#### Isle Royale: Predator Prey Interactions

##### Scott Fortmann-Roe

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

- 4 years 9 months ago

#### Prey&Predator

##### Tsogbadrakh Banzragch

**Physical meaning of the equations**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 years 4 months ago

#### Spring and fall bloom

##### Hans Røy

**Introduction**

Simple model of the spring bloom in coastal temperate coastal waters. Nitrogen is assumed to be the limiting nutrient, so the model is based on N only. The model represents one liter of water. Dissolved inorganic nitrogen (DIN) accumulates in the water column during winter and has reached 250 µmol/L on March 1st where the model starts. At this time the light intensity have just reached the level necessary to initiate the bloom.

**Model setup**

N uptake: Michaelis Menten kinetics with a maximum growth rate that doubles the population each day. Km=5µM.

Grazing: Michaelis Menten kinetics with a maximum daily uptake equal to the N in the population. Km=50µM.

Sloppy eating: 60% of the grazing is wasted to PON

Death: 5% of the zooplankton dies each day

Mineralization: 1% of the PON is mineralized to DIN each day

**Results**

For the first 6 days the phytoplankton grows exponentially and depletes the DIN pool. The peak in phytoplankton is followed by a delayed peak in zooplankton due to its slower growth rate. Slowly the zooplankton graze down the spring bloom and the nitrogen is transformed to the pool of particulate dead organic nitrogen (PON). While this happens the phytoplankton is kept low by the still high zooplankton which allow the DIN pool to increase from day 25 to day 55. Eventually the phytoplankton escapes the top down control and we see a secondary bloom based on regenerated DIN.

- 5 years 1 month ago

#### The probability density function (PDF) of the normal distribution or Bell Curve Gaussian Distribution by Guy Lakeman

##### Guy Lakeman

**The probability density function (PDF) of the normal distribution or Bell Curve of Normal or Gaussian Distribution is the mean or expectation of the distribution (and also its median and mode).**

The parameter is its standard deviation with its variance then, A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.However, those who enjoy upskirts are called deviants and have a variable distribution :)

A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.

If mu = 0 and sigma = 1

If the Higher Education Numbers Are Increased then the group decision making ability of society would be raised above that of a middle teenager as it is nowBUT Governments can control children by using bad parenting techniques, pandering to the pleasure principle, so they will make higher education more and more difficult as they are doing

85% of the population has a qualification level equal or below a 12th grader, 17 year old ... the chance of finding someone with any sense is low (~1 in 6) and the outcome of them being chosen by those who are uneducated in the policies they are to decide is even more rare !!!

Experience means little if you don't have enough brain to analyse it

Democracy is only as good as the ability of the voters to FULLY understand the implications of the policies on which they vote., both context and the various perspectives. National voting of unqualified voters on specific policy issues is the sign of corrupt manipulation.

Democracy: Where a group allows the decision ability of a teenager to decide on a choice of mis-representatives who are unqualified to make judgement on social policies that affect the lives of millions.The kind of children who would vote for King Kong who can hold a girl in one hand and swat fighter jets out of teh sky off the tallest building, doesn't have a brain cell or thought to call his own but has a nice smile and offers little girls sweets.

updated 16/3/2020 from 4 years 3 months ago

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

- 11 months 3 weeks ago

#### Plant, Deer and Wolf Population Dynamics

##### leah c

- 4 years 7 months ago

#### Bio 190: BIDE Model With Carrying Capacity

##### Todd Levine

This is a basic BIDE (birth, immigration, death, emigration) model. Not all parts are implemented, however Birth and Death are.

- 6 years 5 months ago

#### Transformative Agency in Social-Ecological System

##### Geoff McDonnell ★

**18**(3): 27. link

- 8 months 1 week ago

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

##### John Evans

- 3 years 5 months ago

#### Predator Prey

##### Scott Fortmann-Roe

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

- 6 years 5 months ago

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

##### Jacek Chmielewski

**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 years 6 months ago

#### Story Telling - Deer Management Under Climate Change

##### Rob Rempel

The purpose of this deer management model is to explore the capacity of wildlife management actions to help us adapt to the effects of climate change.

Environment Ecology Climate Change Deer Cervids Wildlife Management

- 4 years 2 weeks ago

#### YellowstoneEcoClassModel

##### Esther

- 6 years 3 months ago

#### Climate Sector Boundary Diagram of Guy Lakeman

##### Guy Lakeman

**Climate Sector Boundary Diagram By Guy Lakeman**Climate, Weather, Ecology, Economics, Population, Welfare, Energy, Policy, CO2, Carbon Cycle, GHG (green house gasses, combined effects)

As general population is composed of 85% with an education level of a 12 grader or less (a 17 year old), a simple block of components concerning the health of the planet needs to be broken down into simple blocks.Perhaps this picture will show the basics on which to vote for a sustained healthy futureDemocracy is only as good as the ability of the voters to FULLY understand the implications of the policies on which they vote., both context and the various perspectives. National voting of unqualified voters on specific policy issues is the sign of corrupt manipulation.

Climate Weather Ecology Economics Population Welfare Energy Policy CO2 Carbon GHG Green House Gas

- 5 years 2 months ago

#### Population - BIDE

##### Todd Levine

- 8 years 1 month ago

#### Northern Ontario Demographic and Income Trend Model

##### Steve Williams

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.

- 4 years 4 months ago

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

##### Kevin Collins

- 3 years 4 months ago

#### Levels of transition needed to sustainability

##### Ruan Malan

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

- 6 years 5 months ago

#### Caribou Conservation Triage-V2

##### Rob Rempel

This model was developed by Rob Rempel and Jen Shuter at the Centre for Northern Forest Ecosystem Research, and was based in part on input from attendees of a modelling workshop ("Modelling the Caribou Questions") held at the 16th North American Caribou Workshop in Thunder Bay, Ontario, May 2016.

- 1 year 5 months ago

#### Marine Biocontrol in vector hubs

##### Javier Atalah

- 3 years 7 months ago

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

##### John Petersen

**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 10 months ago

#### Bio 101: Basic Population Model

##### Todd Levine

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

- 8 years 2 months ago

#### lynx v. snowshoe hare

##### K Phu

- 5 years 10 months ago

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

##### Andrew E Long

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.};

- 3 years 1 week ago

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

##### Guy Lakeman

**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

- 11 months 3 weeks ago