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]