range expansion

1 collaborator

WHAT IS IT?

This is a model of range expansion of organisms in space. It is an implementation of paper of Edmonds2004 (see references).

HOW IT WORKS

Here one wild individual is create in left boundary with longitude=1 and random latitude. The life cycle is: reproduce with number of children following poisson distribution with parameter g. Each new individual can stay in the same patch that his parent with probability 1-migration or new individual can migrate to n neighbours with probability migration/n. The first individual that reach in green patch becomes mutant. The rules are the same for mutants and wilds. If population in patch is bigger than carrying capacity a random individual is choice to die until reach carrying capacity.

HOW TO USE IT

Click in setup and go

THINGS TO NOTICE

This is a stochastic model so every time is different realization. Try some times with the same set of parameters to see what happen. Sometimes the mutants are extinct, sometimes mutants are bigger than wild. The size of patches occupied by mutants also varying.

THINGS TO TRY

Try put migration rate bigger, the time to finish should be less.

EXTENDING THE MODEL

(suggested things to add or change in the Code tab to make the model more complicated, detailed, accurate, etc.)

NETLOGO FEATURES

This is first implementation. The model here does not follow exactly the paper. Just qualitative behavior looks like the same of paper

RELATED MODELS

CREDITS AND REFERENCES

For any commentary write to me carlostomate at gmail.com

Christopher A. Edmonds, Anita S. Lillie, and L. Luca Cavalli-Sforza Mutations arising in the wave front of an expanding population PNAS 2004 101 (4) 975-979; published ahead of print January 19, 2004, doi:10.1073/pnas.0308064100

Comments and Questions

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Click to Run Model

extensions[profiler] 
extensions[bitmap]
extensions[matrix]

globals [ arrive arrived chance-to-stay    x y c bd mutx muty  t.dimension]
;turtles-own[]

to setup 
  clear-all
  create-turtles 1 
  ask turtles [ setxy 0 random-ycor set color violet + 3 set shape "dot"]
  set chance-to-stay 1 - migration
   
  
    ; point of mutation
  set mutx 10
  set muty random-ycor
  ask patch  mutx muty [set pcolor green]
  set arrive false
  set arrived false
  reset-ticks
  set x 0
  set y 0
  set c 0
end 

to go   
  ;profiler:start
    reproduce-turtles
    ask patch mutx muty[if any? turtles-here [set arrive true]]
    if arrive = true[ 
                      if arrived = false
                           [ask patch mutx muty [ask turtles-here [set color blue]] 
                            ask turtles [set arrived true]
                           ]
                            ]
    cut2 
    tick
   ;profiler:stop
   ;print profiler:report
   ;profiler:reset
end 

to reproduce-turtles
       ask turtles [hatch random-poisson g [
                                         if random-float 1.0 < chance-to-stay
                                          [stop] 
         
                                         let neigb count neighbors4 
                                          if random-float 1.0 <  migration / neigb 
                                           [rt one-of [0 90 180 270] fd 1]
                                        ] 
                   ]    
end 

to cut2
  ask patches[
  let lista 0
  let num-turtles count turtles-here
  let diff num-turtles - carrying-capacity
  
  if  diff > 0
     [ repeat diff [
                 ask turtles-here [set lista [who] of turtles-here]
                 let to-die one-of lista
                 ask turtle to-die [die]]
     ]
  ]
end 

to-report howmany
  let how 0
  ask patch 0 0 [set how count turtles-here]
   report how
end 

to-report total 
  let total-t 0
  ask turtles [set total-t count other turtles]
  report total
end 

to-report time
  report ticks
end 

to-report extinction
     let extinct false
    if not any? turtles with [color = blue] and arrived = true
    [set extinct true]
    report extinct
end 

;to-report turtlesdimension
 ;  
 ; ask turtles [set x [xcor] of turtles
  ;             set y [ycor] of turtles
   ;            set c [color]of turtles]
  
   ;ask turtles [set t.dimension matrix:from-column-list [[x] [y] [c]]]
 ;report t.dimension
;end
 ;; not in use
  ;;
;to blue-dimension
 ;    
  ;    if any? turtles with [color = blue]
   ;     [ask one-of turtles [set bd-max-x max [xcor] of turtles with [color = blue]
;                      set bd-min-x min  [xcor] of turtles with [color = blue]
;                      set bd-max-y max [ycor] of turtles with [color = blue]
;                      set bd-max-y min [ycor] of turtles with [color = blue]
;                      ]
;        ]
;       
;  print (list bd-max-x bd-min-x bd-max-y bd-min-y)
;end
 


 
  ;;
  ;;
  ;;
  ;;
  ;;
  ;;
  
  ;to cut
  ;let num-turtles count turtles 
  ;:if num-turtles <= carrying-capacity
  ;[stop]
  
  ;let chance-to-die ( num-turtles - carrying-capacity)/ num-turtles
  ;ask turtles 
  ;[
   ; if random-float 1.0 < chance-to-die
   ; [die]
  ;]
  
;end

to move-turtles
  ask turtles[
       ; let chance-to-stay 1 - migration
        if random-float 1.0 < chance-to-stay
         [stop] 
         
        let neigb count neighbors4 
        if random-float 1.0 <  migration / neigb 
         [rt one-of [0 90 180 270] fd 1]
         ]     
end 

to reproduce-turtles2
    ask turtles [hatch random-poisson 2 []]    
end

There is only one version of this model, created over 10 years ago by carlos tonhatti.

Attached files

File	Type	Description	Last updated
range expansion.png	preview	Preview for 'range expansion'	over 10 years ago, by carlos tonhatti	Download

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