(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 2923479, 54882] NotebookOptionsPosition[ 2897501, 54074] NotebookOutlinePosition[ 2898030, 54095] CellTagsIndexPosition[ 2897987, 54092] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["PARAMETER CHOICES\n\nGuide to file names:", FontWeight->"Bold"], "\nExample- \[OpenCurlyDoubleQuote]1-0.85-0-0.02-0.0015-0-Fast (+).txt\ \[CloseCurlyDoubleQuote] [\[OpenCurlyDoubleQuote]A-B-C-D-E-F-G(H).txt\ \[CloseCurlyDoubleQuote]]\n(A)\t#spp - number of species ( 1 or 2 )\n(B)\t", Cell[BoxData[ FormBox[ SubscriptBox["\[Sigma]", "\[Alpha]"], TraditionalForm]]], " - width of the competition kernel (0.85) ", StyleBox["[Called ", FontWeight->"Bold"], "\[Sigma]\[Alpha]", StyleBox[" in code]", FontWeight->"Bold"], "\n(C)\t\[Kappa] - skewness of the carrying capacity kernel ( \ \[OpenCurlyDoubleQuote]0\[CloseCurlyDoubleQuote] = no skew, \ \[OpenCurlyDoubleQuote]4\[CloseCurlyDoubleQuote] = skew)", StyleBox[" ", FontWeight->"Bold"], "\n(D)\t\[Nu] - mutation rate (\[OpenCurlyDoubleQuote]low\ \[CloseCurlyDoubleQuote] = 0.02 or \[OpenCurlyDoubleQuote]high\ \[CloseCurlyDoubleQuote] = 0.2)\n(E)\t", Cell[BoxData[ FormBox[ SubscriptBox["\[Sigma]", "\[Nu]"], TraditionalForm]]], " - mutational effect size (\[OpenCurlyDoubleQuote]low\ \[CloseCurlyDoubleQuote] = 0.0015 or \[OpenCurlyDoubleQuote]high\ \[CloseCurlyDoubleQuote] = 0.015) ", StyleBox["[Called \[Sigma]\[Nu] In code]", FontWeight->"Bold"], "\n(F)\t\[Beta] - skewness in the competition kernel \ (\[OpenCurlyDoubleQuote]0\[CloseCurlyDoubleQuote] = symmetric, \ \[OpenCurlyDoubleQuote]0.6\[CloseCurlyDoubleQuote] = asymmetric)\n(G)\tvm - \ speed of environmental change ( 0.0005 = \[OpenCurlyDoubleQuote]fast\ \[CloseCurlyDoubleQuote], 0.00005 = \[OpenCurlyDoubleQuote]slow\ \[CloseCurlyDoubleQuote])\n(H)\tdirection - sign of \[Kappa] or \[Beta] \ (whichever is non-zero) ( \[OpenCurlyDoubleQuote]+\[OpenCurlyDoubleQuote] = \ positive, \[OpenCurlyDoubleQuote]-\[OpenCurlyDoubleQuote] = negative )\n\n", StyleBox["Fixed parameters:", FontWeight->"Bold"], "\n\[Sigma] = ", Cell[BoxData[ FormBox[ SubscriptBox["\[Sigma]", "K"], TraditionalForm]]], " - width of the resource distribution (set to 1)", StyleBox[" [Called \[Sigma]k in code]", FontWeight->"Bold"], "\n\[Mu] = ", Cell[BoxData[ FormBox[ SubscriptBox["\[Mu]", "K"], TraditionalForm]]], " - initial mean trait of the resource distribution (set to 0)\nloci - \ number of loci (set to 10), i.e., 20 alleles\nF - fecundity of each parent \ (set to 4)\nr - intrinsic growth rate of a species per generation (set to 1)\n\ \n", StyleBox["Calculated parameters:", FontWeight->"Bold"], "\nKm - amount of resources, chosen such that the average inital equilibrium \ population size was 2500 individuals.\n\n", StyleBox["Time:", FontWeight->"Bold"], "\nIn the text, time is measured relative to the point of environmental \ change (t=0). In the simulations, however, time was started at the beginning \ of the runs, so that we must subtract 5000 from the generations in the code \ to get the generations in the text." }], "Text", CellChangeTimes->{{3.6387187358712587`*^9, 3.638718819127743*^9}, { 3.6387189270350103`*^9, 3.638719078692966*^9}, {3.638720164178071*^9, 3.638720221442553*^9}, {3.638720371330275*^9, 3.638720372795931*^9}, { 3.638720416324606*^9, 3.638720611198151*^9}, {3.638720702288377*^9, 3.638720743381325*^9}, {3.638720778292109*^9, 3.638720910893894*^9}, { 3.638720950288766*^9, 3.638720964393516*^9}, {3.638721094610753*^9, 3.63872112788477*^9}, {3.6387211831459713`*^9, 3.638721224981522*^9}, 3.649590022189939*^9, {3.658075983868826*^9, 3.658075984617874*^9}, { 3.661180707716226*^9, 3.661180717280942*^9}, {3.661180814602475*^9, 3.661180818554213*^9}, {3.6611863184028378`*^9, 3.661186374691861*^9}, { 3.661186485236309*^9, 3.661186485713958*^9}, 3.661186927641089*^9, { 3.661187122818047*^9, 3.661187140579206*^9}, {3.661360023700308*^9, 3.661360023770093*^9}, {3.668884232711216*^9, 3.668884276526415*^9}, { 3.668888974980728*^9, 3.6688889762580976`*^9}, {3.669212415853899*^9, 3.669212423964223*^9}, {3.669212641934455*^9, 3.669212669573071*^9}, { 3.6692127081421957`*^9, 3.669212709146142*^9}, {3.6693178689758453`*^9, 3.669317876131034*^9}, 3.66932009234226*^9, {3.669327414255083*^9, 3.6693274530444927`*^9}, {3.669327505995363*^9, 3.66932754417387*^9}}], Cell[TextData[{ StyleBox["Set Directory:\n", FontWeight->"Bold"], "Set the directory of files to the name of the main folder obtained from \ DRYAD. Edit BaseDirectory below as needed (i.e. to match name of folder that \ contains folder obtained from Dryad)." }], "Text", CellChangeTimes->{{3.662577524248315*^9, 3.6625775422224627`*^9}, { 3.668283279372768*^9, 3.668283297323131*^9}, {3.668283621536635*^9, 3.6682836266139812`*^9}, {3.668283680528104*^9, 3.668283680983057*^9}, { 