UDB101 Assignment 1D  Koala Population Case Study  Sian Phillips
UDB101 Assignment 1D

Koala Population Case Study

Sian Phillips

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.
 The L ogistic Map  is a polynomial mapping (equivalently,  recurrence relation ) of  degree 2 , often cited as an archetypal example of how complex,  chaotic  behaviour can arise from very simple  non-linear  dynamical equations. The map was popularized in a seminal 1976 paper by the biologist  Rob

The Logistic Map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. The map was popularized in a seminal 1976 paper by the biologist Robert May, in part as a discrete-time demographic model analogous to the logistic equation first created by Pierre François Verhulst

Mathematically, the logistic map is written

where:

 is a number between zero and one, and represents the ratio of existing population to the maximum possible population at year n, and hence x0 represents the initial ratio of population to max. population (at year 0)r is a positive number, and represents a combined rate for reproduction and starvation. To generate a bifurcation diagram, set 'r base' to 2 and 'r ramp' to 1
To demonstrate sensitivity to initial conditions, try two runs with 'r base' set to 3 and 'Initial X' of 0.5 and 0.501, then look at first ~20 time steps

Modelagem do estado psicológico de uma população. Inicialmente, todos os indivíduos estão no estado "Calmo". Com o passar do tempo e com as interações mútuas, há o surgimento e progressivo aumento do total de indivíduos com raiva (estado "Raivoso"). Deste estado e, com o passar do tempo, os indivídu
Modelagem do estado psicológico de uma população. Inicialmente, todos os indivíduos estão no estado "Calmo". Com o passar do tempo e com as interações mútuas, há o surgimento e progressivo aumento do total de indivíduos com raiva (estado "Raivoso"). Deste estado e, com o passar do tempo, os indivíduos podem evoluir mentalmente e atingirem o estado "Indiferente", nos quais eles se tornam indiferentes à qualquer interação. Outra possibilidade é o indivíduo se enriquecer e, assim, atingir a felicidade (estado "Feliz"). (Esse modelo foi feito em conjunto com João Schoralick)
 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 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.

 The World3 model is a detailed simulation of human population growth from 1900 into the future. It includes many environmental and demographic factors. THIS MODEL BY GUY LAKEMAN, FROM METRICS OBTAINED USING A MORE COMPREHENSIVE VENSIM SOFTWARE MODEL, SHOWS CURRENT CONDITIONS CREATED BY THE LATEST W

The World3 model is a detailed simulation of human population growth from 1900 into the future. It includes many environmental and demographic factors.

THIS MODEL BY GUY LAKEMAN, FROM METRICS OBTAINED USING A MORE COMPREHENSIVE VENSIM SOFTWARE MODEL, SHOWS CURRENT CONDITIONS CREATED BY THE LATEST WEATHER EXTREMES AND LOSS OF ARABLE LAND BY THE  ALBEDO EFECT MELTING THE POLAR CAPS TOGETHER WITH NORTHERN JETSTREAM SHIFT NORTHWARDS, AND A NECESSITY TO ACT BEFORE THERE IS HUGE SUFFERING.
BY SETTING THE NEW ECOLOGICAL POLICIES TO 2015 WE CAN SEE THAT SOME POPULATIONS CAN BE SAVED BUT CITIES WILL SUFFER MOST. 
CURRENT MARKET SATURATION PLATEAU OF SOLID PRODUCTS AND BEHAVIORAL SINK FACTORS ARE ALSO ADDED

Use the sliders to experiment with the initial amount of non-renewable resources to see how these affect the simulation. Does increasing the amount of non-renewable resources (which could occur through the development of better exploration technologies) improve our future? Also, experiment with the start date of a low birth-rate, environmentally focused policy.

Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
  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.
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.


 FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION     BEWARE pushing increased growth blows the system!    (governments are trying to push growth on already unstable systems !)  The existing global capitalistic growth paradigm is totally flawed  The chaotic turbulence is the result of th
FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION 
 BEWARE pushing increased growth blows the system!
(governments are trying to push growth on already unstable systems !)

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept and flawed strategy of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)

Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."  ​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for
Adapted from Hartmut Bossel's "System Zoo 3 Simulation Models, Economy, Society, Development."

​Population model where the population is summarized in four age groups (children, parents, older people, old people). Used as a base population model for dealing with issues such as employment, care for the elderly, pensions dynamics, etc.
Influence of migration on the number of working-age population.
Influence of migration on the number of working-age population.
   THE 2017 MODEL (BY GUY LAKEMAN) EMPHASIZES THE PEAK IN POLLUTION BEING CREATED BY OVERPOPULATION WITH THE CARRYING CAPACITY OF ARABLE LAND NOW BEING 1.5 TIMES OVER A SUSTAINABLE FUTURE (PASSED IN 1990) AND NOW INCREASING IN LOSS OF HUMAN SUSTAINABILITY DUE TO SEA RISE AND EXTREME GLOBAL WATER REL

THE 2017 MODEL (BY GUY LAKEMAN) EMPHASIZES THE PEAK IN POLLUTION BEING CREATED BY OVERPOPULATION WITH THE CARRYING CAPACITY OF ARABLE LAND NOW BEING 1.5 TIMES OVER A SUSTAINABLE FUTURE (PASSED IN 1990) AND NOW INCREASING IN LOSS OF HUMAN SUSTAINABILITY DUE TO SEA RISE AND EXTREME GLOBAL WATER RELOCATION IN WEATHER CHANGES IN FLOODS AND DROUGHTS AND EXTENDED TROPICAL AND HORSE LATTITUDE CYCLONE ACTIVITY AROUND HADLEY CELLS

The World3 model is a detailed simulation of human population growth from 1900 into the future. It includes many environmental and demographic factors.

