#### Dufek Isle Royale: Predator Prey Interactions

##### Sally Dufek

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

- 2 years 10 months ago

#### Clone of Clone of Levels of transition needed to sustainability

##### Charles Anosike

This diagram attempts to summarize levels of self reinforcing destructive dynamics, authors that deal with them, and point of leverage for change.

The base of the crisis is a mechanistic rather than ecological worldview. This mechanistic worldview is based on outdated science that assumed the universe to be a large machine. In a machine there is an inside and an outside. The health of the inside is important for the machine, the outside not. In an ecological view everything is interconnected, there is no clear separation in the future of self and other. All parts influence the health of other parts. To retain health sensitivity and democracy are inherent. The sense of separation from other that keeps the mechanistic worldview dominant is duality. Being cut off from spiritual traditions due to a mechanistic view of science people need access to inter-spirituality to reconnect with the human traditions and tools around connectedness, inner discovery, and compassion. Many books on modern physics and biology deal with the system view implications. "The coming interspiritual age" deals with the need to connect spiritual traditions and science.

At the bottom for the dynamic is an individual a sense of disconnectedness leads to a dependency on spending and having rather than connecting. The connecting has become too painful and dealing with it unpopular in our culture. Joanna Macy deals with this in Active Hope.

This affluenza and disconnection is worsened by a market that floods one with advertisements aimed at creating needs and a sense of dissatisfaction with that one has.

National economies are structured around maximising GDP which means maximising consumption and financial capital movement. This is at the cost of local economies. These same local economies are needed for balanced happiness as well as for sustainability.

Generally institutions focus on maximising consumption rather than sustaining life support systems. David Korten covers this well.

Power and wealth is confused in this worldview. In striving for wealth only power is striven for in the form of money and monopoly.

Those at the head of large banks and corporations tend to be there because they exemplify this approach. They have few scruples about enforcing this approach onto everyone through wars and disaster capitalism. Naomi Klein and David Estulin documented this.

Power has become so centralized that we need this understanding to be widespread and include many of those in power. Progress of all of these levels are needed to show them and all that another way is possible.

Environment Power Capitalism Exploitation Affluenza Sustainability Crisis Ecology Transition The Great Turning

- 7 years 2 months ago

#### Limnología

##### Andrea Fandiño

- 2 years 9 months ago

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

##### Bob Jones

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

- 5 years 8 months ago

#### Coral Reef Population

##### Dana Murtada

Experiment with adjusting the initial number of corals on the island.

- 9 months 2 weeks ago

#### Food Web of Pennsylvania State Organisms

##### Ashley Cassano

- 1 year 8 months ago

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

##### Bob Jones

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

- 5 years 9 months ago

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

##### Valerya

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

- 6 years 6 months ago

#### Prey&Predator

##### ilya

**Физический смысл уравнений**

**Модель Лотки-Вольтерры делает ряд предположений об окружающей среде и эволюции популяций хищников и жертв:**

1. Хищная популяция всегда находит достаточно пищи.2. Продовольственная обеспеченность популяции хищника полностью зависит от размера популяции жертвы.3. Скорость изменения численности населения пропорциональна его численности.4. В ходе этого процесса окружающая среда не меняется в пользу одного вида, и генетическая адаптация не имеет существенного значения.5. Хищники обладают безграничным аппетитом.Поскольку используются дифференциальные уравнения, решение является детерминированным и непрерывным. Это, в свою очередь, означает, что поколения как хищника, так и жертвы постоянно пересекаются.

**Добыча**Когда умножается, уравнение добычи становится

dx/dt = αx - βxy Предполагается, что добыча имеет неограниченный запас пищи и размножается экспоненциально, если только она не подвержена хищничеству; этот экспоненциальный рост представлен в приведенном выше уравнении термином αx. Предполагается, что скорость хищничества на добыче пропорциональна скорости, с которой встречаются хищники и добыча; это представлено выше в виде βxy.Если либо x, либо y равно нулю, то хищничества быть не может.С помощью этих двух терминов приведенное выше уравнение можно интерпретировать следующим образом: изменение численности добычи определяется ее собственным ростом минус скорость, с которой она охотится.ХищникиУравнение хищника становится

dy/dt = -

В этом уравнении, представляет рост популяции хищника. (Обратите внимание на сходство со скоростью хищничества; однако используется другая константа, поскольку скорость роста популяции хищника не обязательно равна скорости, с которой он потребляет добычу). представляет собой уровень потерь хищников вследствие естественной смерти или эмиграции; это приводит к экспоненциальному распаду в отсутствие добычи.

Следовательно, уравнение выражает изменение популяции хищников как рост, подпитываемый запасом пищи, минус естественная смерть.

- 1 year 1 month ago

#### Clone of MAT 375 Midterm file: 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.

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 10 months ago

#### MAT375 Clone of Bio103 Predator-Prey Model ("Lotka'Volterra")

##### Andrew E Long

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

Tags: Education, Chaos, Ecology, Biology, PopulationThanks to Insight Author: John Petersen

Edits by Andy Long

Everything that follows the dashes was created by John Petersen (or at least came from his Insight model). I just wanted to make a few comments.

We are looking at Hare and Lynx, of course. Clone this insight, and change the names.

Then read the text below, to get acquainted with one of the most important and well-known examples of a simple system of differential equations in all of mathematics.

http://www.nku.edu/~longa/classes/mat375/mathematica/Lotka-Volterra.nb------------------------------------------------------------

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 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.

Education Chaos Ecology Biology Population Mat375 Lotka Volterra

- 10 months 4 days ago

#### Clone of Bio 101: Basic Population Model

##### ruta

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

- 5 years 9 months ago

#### Food Web

##### Brandon Nguyen

- 4 years 10 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.

- 1 year 6 months ago

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

##### franzol

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

- 5 years 8 months ago

#### Clone of Insect Pest Control

##### Ivo Velitchkov

Implications of spraying pesticides to control insects. http://bit.ly/diYPED

- 8 years 2 months ago

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

##### Eliecer Alvarado Rodriguez

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

- 6 years 2 months 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

- 2 years 10 months ago

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

##### Stefan Koester

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

- 4 years 2 months ago

#### Clone of Clone of BirthRateDeathRateAndR

##### Dylan

- 7 years 9 months ago

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

##### Gulyaeva Kseniya

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

- 6 years 6 months ago

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

##### Eliecer Alvarado Rodriguez

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

- 6 years 2 months ago

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

##### Lindsey Watch

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

- 10 months 3 weeks ago

#### Predator Prey Dynamics

##### Osman Murat Anlı

- 1 year 3 weeks ago