3.9-voter-model-with-mutation.nlogo

;; The MIT License (MIT)
;;
;; Copyright (c) 2011-24 David O'Sullivan and George Perry
;;
;; Permission is hereby granted, free of charge, to any person
;; obtaining a copy of this software and associated documentation
;; files (the "Software"), to deal in the Software without restriction,
;; including without limitation the rights to use, copy, modify, merge,
;; publish, distribute, sublicense, and/or sell copies of the Software,
;; and to  permit persons to whom the Software is furnished to do so,
;; subject to the following conditions:
;;
;; The above copyright notice and this permission notice shall be included
;; in all copies or substantial portions of the Software.
;;
;; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
;; OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
;; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
;; THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
;; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
;; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
;; DEALINGS IN THE SOFTWARE.
;;


breed [
  states state ;; use these to store model states and associated colours
]

globals [
  N
  all-states-ever
]

patches-own [
  my-state ;; a reference to a state turtle
]


to setup
  clear-all

  set N count patches
  ;; create a set of initial possible states
  create-states initial-n-states [
    set hidden? true
    ;; note that random default colours are limited below 140 available
    set color random 140
  ]
  set all-states-ever initial-n-states
  ask patches [
    ;; set patch state and colour at random
    set my-state one-of states
    set pcolor [color] of my-state
  ]
  reset-ticks
end


to go
  if count states = 1 [ stop ]
  repeat N [
    ask one-of patches [
      update-state
      set pcolor [color] of my-state
    ]
  ]
  reorganise-states
  tick
end


;; tidy up the current set of states
;; to reflect disappearance of some from the system
to reorganise-states
  ask states [
    if not any? patches with [my-state = myself] [
      die
    ]
  ]
  clear-output
  output-print reduce [ [s1 s2] -> (word s1 "\n" s2) ] lput "" sort [who] of states
end


;; the main code
to update-state
  let choice get-weighted-choice
  if choice = 1 [ ;; local update
    set my-state [my-state] of one-of neighbors4
    stop ;; don't waste time testing for other choices
  ]
  if choice = 2 [ ;; non-local update
    set my-state [my-state] of one-of patches with [ not (self = myself) ]
    stop
  ]
  if choice = 3 [ ;; mutation
    ;; make a new state
    sprout-states 1 [
      set hidden? true
      set color random 140
      set my-state self
    ]
    set all-states-ever all-states-ever + 1
  ]
end


to-report get-weighted-choice
  let x random-float 1
  if x < (1 - p-mutate - p-global-dispersal) [ report 1]
  if x < (1 - p-mutate) [report 2]
  report 3
end


;; plotting code if needed
;to r-plot-world
;  reorganise-states
;  let z map [position ([my-state] of ?) sort states] (sort patches)
;  r:put "z" z
;  let n-states count states
;  r:put "nr" world-height
;  r:put "nc" world-width
;  r:put "n_states" n-states
;  r:eval("map <- matrix(z, ncol=nc, nrow=nr)")
;  r:eval("image(map, col=grey(seq(n_states,0,-1)/n_states), asp=1, axes=F)")
;end
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"" ""
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@#$#@#$#@
## WHAT IS IT?

This is an implementation of a simple two dimensional voter model with the chance of site update to the state of a randomly selected non-neighbouring cell, or random mutation of site state to a new state not present in the system.

This model is discussed in Chapter 3 of

+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.

You should consult that book for more information and details of the model.

## THINGS TO NOTICE

This model uses some novel NetLogo techniques.

First, 'dummy' `state` turtles are used to store the states in the model. This has the advantage of making it easy to manage colours for the states, since each state turtle has an associated colour. It would also be possible to maintain a list of colours for the states present in the system, but managing two lists (one of states and one of colours) gets fiddly especially when states disappear. Since we don't need turtles as 'agents', we can use them for this instead, and have each patch maintain a reference (`my-state`) to the `state` turtle it is associated with.

If we knew that the total number of states ever in the system would not get large, we could use this 'trick' to make keeping track of the count of all states that ever existed in the system simple (it would be given by `count states`).  Because the number of states can get large it is better to kill off unused states, which is done in the `reorganise-states` procedure, and we maintain a global count variable `all-states-ever`.

Second, for non-local updates, the obvious approach would be to use

    set my-state [my-state] of one-of other patches

in the `update-state` procedure, but this turns out to be slow, presumably due to the internal implementation of patch-sets in NetLogo.  Instead, we provide our own reporter

    to-report random-other-patch
      let p self
      while [p = self] [ ;; try again
        set p one-of patches
      ]
      report p
    end

which avoids the `other patches` problem.  Occasionally, it will have to 'try again' to pick a patch if the first pick `p` is the same as `self` but compared to the overhead of using `one-of other patches` every time there is a big improvement in speed.

## THINGS TO TRY

**Hard!** It's interesting in this model to explore the interactions between the durability of mutations and non-local propagation.  Think about how you might conduct experiments on this relationship.

## HOW TO CITE

If you mention this model in a publication, please include these citations for the model itself and for NetLogo

+   O'Sullivan D and Perry GLW 2013 _Spatial Simulation: Exploring Pattern and Process_. Wiley, Chichester, England.
+   Wilensky U 1999 NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
## COPYRIGHT AND LICENSE

The MIT License (MIT)

Copyright &copy; 2011-24 David O'Sullivan and George Perry

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to  permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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