mymodel

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## ABSTRACT

The agent model modeling is an abstract design technique used to understand and comprehend a complex system having many feedback loops with many agents. In the competitive grazer model, the system dynamics modeling helps to understand the behavior of the territory having two species, namely Cows and Moose. The model includes both positive and negative feedback. The positive feedback follows the increment in population as per the growth rate. As the grass reduces or the energy of the species goes to zero, the population dampened and reduced due to death, which becomes apparent through a negative feedback loop. The growth of the species only grows with the population following the exponential distribution. Lastly, the outcome of the competition grazer model that the competitive advantage of a species will continue to change when all individuals are identical to each other.This model explores the stability of critter grazer ecosystems. Such a system is called unstable if it tends to result in extinction for one or more species involved. In contrast, a system is stable if it tends to maintain itself over time, despite fluctuations in population sizes.

## INTRODUCTION

The "cow-moose-grass" model explictly models grass (green) in addition to cows and moose. The behavior of the mooses is identical to the first variation, however this time the cows must eat grass in order to maintain their energy - when they run out of energy they die. Once grass is eaten it will only regrow after a fixed amount of time. This variation is more complex than the first, but it is generally stable. It is a closer match to the classic Lotka Volterra population oscillation models. The classic LV models though assume the populations can take on real values, but in small populations these models underestimate extinctions and agent-based models such as the ones here, provide more realistic results. (See Wilensky & Rand, 2015; chapter 4).

The construction of this model is described in two papers by Wilensky & Reisman (1998; 2006) referenced below.

## HOW TO USE IT

1. Set the model-version chooser to "cows-mooses-grass" to include grass eating and growth in the model, or to "cows-mooses" to only include mooses (black) and cows (white).

2. Adjust the slider parameters (see below), or use the default settings.

3. Press the SETUP button.

4. Press the GO button to begin the simulation.

5. Look at the monitors to see the current population sizes

6. Look at the POPULATIONS plot to watch the populations fluctuate over time

Parameters:

INITIALCows: The initial size of cows population

INITIALMooses: The initial size of moose population

GRASS-REGROWTH-Rate: How long it takes for grass to regrow once it is eaten (Note this is not used in the cows-mooses model version)

Assumptions:

- Two unit of energy is deducted for every step a moose takes while three unit is deducted for 3 units a cow takes

There are three monitors to show the populations of the mooses, cows and grass and a populations plot to display the population values over time.

If there are no mooses left and too many cows, the model run stops.

## REFERENCES

Wilensky, U. & Reisman, K. (1998). Connected Science: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. International Journal of Complex Systems, M. 234, pp. 1 - 12. (The moose-cows-Predation model is a slightly extended version of the model described in the paper.)

Wilensky, U. & Reisman, K. (2006). Thinking like a moose, a cows or a Firefly: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. Cognition & Instruction, 24(2), pp. 171-209. http://ccl.northwestern.edu/papers/moosecows.pdf .

Wilensky, U., & Rand, W. (2015). An introduction to agent-based modeling: Modeling natural, social and engineered complex systems with NetLogo. Cambridge, MA: MIT Press.

Lotka, A. J. (1925). Elements of physical biology. New York: Dover.

Volterra, V. (1926, October 16). Fluctuations in the abundance of a species considered mathematically. Nature, 118, 558–560.

Gause, G. F. (1934). The struggle for existence. Baltimore: Williams & Wilkins.

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Click to Run Model 

breed [cows cow]
breed [mooses moose]

turtles-own [ energy ]  ;; agents own energy
patches-own [ grass-amount]  ;; patches have grass

;; this procedures sets up the model

to setup
  clear-all
  ask patches [
    ;; give grass to the patches, color it shades of green
     set pcolor one-of [ green brown ]
     ifelse pcolor = green
        [ set grass-amount GrassReGrowthRate]
      [ set grass-amount random-float 10.0 ] ; initialize grass regrowth clocks randomly for brown patches
  ]
  create-cows InitialCows [  ;; create the initial Cow
    setxy random-xcor random-ycor
    set color white
    set shape "cow"
    set size 1.5  ; easier to see
    set label-color blue - 2
    set energy 50  ;; set the initial energy to 50
  ]
  create-mooses InitialMoose [  ;; create the initial Moose
    setxy random-xcor random-ycor
    set color black
    set shape "wolf"
    set size 1 ;; increase their size so they are a little easier to see
    set energy 50  ;; set the initial energy to 50
  ]
  reset-ticks
end 

;; make the model run

to go
  if not any? turtles [  ;; now check for any turtles, that is both cows and moose
    stop
  ]
  ask cows [
    move
    set energy energy - 3  ;
    eat-grass  ;
    death ;
    reproduce-cows ;
  ]
  ask mooses [
    move
    set energy energy - 2  ; =
    eat-grass  ;
    death ;
    reproduce-mooses ;
  ]
  ask patches [ grow-grass ]
  my-update-plots
  tick
end 

to move  ; turtle procedure
  rt random 50
  lt random 50
  fd 1
end 

to eat-grass  ;
  ; eat grass and turn the patch brown
  if pcolor = green [
    set pcolor brown
    set energy energy + 10 ; turtle gain energy by eating
  ]
end 

to reproduce-cows
  if energy > 50 [
    set energy (energy - CowBirthRate)  ;; reproduction transfers energy

    hatch CowBirthRate [ set energy 50 ] ;; to the new agent
  ]
end 

to reproduce-mooses
  if energy > 50 [
    set energy (energy - MooseBirthRate)  ;; reproduction transfers energy
    hatch MooseBirthRate [ set energy 50] ;; to the new agent
  ]
end 

to death  ; turtle procedure
  ; when energy dips below zero, die
  if energy < 0 [ die ]
end 

to grow-grass  ; patch procedure
  ; countdown on brown patches: if you reach 0, grow some grass
  if pcolor = brown [
    ifelse grass-amount <= 0
      [ set pcolor green
        set grass-amount GrassReGrowthRate ]
      [ set grass-amount grass-amount - 1 ]
  ]
end 

to-report grass
    report patches with [pcolor = green]
end 

;; update the plots

to my-update-plots
  set-current-plot-pen "cows"
  plot count cows
  set-current-plot-pen "moose"
  plot count mooses * 2 ;; scaling factor so plot looks nice
  set-current-plot-pen "grass"
  plot sum [ grass-amount ] of patches / 50 ;; scaling factor so plot looks nice
end

There is only one version of this model, created over 3 years ago by Sai Sruthi Tatineni.

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