Manipulate[h[x_]:=(((x^2) wrr+x (1-x) wrs)/((x^2) wrr+2 x (1-x) wrs+(((1-x))^2) wss));ListPlot[Table[{t,Nest[h,0.5,t]},{t,0,time}],PlotRange->{{0,20},{0,1}},PlotStyle->PointSize[.02],Frame->True,FrameLabel->{"Time, t","p"},LabelStyle->Directive[FontSize->14],PlotStyle->{Black}],{time,1,20,1},{{wrr,1/4,(Subscript[W, rr])},{1/4,1/2}},{{wrs,1/2,(Subscript[W, rs])},{1/2,1/4}},{{wss,1/2,(Subscript[W, ss])},{1/2,1}}]

Manipulate[h[x_]:=(((x^2) wrr+x (1-x) wrs)/((x^2) wrr+2 x (1-x) wrs+(((1-x))^2) wss));ListPlot[Table[{t,Nest[h,0.5,t]},{t,0,time}],PlotRange->{{0,20},{0,1}},PlotStyle->PointSize[.02],Frame->True,FrameLabel->{"Time, t","p"},LabelStyle->Directive[FontSize->14],PlotStyle->{Black}],{time,1,20,1},{{wrr,0.25,(Subscript[W, RR])},0.1,1,1/100,Appearance->"Labeled"},{{wrs,0.5,(Subscript[W, RS])},0.1,1,1/100,Appearance->"Labeled"},{{wss,0.5,(Subscript[W, SS])},0.1,1,1/100,Appearance->"Labeled"}]