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File:Predator-prey toy model.gif

Original file (576 × 489 pixels, file size: 6.35 MB, MIME type: image/gif, looped, 244 frames, 24 s)

Summary

Description
English: An extremely simple predator-prey toy model. At each time step each pray (black dot) has a chance to duplicate, but is eaten if within a distance from predator (red circle). Predators can also duplicate, but have a chance to die, if they don't eat. To avoid the predator extinction one can either fine-tune the parameter, or build a more complex model.
Date
Source https://twitter.com/j_bertolotti/status/1424778017902039054
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929
GIF development
InfoField
 This diagram was created with Mathematica.

Mathematica 12.0 code

nprey = 2*10^3; npredator = 5; predatorradius = 0.3; stepprey = 0.2; steppredator = 0.2;
prey0 = RandomReal[{-10, 10}, {nprey, 2}];
predator0 = RandomReal[{-10, 10}, {npredator, 2}];
prey = prey0; predator = predator0;
probpreybreed = 0.025; probpredatordie = 0.2; probpredatorbreed = 0.2;
histnprey = {}; histnpredator = {};
evo = Reap[
    Do[
      feedingpredators = Table[0, npredator];
      For[j = 1, j <= npredator, j++,
       feeding = Position[Norm[# - predator[[j]]] & /@ prey, x_ /; (x < predatorradius)];
       prey = Delete[prey, feeding];
       If[Total[Flatten@feeding] > 0, feedingpredators[[j]] = 1];
        ];
      random = RandomReal[{0, 1}, npredator];
      dyingpredators = Position[random, x_ /; (x <= probpredatordie)];
      dyingpredators = DeleteCases[ Abs[(feedingpredators[[Flatten@dyingpredators]] - 1)*dyingpredators], {0}];
      predator = Delete[predator, dyingpredators];
      nprey = Dimensions[prey][[1]]; 
      npredator = Dimensions[predator][[1]];
      
      random = RandomReal[{0, 1}, npredator];
      breedingpredators = Flatten@Position[random, x_ /; (x <= probpredatorbreed)];
      predator = Join[predator, predator[[breedingpredators]] ];
      nprey = Dimensions[prey][[1]]; 
      npredator = Dimensions[predator][[1]];
      
      random = RandomReal[{0, 1}, nprey];
      breedingpreys = Flatten@Position[random, x_ /; (x <= probpreybreed)];
      prey = Join[prey, prey[[breedingpreys]] ];
      nprey = Dimensions[prey][[1]]; 
      npredator = Dimensions[predator][[1]];
      
      prey = Clip[prey + RandomVariate[NormalDistribution[0, stepprey], {nprey, 2}], {-10, 10}];
      predator = Clip[predator + RandomVariate[NormalDistribution[0, steppredator], {npredator, 2}], {-10, 
         10}];
      
      If[npredator < 1, Break[]];
      
      Sow[{prey, predator}]
      , {500}];
    ][[2]];

history = Table[(Dimensions /@ evo[[1, k]] )[[All, 1]], {k, 1, Dimensions[evo[[1]] ][[1]]}];
frames = Table[
   GraphicsRow[{
     Graphics[{Point[evo[[1, j, 1]]], Red, Thick, Circle[#, predatorradius] & /@ evo[[1, j, 2]] }, PlotRange -> {{-10, 10}, {-10, 10}}, ImageSize -> Large]
     ,
     GraphicsColumn[{
       ListLinePlot[history[[1 ;; j]], PlotRange -> {{0, Max@history[[All, 1]] + 100}, {-1, Max@history[[All, 2]] + 10}}, Axes -> False, Frame -> True, FrameLabel -> {"Prey", "Predators"}, LabelStyle -> {Black, Bold}, FrameTicks -> None, PlotStyle -> {Gray, Thick}, AspectRatio -> 1]
       ,
       ListLinePlot[history[[1 ;; j, 1]], PlotRange -> {{0, Dimensions[evo[[1]] ][[1]]}, {-1, Max@history[[All, 1]] + 10}}, Axes -> False, Frame -> True, FrameLabel -> {"Time", "Prey"}, LabelStyle -> {Orange, Bold}, FrameTicks -> None, PlotStyle -> {Orange, Thick}, AspectRatio -> 1]
       ,
       ListLinePlot[history[[1 ;; j, 2]], PlotRange -> {{0, Dimensions[evo[[1]] ][[1]]}, {-1, Max@history[[All, 2]] + 10}}, Axes -> False, Frame -> True, FrameLabel -> {"Time", "Predators"}, LabelStyle -> {Purple, Bold}, FrameTicks -> None, PlotStyle -> {Purple, Thick}, AspectRatio -> 1]
       }]
     }, ImageSize -> Large]
   , {j, 1, Dimensions[evo[[1]] ][[1]]}];
ListAnimate[frames]

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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An extremely simple predator-prey toy model.

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inception

9 August 2021

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image/gif

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Date/TimeThumbnailDimensionsUserComment
current14:10, 11 August 2021Thumbnail for version as of 14:10, 11 August 2021576 × 489 (6.35 MB)BertoUploaded own work with UploadWizard

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