#### Clone of lynx v. snowshoe hare

##### John Alonte

- 1 year 10 months ago

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

##### M Charnell

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

- 3 months 1 week 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 7 months ago

#### Clone of wolf ~ logistic growth

##### Dominic Jones

- 2 years 9 months ago

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

##### Ismael Costa

- 9 months 2 weeks ago

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

##### Maria E Ruwe

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

- 1 year 4 months ago

#### Clone of lynx v. snowshoe hare

##### Jonilee Carroll

- 1 year 10 months ago

#### Clone of S-Curve + Delay for Bell Curve by Guy Lakeman

##### Ray Madachy

**S-Curve + Delay for Bell Curve Showing Erlang Distribution**

Generation of Bell Curve from Initial Market through Delay in Pickup of Customers

This provides the beginning of an Erlang distribution model

The **Erlang distribution** is a two parameter family of continuous probability distributions with support . The two parameters are:

- a positive integer '
**shape'** - a positive real '
**rate'**; sometimes the scale , the inverse of the rate is used.

MATHS Statistics Physics Science Ecology Climate Weather Intelligence Education Probability Density Function Normal Bell Curve Gaussian Distribution Democracy Voting Politics Policy Erlang

- 4 months 1 day ago

#### 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 4 months ago

#### Clone of Predator Prey

##### Kelsey Hasler

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

- 1 year 10 months ago

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

##### Jonilee Carroll

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

- 1 year 10 months ago

#### Clone of Prey&Predator

##### Mark Moylan

- 9 months 3 weeks ago

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

##### D L

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

- 3 weeks 4 days ago

#### Clone of lynx v. snowshoe hare

##### Melissa Richardson

- 1 year 10 months ago

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

##### Khushal Polepalle

**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.

- 3 months 3 weeks ago

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

##### Robert J. Scott

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

- 8 months 3 weeks ago

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

##### Urasa Kongdechakul

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 week 2 days ago

#### Clone of Royal Island- Resilience

##### marcus james thomson

Experiment with adjusting the moose birth-rate to simulate Over-shoot followed by environmental recovery

- 2 years 2 months ago

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

##### Scott Jorgensen

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

- 3 months 1 week ago

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

##### Peter Hungyu Lee

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

- 1 week 3 days ago

#### Clone of Lab 2 Part 3

##### Kaitlynne Thornton

- 5 months 4 days ago

#### Clone of Predator Prey

##### Kelsey Hasler

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

- 1 year 10 months ago

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

##### Jenny Pham

**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.

- 1 week 3 days ago

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

##### Casper Timmermans

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

- 9 months 2 weeks ago