3.6682837587159243`*^9, 3.668283794745434*^9}, {3.669327583163005*^9, 3.6693276702747498`*^9}, {3.669327704305519*^9, 3.669327728824717*^9}, { 3.703194028979278*^9, 3.703194084265314*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ "BaseDirectory", "=", "\"\\""}], ";"}], " "}]], "Input", CellChangeTimes->{{3.668283677378977*^9, 3.668283688137865*^9}, { 3.668283729008216*^9, 3.66828374463734*^9}, 3.668283866569931*^9, { 3.669307461362237*^9, 3.669307463504999*^9}, 3.669327678107033*^9, { 3.7031939671168337`*^9, 3.7031940116712313`*^9}}], Cell[CellGroupData[{ Cell["Definitions [ENTER]", "Section", CellChangeTimes->{{3.6580709274791603`*^9, 3.658070930549304*^9}, { 3.6580756578279*^9, 3.658075659467235*^9}}], Cell[TextData[{ "The definitions below are required to find the ESS points of the system. \ \[Omega] is the scale parameter and \[Xi] is the location parameter for the \ Skew-normal distribution. Here we standardize \[Omega] and \[Xi] such that \ the mean (\[Mu]) and variance (", Cell[BoxData[ SuperscriptBox["\[Sigma]", "2"]], CellChangeTimes->{3.6495875161633377`*^9, 3.658071081770849*^9, 3.658071471377894*^9, 3.6580749455730743`*^9, 3.65807565749862*^9, 3.6611746054406557`*^9, 3.6613457046268806`*^9, 3.6613487657142143`*^9, 3.6613552992714157`*^9, 3.661355802930806*^9, 3.6613558413009777`*^9, 3.66135651883119*^9, 3.6613607581628733`*^9, 3.661361139627762*^9, 3.661363530340844*^9, 3.661363848984345*^9, 3.6613644859882174`*^9, 3.661367550766671*^9, 3.6625626269493713`*^9, 3.6625779224352217`*^9, 3.662580999335812*^9, 3.662937786708641*^9, 3.6629378210914516`*^9, 3.668170302672791*^9, 3.669213192314025*^9, 3.6693089484716387`*^9, 3.669329537782708*^9}], ") of the distribution are independent of the skew parameter, \[Kappa]. " }], "Text", CellChangeTimes->{{3.6693277745969973`*^9, 3.6693277944779587`*^9}, { 3.6693278306653767`*^9, 3.6693278713088923`*^9}, {3.669327906687851*^9, 3.6693280565600557`*^9}, 3.669328117665786*^9, {3.669329580702312*^9, 3.669329614651134*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"\[Omega]", "[", RowBox[{"\[Sigma]_", ",", "\[Kappa]_"}], "]"}], ":=", FractionBox[ RowBox[{ SqrtBox["\[Pi]"], " ", "\[Sigma]"}], SqrtBox[ RowBox[{ RowBox[{"-", "2"}], "+", "\[Pi]", "+", FractionBox["2", RowBox[{"1", "+", SuperscriptBox["\[Kappa]", "2"]}]]}]]]}], " "}], "\n", RowBox[{ RowBox[{"\[Xi]", "[", RowBox[{"\[Kappa]_", " ", ",", "\[Sigma]_", ",", "\[Mu]_"}], "]"}], ":=", FractionBox[ RowBox[{ RowBox[{ SqrtBox[ RowBox[{"1", "+", SuperscriptBox["\[Kappa]", "2"]}]], " ", "\[Mu]"}], "-", FractionBox[ RowBox[{ SqrtBox["2"], " ", "\[Kappa]", " ", "\[Sigma]"}], SqrtBox[ RowBox[{ RowBox[{"-", "2"}], "+", "\[Pi]", "+", FractionBox["2", RowBox[{"1", "+", SuperscriptBox["\[Kappa]", "2"]}]]}]]]}], SqrtBox[ RowBox[{"1", "+", SuperscriptBox["\[Kappa]", "2"]}]]]}], "\n", RowBox[{ RowBox[{ RowBox[{"k", "[", RowBox[{ "\[Mu]_", ",", "\[Sigma]k_", ",", "\[Kappa]_", ",", "u_", ",", "Km_"}], "]"}], ":=", RowBox[{"Km", "*", RowBox[{"PDF", "[", RowBox[{ RowBox[{"SkewNormalDistribution", "[", RowBox[{ RowBox[{"\[Xi]", "[", RowBox[{"\[Kappa]", ",", "\[Sigma]k", ",", "\[Mu]"}], "]"}], ",", RowBox[{"\[Omega]", "[", RowBox[{"\[Sigma]k", ",", "\[Kappa]"}], "]"}], ",", "\[Kappa]"}], "]"}], ",", "u"}], "]"}]}]}], ";"}]}], "Input", CellChangeTimes->{ 3.609776602968527*^9, {3.6493381627451468`*^9, 3.6493381823333073`*^9}, 3.649530840487455*^9, {3.66118119728854*^9, 3.661181209584093*^9}, { 3.661360964403531*^9, 3.6613609701695213`*^9}, {3.669328060840147*^9, 3.669328143544745*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"Mean", "[", RowBox[{"SkewNormalDistribution", "[", RowBox[{ RowBox[{"\[Xi]", "[", RowBox[{"\[Kappa]", ",", "\[Sigma]", ",", "\[Mu]"}], "]"}], ",", RowBox[{"\[Omega]", "[", RowBox[{"\[Sigma]", ",", "\[Kappa]"}], "]"}], ",", "\[Kappa]"}], "]"}], "]"}], "//", "Factor"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Variance", "[", RowBox[{"SkewNormalDistribution", "[", RowBox[{ RowBox[{"\[Xi]", "[", RowBox[{"\[Kappa]", ",", "\[Sigma]", ",", "\[Mu]"}], "]"}], ",", RowBox[{"\[Omega]", "[", RowBox[{"\[Sigma]", ",", "\[Kappa]"}], "]"}], ",", "\[Kappa]"}], "]"}], "]"}], "//", "Factor"}]}], "Input", CellChangeTimes->{ 3.64958751527136*^9, {3.669212766294774*^9, 3.669212766682002*^9}, { 3.6693281473910303`*^9, 3.66932815189268*^9}, {3.6693293863155947`*^9, 3.66932939876849*^9}}], Cell[BoxData["\[Mu]"], "Output", CellChangeTimes->{3.6495875161633377`*^9, 3.658071081770849*^9, 3.658071471377894*^9, 3.6580749455730743`*^9, 3.65807565749862*^9, 3.6611746054406557`*^9, 3.6613457046268806`*^9, 3.6613487657142143`*^9, 3.6613552992714157`*^9, 3.661355802930806*^9, 3.6613558413009777`*^9, 3.66135651883119*^9, 3.6613607581628733`*^9, 3.661361139627762*^9, 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"+", RowBox[{"vm", "*", "t"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.6693294077939587`*^9, 