THIS MODEL BY GUY LAKEMAN, FROM METRICS OBTAINED USING A MORE COMPREHENSIVE VENSIM SOFTWARE MODEL, SHOWS CURRENT CONDITIONS CREATED BY THE LATEST WEATHER EXTREMES AND LOSS OF ARABLE LAND BY THE  ALBEDO EFECT MELTING THE POLAR CAPS TOGETHER WITH NORTHERN JETSTREAM SHIFT NORTHWARDS, AND A NECESSITY TO ACT BEFORE THERE IS HUGE SUFFERING.
BY SETTING THE NEW ECOLOGICAL POLICIES TO 2015 WE CAN SEE THAT SOME POPULATIONS CAN BE SAVED BUT CITIES WILL SUFFER MOST. 
CURRENT MARKET SATURATION PLATEAU OF SOLID PRODUCTS AND BEHAVIORAL SINK FACTORS ARE ALSO ADDED

Use the sliders to experiment with the initial amount of non-renewable resources to see how these affect the simulation. Does increasing the amount of non-renewable resources (which could occur through the development of better exploration technologies) improve our future? Also, experiment with the start date of a low birth-rate, environmentally focused policy.

Modeling water saving potential with urban planning, demand management practice, and alternative technologies
Modeling water saving potential with urban planning, demand management practice, and alternative technologies
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.
Just a little model put together for training purposes
Just a little model put together for training purposes
 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 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.

  ​Predator-prey
models are the building masses of the bio-and environments as bio
masses are become out of their asset masses. Species contend, advance and
scatter essentially to look for assets to support their battle for their very
presence. Contingent upon their particular settings of uses, they

​Predator-prey models are the building masses of the bio-and environments as bio masses are become out of their asset masses. Species contend, advance and scatter essentially to look for assets to support their battle for their very presence. Contingent upon their particular settings of uses, they can take the types of asset resource-consumer, plant-herbivore, parasite-have, tumor cells- immune structure, vulnerable irresistible collaborations, and so on. They manage the general misfortune win connections and thus may have applications outside of biological systems. At the point when focused connections are painstakingly inspected, they are regularly in actuality a few types of predator-prey communication in simulation. 

 Looking at Lotka-Volterra Model:

The well known Italian mathematician Vito Volterra proposed a differential condition model to clarify the watched increment in predator fish in the Adriatic Sea during World War I. Simultaneously in the United States, the conditions contemplated by Volterra were determined freely by Alfred Lotka (1925) to portray a theoretical synthetic response wherein the concoction fixations waver. The Lotka-Volterra model is the least complex model of predator-prey communications. It depends on direct per capita development rates, which are composed as f=b−py and g=rx−d. 

A detailed explanation of the parameters:

  • The parameter b is the development rate of species x (the prey) without communication with species y (the predators). Prey numbers are reduced by these collaborations: The per capita development rate diminishes (here directly) with expanding y, conceivably getting to be negative. 
  • The parameter p estimates the effect of predation on x˙/x. 
  • The parameter d is the death rate of species y without connection with species x. 
  • The term rx means the net rate of development of the predator population in light of the size of the prey population.

Reference:

http://www.scholarpedia.org/article/Predator-prey_model

 

Simulation of MTBF with controls   F(t) = 1 - e ^ -λt   Where    • F(t) is the probability of failure    • λ is the failure rate in 1/time unit (1/h, for example)   • t is the observed service life (h, for example)  The inverse curve is the trust time On the right the increase in failures brings its
Simulation of MTBF with controls

F(t) = 1 - e ^ -λt 
Where  
• F(t) is the probability of failure  
• λ is the failure rate in 1/time unit (1/h, for example) 
• t is the observed service life (h, for example)

The inverse curve is the trust time
On the right the increase in failures brings its inverse which is loss of trust and move into suspicion and lack of confidence.
This can be seen in strategic social applications with those who put economy before providing the priorities of the basic living infrastructures for all.

This applies to policies and strategic decisions as well as physical equipment.
A) Equipment wears out through friction and preventive maintenance can increase the useful lifetime, 
B) Policies/working practices/guidelines have to be updated to reflect changes in the external environment and eventually be replaced when for instance a population rises too large (constitutional changes are required to keep pace with evolution, e.g. the concepts of the ancient Greeks, 3000 years ago, who based their thoughts on a small population cannot be applied in 2013 except where populations can be contained into productive working communities with balanced profit and loss centers to ensure sustainability)

Early Life
If we follow the slope from the leftmost start to where it begins to flatten out this can be considered the first period. The first period is characterized by a decreasing failure rate. It is what occurs during the “early life” of a population of units. The weaker units fail leaving a population that is more rigorous.

Useful Life
The next period is the flat bottom portion of the graph. It is called the “useful life” period. Failures occur more in a random sequence during this time. It is difficult to predict which failure mode will occur, but the rate of failures is predictable. Notice the constant slope.  

Wearout
The third period begins at the point where the slope begins to increase and extends to the rightmost end of the graph. This is what happens when units become old and begin to fail at an increasing rate. It is called the “wearout” period. 
 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.