Generating the Figures in Chapter 12 of Otto and Day

Clear["Global`*"]

Figure 12.1 - Reproductive Effort

b[x_]:=Exp[x]
p[x_]:=po-(x^2)

Show[
Plot[((b[x])/(1-p[x]))/.po->.25,{x,0,1},PlotRange->{0,5}],
Plot[((b[x])/(1-p[x]))/.po->.5,{x,0,1},PlotRange->{0,5},PlotStyle->{Dashing[{.015}]}],
Plot[((b[x])/(1-p[x]))/.po->.75,{x,0,1},PlotRange->{0,5},PlotStyle->{Dashing[{.035}]}]
]

Figure 12.2 - Dispersal Rate Evolution

Plot[Evaluate[{1,((1-d)/((1-d)+dhat p))+((d p)/((1-dhat)+dhat p))}/.{dhat->.25,p->2/3}],{d,0,1},PlotRange->{.6,1.2},AxesOrigin->{0,.6},PlotStyle->{Dashing[{.01}],Dashing[{0}]}]
Plot[Evaluate[{1,((1-d)/((1-d)+dhat p))+((d p)/((1-dhat)+dhat p))}/.{dhat->.5,p->2/3}],{d,0,1},PlotRange->{.6,1.2},AxesOrigin->{0,.6},PlotStyle->{Dashing[{.01}],Dashing[{0}]}]
Plot[Evaluate[{1,((1-d)/((1-d)+dhat p))+((d p)/((1-dhat)+dhat p))}/.{dhat->.75,p->2/3}],{d,0,1},PlotRange->{.6,1.2},AxesOrigin->{0,.6},PlotStyle->{Dashing[{.01}],Dashing[{0}]}]
Plot[Evaluate[{1,((1-d)/((1-d)+dhat p))+((d p)/((1-dhat)+dhat p))}/.{dhat->.9,p->2/3}],{d,0,1},PlotRange->{.6,1.2},AxesOrigin->{0,.6},PlotStyle->{Dashing[{.01}],Dashing[{0}]}]

Figure 12.4 - Competition for Resources

k[s_]:=κ Exp[((-(((s-s0))^2))/(2 σk))]
α[sm_,s_]:=Exp[((-(((sm-s))^2))/(2 σα))]

Show[Plot[k[s]/.{s0->5,σk->1/2,κ->100},{s,0,10},PlotRange->{0,100}],
Plot[k[s]/.{s0->5,σk->3,κ->100},{s,0,10},PlotStyle->{Dashing[{.025}]}],
Plot[k[s]/.{s0->5,σk->10,κ->100},{s,0,10},PlotStyle->{Dashing[{.012}]}]
]

Show[
Plot[Exp[((-(((x))^2))/(2 σα))]/.{σα->1/2},{x,-10,10},PlotRange->{0,1}],
Plot[Exp[((-(((x))^2))/(2 σα))]/.{σα->10},{x,-10,10},PlotStyle->{Dashing[{.012}]},PlotRange->{0,1}]
]

Figure 12.5 - Reproductive factor in the Daphnia model

s0=0;σα=1.5;σk=1;r=1.1;
plot1=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->.5},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]
plot2=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->0},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]
plot3=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->-.5},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]

Export["fig12-5a.eps",plot1];
Export["fig12-5b.eps",plot2];
Export["fig12-5c.eps",plot3];

s0=0;σα=.7;σk=1;r=1.1;
plot4=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->.5},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]
plot5=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->0},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]
plot6=Plot[{1,1+r-r ((Exp[((-(((sm-s))^2))/(2 σα))] Exp[((-(((s-s0))^2))/(2 σk))])/(Exp[((-(((sm-s0))^2))/(2 σk))]))/.s->-.5},{sm,-2,2},PlotRange->{0,2},PlotStyle->{Dashing[{0.01}],Dashing[{0}]}]

Export["fig12-5d.eps",plot4];
Export["fig12-5e.eps",plot5];
Export["fig12-5f.eps",plot6];

Figure 12.7 - Adaptation to a boundary habitat

γ=((ρb)/(ρc));

Plot[{(fb/(γ-(1-fb)))/.γ->2,(fb/(γ-(1-fb)))/.γ->1.2},{fb,0,1},PlotRange->{0,1},PlotStyle->{Dashing[{0}],Dashing[{.015}]}]

Export["Fig12-7.eps",%];

