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.
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.
   ​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 Gaussi
​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 now
BUT 
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
Westley, F. R., O. Tjornbo, L. Schultz, P. Olsson, C. Folke, B. Crona and Ö. Bodin. 2013. A theory of transformative agency in linked social-ecological systems.  Ecology and Society   18 (3): 27.  link
Westley, F. R., O. Tjornbo, L. Schultz, P. Olsson, C. Folke, B. Crona and Ö. Bodin. 2013. A theory of transformative agency in linked social-ecological systems. Ecology and Society 18(3): 27. link

 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 rea
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.
 ​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
​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 becomes
dx/dtαx - 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.

Predators

The 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.


This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
 This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

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

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.


This model describes how costs, income and ecosystem services change with stocking rate.
This model describes how costs, income and ecosystem services change with stocking rate.
14 11 months ago
    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 int

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 becomes
dx/dtαx - 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.

Predators

The 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.


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

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

 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

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.

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at  https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions  Thanks Scott Fortmann-Roe.
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at
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.};

A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
    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 int

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 becomes
dx/dtαx - 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.

Predators

The 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.


This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
  ​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),
​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 future
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.

 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.

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.

This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.
This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.


This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
 This is a basic model for use with our lab section.  The full BIDE options.

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

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

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

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.
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.