3.669329419724358*^9}, 3.6693295479078608`*^9}], Cell["\<\ which corresponds to a shift in the mean \[Mu] by vm*t:\ \>", "Text", CellChangeTimes->{{3.661181313301227*^9, 3.661181322573019*^9}, { 3.661181446586465*^9, 3.661181450119781*^9}, {3.661361042530306*^9, 3.66136104409549*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Mean", "[", RowBox[{"SkewNormalDistribution", "[", RowBox[{ RowBox[{"\[Xi]t", "[", RowBox[{ "\[Kappa]", ",", "\[Sigma]", ",", "\[Mu]", ",", "vm", ",", "t"}], "]"}], ",", RowBox[{"\[Omega]", "[", RowBox[{"\[Sigma]", ",", "\[Kappa]"}], "]"}], ",", "\[Kappa]"}], "]"}], "]"}], "//", "Factor"}]], "Input", CellChangeTimes->{{3.661181467229384*^9, 3.661181468435837*^9}, 3.6611814986361094`*^9, {3.6693294236761093`*^9, 3.669329427491535*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"t", " ", "vm"}], "+", "\[Mu]"}]], "Output", CellChangeTimes->{{3.661181468921118*^9, 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the influence of an individual on others of the \ same phenotype is, by definition, equal to one:\ \>", "Text", CellChangeTimes->{{3.6580711245263977`*^9, 3.6580711824762077`*^9}, { 3.662562585684505*^9, 3.6625625918989677`*^9}, {3.669329692119699*^9, 3.66932969928155*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"a", "[", RowBox[{"u1", ",", "u1", ",", "\[Sigma]\[Alpha]", ",", "\[Beta]"}], "]"}]], "Input", CellChangeTimes->{{3.658071108590219*^9, 3.658071113087834*^9}, { 3.6613610958069153`*^9, 3.6613610959104147`*^9}, 3.669320106855537*^9}], Cell[BoxData["1"], "Output", CellChangeTimes->{3.658071113575882*^9, 3.6580714715616817`*^9, 3.65807494570352*^9, 3.658075657639893*^9, 3.66117460563866*^9, 3.6613457050438833`*^9, 3.661348765979933*^9, 3.661355299572507*^9, 3.661355803197839*^9, 3.6613558415693274`*^9, 3.6613565191317377`*^9, 3.661360758579176*^9, 3.6613610921209917`*^9, 3.661361139858418*^9, 3.661363530640251*^9, 3.661363849279333*^9, 3.6613644862043*^9, 3.66136755097913*^9, 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These points vary with the parameter \ choices and the number of species in the community. Below we calculate the \ ESS points for all of the parameter combinations we tested. \ \>", "Text", CellChangeTimes->{{3.669329808107808*^9, 3.669329849083624*^9}, { 3.669330043302411*^9, 3.6693301114779367`*^9}, {3.6693301699254837`*^9, 3.669330188153165*^9}}], Cell["Common parameters", "Text", CellChangeTimes->{{3.661355852080145*^9, 3.661355856383094*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"try\[Sigma]\[Alpha]", "=", RowBox[{"85", "/", "100"}]}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "width", " ", "of", " ", "the", " ", "competition", " ", "kernel"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"try\[Mu]", "=", "0"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "mean", " ", "of", " ", "the", " ", "resource", " ", "distribution"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"try\[Sigma]", "=", "1"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "width", " ", "of", " ", "the", " ", "resource", " ", "distribution"}], " ", "*)"}]}], 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RectangleBox[{-2.335, 0}, {-2.325, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3249999999999997`, 0}, {-2.315, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.315, 0}, {-2.305, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3049999999999997`, 0}, {-2.295, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.295, 0}, {-2.285, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.2849999999999997`, 0}, {-2.275, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.275, 0}, {-2.265, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.2649999999999997`, 0}, {-2.255, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.255, 0}, {-2.245, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.245, 0}, {-2.2350000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.235, 0}, {-2.225, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.2249999999999996`, 0}, {-2.215, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.215, 0}, {-2.205, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.205, 0}, {-2.1950000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.195, 0}, {-2.185, 0}]}, 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RectangleBox[{-1.505, 0}, {-1.495, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4949999999999999`, 0}, {-1.485, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4849999999999999`, 0}, {-1.475, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4749999999999999`, 0}, {-1.465, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4649999999999999`, 0}, {-1.455, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4549999999999998`, 