

- 6 years 2 months ago

#### Clone of Predator Prey

##### Ciro

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

- 3 years 6 months ago

#### Clone of Insect Pest Control

##### Sam Russell

- 6 years 12 months ago

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

##### Bechara Assouad

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

- 4 years 2 months ago