Fixation probability for complete graph: Bd

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

Fixation probability for star graph: uniform initialised (parent moving) Bd and temperature initialised (offspring moving) dB

FixprobstaruniformBd[fp_,f_,n_,x_,y_]:=((1-((((fp/f)))^2))((n^3)(x^2)+(n+1)n (fp/f) x y+(y^2)))/((n+1)(n (fp/f) x+y)((n (fp/f) x+y)(((((n x+(fp/f) y)/(n ((((fp/f)))^2)x+(fp/f) y))))^n)-(fp/f)(n x+(fp/f) y)));

FixprobstartempBd[fp_,f_,n_,x_,y_]:=(((1-((((fp/f)))^2))((n^3)(-(x-1))(x^2)+(n^2)  x y((fp/f)+x)+n x y((fp/f)+y)-(y-1)(y^2)))/((n+1)(n (fp/f) x+y)((n (fp/f) x+y)(((((n x+(fp/f) y)/(n ((((fp/f)))^2)x+(fp/f) y))))^n)-(fp/f)(n x+(fp/f) y))));

The formulae for the Bd fixation probability on the star graph have been adapted from Adlam et al. Proc. A, 2015. We set x=y=1 to obtain the transition probability for the undirected star graph.

LogLinearPlot[{FixprobstaruniformBd[fp,1,99,1,1],FixprobcompBd[fp,1,100],FixprobstartempBd[fp,1,99,1,1]},{fp,.1,10},PlotRange->{-.02,1.1},  PlotStyle->{{Thickness[0.01],Darker[Green]},{Thickness[0.01],Blue},{  Thickness[0.01],Magenta}},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 relative fitness",18,Black],Style["Fixation probability",18,Black]},FrameTicksStyle->12]

labeledTicks=Table[{10^i,Superscript[10,i]},{i,-20,1,8}];

LogLogPlot[{FixprobcompBd[fp,1,100],FixprobstaruniformBd[fp,1,99,1,1],FixprobstartempBd[fp,1,99,1,1]},{fp,.8,1.2},PlotRange->{-.02,0.31},  PlotStyle->{{Thickness[0.01],Blue},{Thickness[0.01],Darker[Green]},{  Thickness[0.01],Magenta}},Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{labeledTicks,Automatic},{Automatic, Automatic}}, GridLines->{{1},None},GridLinesStyle->Directive[Black,Thickness[0.003]],Background->None, PlotRange->All,FrameTicksStyle->12,FrameLabel->{Style["Mutant relative fitness",18,Black],Style["Fixation probability",18,Black]}]

Fixation probability on the complete graph with dB updating

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

Fixation probability for star graph : uniform initialised (offspring moving) dB and temperature initialised (parent moving) dB

The formulae for the dB fixation probability on the star graph have been computed in SI Appendix A .

FixprobstardB[fp_,f_,N_]:=((((N-1)/N)+(((N-1) (fp/f))/(-1+N-1+2 (fp/f))))/((N )(1+((-1+N-1)/(1+(N-1) (fp/f))))));
FixprobstartempdB[fp_,f_,N_]:=(((1+(N-1) (fp/f)) (((((N-1))^2)/N)+((fp/f)/(-1+N-1+2 (fp/f)))))/((N-1)*N (1+(fp/f))));

LogLinearPlot[{FixprobstardB[fp,1,100],FixprobcompdB[fp,1,100],FixprobstartempdB[fp,1,100]},{fp,.1,10},PlotRange->{-.02,1.1},  PlotStyle->{{Thickness[0.01],Red},{Thickness[0.01],Blue},{Thickness[0.01],Orange}},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["Fixation probability",18,Black]},FrameTicksStyle->12]

LogLogPlot[{FixprobstardB[fp,1,100],FixprobcompdB[fp,1,100],FixprobstartempdB[fp,1,100]},{fp,.8,1.2},PlotRange->{-.02,2.81},  PlotStyle->{{Thickness[0.01],Red},{Thickness[0.01],Blue},{Thickness[0.01],Orange}},Frame->True,FrameStyle->Directive[Black,Thickness[0.004]],FrameTicks->{{labeledTicks,Automatic},{Automatic, Automatic}}, GridLines->{{1},None},GridLinesStyle->Directive[Black,Thickness[0.003]],Background->None, PlotRange->All, FrameLabel->{Style["Mutant's fitness",18,Black],Style["Fixation probability",18,Black]},FrameTicksStyle->12]