0}, {-1.445, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4449999999999998`, 0}, {-1.435, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4349999999999998`, 0}, {-1.425, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4249999999999998`, 0}, {-1.415, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4149999999999998`, 0}, {-1.405, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4049999999999998`, 0}, {-1.395, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.3949999999999998`, 0}, {-1.385, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.3849999999999998`, 0}, {-1.375, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.375, 0}, 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RectangleBox[{-1.105, 0}, {-1.0950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.095, 0}, {-1.0850000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.085, 0}, {-1.0750000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.075, 0}, {-1.0650000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.065, 0}, {-1.0550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.055, 0}, {-1.0450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.045, 0}, {-1.0350000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.035, 0}, {-1.0250000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.025, 0}, {-1.0150000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.015, 0}, {-1.0050000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.005, 0}, {-0.995, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.995, 0}, {-0.985, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.985, 0}, {-0.975, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.975, 0}, {-0.965, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.965, 0}, {-0.955, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.955, 0}, {-0.945, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.945, 0}, {-0.9349999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9349999999999999, 0}, {-0.9249999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9249999999999999, 0}, {-0.9149999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9149999999999999, 0}, {-0.9049999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9049999999999999, 0}, {-0.8949999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8949999999999999, 0}, {-0.8849999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8849999999999999, 0}, {-0.8749999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8750000000000001, 0}, {-0.8650000000000001, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8650000000000001, 0}, {-0.8550000000000001, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8550000000000001, 0}, {-0.8450000000000001, 0}]}, {RGBColor[0, 0, 1], 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RectangleBox[{-2.175, 0}, {-2.165, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.165, 0}, {-2.1550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.155, 0}, {-2.145, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.145, 0}, {-2.1350000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.135, 0}, {-2.125, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.125, 0}, {-2.115, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.1149999999999998`, 0}, {-2.105, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.105, 0}, {-2.095, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0949999999999998`, 0}, {-2.085, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.085, 0}, {-2.075, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0749999999999997`, 0}, {-2.065, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.065, 0}, {-2.055, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0549999999999997`, 0}, {-2.045, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.045, 0}, {-2.035, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.035, 0}, {-2.0250000000000004`, 0}]}, 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RectangleBox[{-1.625, 0}, {-1.6150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.6149999999999998`, 0}, {-1.605, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.605, 0}, {-1.5950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.5949999999999998`, 0}, {-1.585, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.585, 0}, {-1.5750000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.5749999999999997`, 0}, {-1.565, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.565, 0}, {-1.5550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.555, 0}, {-1.5450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.545, 0}, {-1.5350000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.535, 0}, {-1.5250000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.525, 0}, {-1.5150000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.515, 0}, {-1.5050000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.505, 