Complete Graph (dB)

FixprobcompdB[fp_,f_,N_]:=((N-1)/N)((1-(f/fp))/(1-((((f/fp)))^(N-1))));

FixprobfraccompdB[fp_,f_,N_]:=((FixprobcompdB[fp,f,N])/(FixprobcompdB[f,fp,N]));

probcompdB[f_?NumericQ,N_?NumericQ,a_?NumericQ,b_?NumericQ]:=(((NIntegrate[FixprobfraccompdB[fp,f,N],{fp,a,b}]))^(-1));
meancompdB[N_?NumericQ,a_?NumericQ,b_?NumericQ]:=NIntegrate[f*probcompdB[f,N,a,b],{f,a,b}];

meandatacompdB=Table[{n,meancompdB[n,0.1,10]},{n,4,106}];

Cycle Graph (dB)

FixprobcycledB[fp_,f_,N_]:=((2((fp/f)-1))/(3(fp/f)-1+((fp/f)-3)((((fp/f)))^(2-N))));
FixprobfraccycledB[fp_,f_,N_]:=((FixprobcycledB[fp,f,N])/(FixprobcycledB[f,fp,N]));

probcycledB[f_?NumericQ,N_?NumericQ,a_?NumericQ,b_?NumericQ]:=(((NIntegrate[FixprobfraccycledB[fp,f,N],{fp,a,b}]))^(-1));
meancycledB[N_?NumericQ,a_?NumericQ,b_?NumericQ]:=NIntegrate[f*probcycledB[f,N,a,b],{f,a,b}];

meandatacycledB=Table[{n,meancycledB[n,0.1,10]},{n,8,96,4}];

2 d lattice (dB)

Fixprob2DdB[k_,fp_,f_,N_]:=(1/(1+((((1-((((f/fp)))^(N-2))))/(1-(f/fp))))((((fp/f)+k-1))/(k (fp/f)))));

Fixprobfrac2DdB[k_,fp_,f_,N_]:=((
Fixprob2DdB[k,fp,f,N])/(Fixprob2DdB[k,f,fp,N]));

prob2DdB[f_?NumericQ,k_?NumericQ,N_?NumericQ,a_?NumericQ,b_?NumericQ]:=(((NIntegrate[Fixprobfrac2DdB[k,fp,f,N],{fp,a,b}]))^(-1));
mean2DdB[N_?NumericQ,k_?NumericQ,a_?NumericQ,b_?NumericQ]:=NIntegrate[f*prob2DdB[f,k,N,a,b],{f,a,b}];

meandata2DdB=Table[{n,mean2DdB[n,4,0.1,10]},{n,10,94,4}];

Show[Plot[{1-1/r,((2 (1-r))/(1-3r)), ((4 (-1+r))/(-1+5r))},{r,1.000001,10.5},PlotRange->{{-0.1,10.5},{-.05,1.05}},PlotStyle->{{Thickness[0.004],Blue},{Thickness[0.004],RGBColor["#7F00FF"]},{Thickness[0.004],Darker[Purple]}},Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{Automatic,Automatic},{Automatic, Automatic}}, GridLines->{{1},None},GridLinesStyle->Directive[Black,Thickness[0.003]],Background->None, PlotRange->All,FrameTicksStyle->12],Plot[{FixprobcompdB[fp,1,10],FixprobcycledB[fp,1,10],Fixprob2DdB[4,fp,1,10]},{fp,.1,10},  PlotStyle->{{Thickness[0.008],Blue},{Thickness[0.008],RGBColor["#7F00FF"]},{Thickness[0.008],Darker[Purple]}}],FrameLabel->{Style["Mutant's fitness",18,Black],Style["Fixation probability",18,Black]}]

LogLogPlot[{FixprobcompdB[fp,1,10]-FixprobcycledB[fp,1,10]},{fp,.1,10}, PlotRange->{-.02,1.1}, PlotStyle->{{Thickness[0.008],RGBColor["#7F00FF"]}},Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{Automatic,Automatic},{Automatic, Automatic}}, GridLines->{{1},None},GridLinesStyle->Directive[Black,Thickness[0.003]],Background->None, PlotRange->All,FrameTicksStyle->14,FrameLabel->{Style["Mutant's fitness",18,Black],Style["(Subscript[Φ, C])(r)-(Subscript[Φ, o])(r)",18,Black]}]

LogPlot[{Abs[FixprobcompdB[fp,1,10]-Fixprob2DdB[4,fp,1,10]]},{fp,.1,10},PlotRange->{{0.1,10},{0.0000000001,.15}},  PlotStyle->{{Thickness[0.008],Darker[Purple]}},Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{Automatic,Automatic},{Automatic, Automatic}}, GridLines->{{1},None},GridLinesStyle->Directive[Black,Thickness[0.003]],Background->None, PlotRange->All, FrameLabel->{Style["Mutant's fitness",18,Black],Style["|(Subscript[ϕ, Comp])-(Subscript[ϕ, 2  D])|",18,Black]},FrameTicksStyle->12]

Show[ListPlot[{meandatacompdB,meandatacycledB,meandata2DdB},Joined->{True,False,False},PlotMarkers->{"",{Graphics[{RGBColor["#7F00FF"],Disk[{0,0}]}],.045},{Graphics[{Darker[Purple],Disk[{0,0}]}],.045}},PlotStyle->{{Blue,Thickness[0.008]},"",""},Frame->True,PlotLegends->LineLegend[{"Complete","Cycle","2D lattice"},LegendMarkerSize->{20,12}]],Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{Automatic,Automatic},{Automatic, Automatic}},FrameLabel->{Style["Population size, N",15,Black],Style["Average steady-state fitness",15,Black]},Background->None,FrameTicksStyle->12]