0}, {-1.495, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4949999999999999`, 0}, 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RectangleBox[{-1.2249999999999999`, 0}, {-1.215, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.2149999999999999`, 0}, {-1.205, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.2049999999999998`, 0}, {-1.195, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1949999999999998`, 0}, {-1.185, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1849999999999998`, 0}, {-1.175, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1749999999999998`, 0}, {-1.165, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1649999999999998`, 0}, {-1.155, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1549999999999998`, 0}, {-1.145, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1449999999999998`, 0}, {-1.135, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1349999999999998`, 0}, {-1.125, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.125, 0}, {-1.1150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.115, 0}, {-1.1050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.105, 0}, {-1.0950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.095, 0}, 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RectangleBox[{-2.0549999999999997`, 0}, {-2.045, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.045, 0}, {-2.035, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.035, 0}, {-2.0250000000000004`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.025, 0}, {-2.015, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0149999999999997`, 0}, {-2.005, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.005, 0}, {-1.995, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9949999999999999`, 0}, {-1.985, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9849999999999999`, 0}, {-1.975, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9749999999999999`, 0}, {-1.965, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9649999999999999`, 0}, {-1.955, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9549999999999998`, 0}, {-1.945, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9449999999999998`, 0}, {-1.935, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.935, 0}, {-1.9250000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9249999999999998`, 0}, {-1.915, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.915, 0}, {-1.9050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.9049999999999998`, 0}, {-1.895, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.895, 0}, {-1.8850000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.8849999999999998`, 0}, {-1.875, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.875, 0}, {-1.8650000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.8649999999999998`, 0}, {-1.855, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.855, 0}, {-1.8450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.8449999999999998`, 0}, {-1.835, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.835, 0}, {-1.8250000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.8249999999999997`, 0}, {-1.815, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.815, 0}, {-1.8050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.805, 0}, {-1.7950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.795, 0}, {-1.7850000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.785, 0}, {-1.7750000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.775, 0}, {-1.7650000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.765, 0}, {-1.7550000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.755, 0}, {-1.745, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.7449999999999999`, 0}, {-1.735, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.7349999999999999`, 0}, {-1.725, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.7249999999999999`, 0}, {-1.715, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.7149999999999999`, 0}, {-1.705, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.7049999999999998`, 0}, {-1.695, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.6949999999999998`, 0}, {-1.685, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.685, 0}, {-1.6750000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.6749999999999998`, 0}, {-1.665, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.665, 0}, {-1.6550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.6549999999999998`, 0}, 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RectangleBox[{-1.3849999999999998`, 0}, {-1.375, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.375, 0}, {-1.3650000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.365, 0}, {-1.3550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.355, 0}, {-1.3450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.345, 0}, {-1.3350000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.335, 0}, {-1.3250000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.325, 0}, {-1.3150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.315, 0}, {-1.3050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.305, 0}, {-1.2950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.295, 0}, {-1.2850000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.285, 0}, {-1.2750000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.275, 0}, {-1.2650000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.265, 0}, {-1.2550000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.255, 0}, 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RectangleBox[{-0.4550000000000002, 0}, {-0.4450000000000002, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.44499999999999995`, 0}, {-0.43499999999999994`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.43500000000000016`, 0}, {-0.42500000000000016`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.42499999999999993`, 0}, {-0.4149999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.41500000000000015`, 0}, {-0.40500000000000014`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.4049999999999999, 0}, {-0.3949999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.39500000000000013`, 0}, {-0.3850000000000001, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.3849999999999999, 0}, {-0.3749999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.3750000000000001, 0}, {-0.3650000000000001, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.3649999999999999, 0}, {-0.35499999999999987`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.3550000000000001, 0}, {-0.3450000000000001, 0}]}, {RGBColor[0, 0, 1], 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{2.4850000000000003`, 0}]}, {RGBColor[1, 0, 0], RectangleBox[{2.4850000000000003`, 0}, {2.495, 0}]}, {RGBColor[1, 0, 0], RectangleBox[{2.495, 0}, {2.505, 0}]}}, {RGBColor[0, 0, 1], EdgeForm[RGBColor[0, 0, 1]], {RGBColor[0, 0, 1], RectangleBox[{-2.495, 0}, {-2.4850000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.485, 0}, {-2.475, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.475, 0}, {-2.4650000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.465, 0}, {-2.455, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.455, 0}, {-2.4450000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.445, 0}, {-2.435, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.435, 0}, {-2.4250000000000003`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.425, 0}, {-2.415, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.415, 0}, {-2.4050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.405, 0}, {-2.395, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.395, 0}, {-2.3850000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.385, 0}, {-2.375, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.375, 0}, {-2.365, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3649999999999998`, 0}, {-2.355, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.355, 0}, {-2.345, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3449999999999998`, 0}, {-2.335, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.335, 0}, {-2.325, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3249999999999997`, 0}, {-2.315, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.315, 0}, {-2.305, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.3049999999999997`, 0}, {-2.295, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.295, 0}, {-2.285, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.2849999999999997`, 0}, {-2.275, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.275, 0}, {-2.265, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.2649999999999997`, 0}, {-2.255, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.255, 0}, {-2.245, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.245, 0}, {-2.2350000000000003`, 0}]}, 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RectangleBox[{-1.4149999999999998`, 0}, {-1.405, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4049999999999998`, 0}, {-1.395, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.3949999999999998`, 0}, {-1.385, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.3849999999999998`, 0}, {-1.375, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.375, 0}, {-1.3650000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.365, 0}, {-1.3550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.355, 0}, {-1.3450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.345, 0}, {-1.3350000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.335, 0}, {-1.3250000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.325, 0}, {-1.3150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.315, 0}, {-1.3050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.305, 0}, {-1.2950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.295, 0}, {-1.2850000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.285, 0}, 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RectangleBox[{-1.015, 0}, {-1.0050000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.005, 0}, {-0.995, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.995, 0}, {-0.985, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.985, 0}, {-0.975, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.975, 0}, {-0.965, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.965, 0}, {-0.955, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.955, 0}, {-0.945, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.945, 0}, {-0.9349999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9349999999999999, 0}, {-0.9249999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9249999999999999, 0}, {-0.9149999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9149999999999999, 0}, {-0.9049999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.9049999999999999, 0}, {-0.8949999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8949999999999999, 0}, {-0.8849999999999999, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-0.8849999999999999, 0}, 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RectangleBox[{-2.175, 0}, {-2.165, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.165, 0}, {-2.1550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.155, 0}, {-2.145, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.145, 0}, {-2.1350000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.135, 0}, {-2.125, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.125, 0}, {-2.115, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.1149999999999998`, 0}, {-2.105, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.105, 0}, {-2.095, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0949999999999998`, 0}, {-2.085, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.085, 0}, {-2.075, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0749999999999997`, 0}, {-2.065, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.065, 0}, {-2.055, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.0549999999999997`, 0}, {-2.045, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.045, 0}, {-2.035, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-2.035, 0}, {-2.0250000000000004`, 0}]}, 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RectangleBox[{-1.625, 0}, {-1.6150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.6149999999999998`, 0}, {-1.605, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.605, 0}, {-1.5950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.5949999999999998`, 0}, {-1.585, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.585, 0}, {-1.5750000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.5749999999999997`, 0}, {-1.565, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.565, 0}, {-1.5550000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.555, 0}, {-1.5450000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.545, 0}, {-1.5350000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.535, 0}, {-1.5250000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.525, 0}, {-1.5150000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.515, 0}, {-1.5050000000000001`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.505, 0}, {-1.495, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.4949999999999999`, 0}, 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RectangleBox[{-1.2249999999999999`, 0}, {-1.215, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.2149999999999999`, 0}, {-1.205, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.2049999999999998`, 0}, {-1.195, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1949999999999998`, 0}, {-1.185, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1849999999999998`, 0}, {-1.175, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1749999999999998`, 0}, {-1.165, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1649999999999998`, 0}, {-1.155, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1549999999999998`, 0}, {-1.145, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1449999999999998`, 0}, {-1.135, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.1349999999999998`, 0}, {-1.125, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.125, 0}, {-1.1150000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.115, 0}, {-1.1050000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.105, 0}, {-1.0950000000000002`, 0}]}, {RGBColor[0, 0, 1], RectangleBox[{-1.095, 0}, 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