Figure 12.4.1 - Pairwise Invasibility Plot for the Competition for Resources Model

Clear["Global`*"]

Off[Solve::"ifun"]

Clear[roots1,roots2]

k[s_]:=κ Exp[((-(((s-s0))^2))/(2 σk))]
α[sm_,s_]:=Exp[((-(((sm-s))^2))/(2 σα))]

roots1[s_]:=sm/.Solve[(1-α[sm,s]k[s]/k[sm]/.σk->1/.σα->0.5/.s0->5)==0,sm][[1]];
roots2[s_]:=sm/.Solve[(1-α[sm,s]k[s]/k[sm]/.σk->1/.σα->0.5/.s0->5)==0,sm][[2]];

tab1=Table[{s,If[roots1[s]>0,If[roots1[s]<10,roots1[s],10],0]},{s,0.01,10.01,0.1}]

tab2=Table[{s,If[roots2[s]>0,If[roots2[s]<10,roots2[s],10],0]},{s,0.01,10.01,0.1}]

tabsoln=Join[Table[{s,If[roots1[s]>0,If[roots1[s]<10,roots1[s],10],0]},{s,0.01,5,0.1}],Table[{s,If[roots2[s]>0,If[roots2[s]<10,roots2[s],10],0]},{s,5.01,10.01,0.1}]]

tabdiag=Table[{x,x},{x,0,10,0.4}];

ListPlot[{tabsoln,tabdiag},Joined->True,PlotStyle->{Automatic,Dashed},Filling->{2->{1}}]

Clear[roots]

roots1[s_]:=sm/.Solve[(1-α[sm,s]k[s]/k[sm]/.σk->1/.σα->1.5/.s0->5)==0,sm][[1]];
roots2[s_]:=sm/.Solve[(1-α[sm,s]k[s]/k[sm]/.σk->1/.σα->1.5/.s0->5)==0,sm][[2]];

tab1=Table[{s,If[roots1[s]>0,If[roots1[s]<10,roots1[s],10],0]},{s,0.01,10.01,0.1}]

tab2=Table[{s,If[roots2[s]>0,If[roots2[s]<10,roots2[s],10],0]},{s,0.01,10.01,0.1}]

tabsoln=Join[Table[{s,If[roots2[s]>0,If[roots2[s]<10,roots2[s],10],0]},{s,0.01,5,0.1}],Table[{s,If[roots1[s]>0,If[roots1[s]<10,roots1[s],10],0]},{s,5.01,10.01,0.1}]]

ListPlot[{tabsoln,tabdiag},Joined->True,PlotStyle->{Automatic,Dashed},Filling->{2->{1}}]

Sup Mat Figure 12.2.1 - Accessory proteins

The following function describes how the number of eggs produced by a female rises as a function of the amount of accessory proteins received:

f[x_]=b x^k

The curvature of this function depends on k.  For k = 1, it is linear.  For k < 1, there is negative curvature:

Show[
Plot[f[a]/.k->0.25/.b->100,{a,0,2},PlotRange->All,PlotStyle->Dashing[{0.005,0.015}]],
Plot[f[a]/.k->0.5/.b->100,{a,0,2},PlotRange->All,PlotStyle->Dashing[{0.02,0.015}]],
Plot[f[a]/.k->0.75/.b->100,{a,0,2},PlotRange->All,PlotStyle->Dashing[{0.04}]],
Plot[f[a]/.k->1/.b->100,{a,0,2},PlotRange->All]
]

Sup Mat Figure 12.2.2 - Accessory proteins - Mutant fitness surface

Clear["Global`*"]

λ= (((1/2)((1-u) f[am]+ u(sm/(sm+s))f[am+a])(R/(sm+am+c)))/((1/2) ((1-u) f[a]+(1/2) u f[2a])(R/(s+a+c))));

f[x_]=b (x^k);

atESS={s->(SuperStar[s]),sm->(SuperStar[s]),a->(SuperStar[a]),am->(SuperStar[a])};

subESS=Solve[{
Factor[D[ λ,am]/.atESS]==0,
Factor[D[ λ,sm]/.atESS]==0},{(SuperStar[a]),(SuperStar[s])}]//FullSimplify//Flatten

{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.3/.c->0.1

Show[Plot3D[λ/.{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.3/.c->0.1,{am,0.,0.1},{sm,0.1,0.2},PlotRange->{0.98,1},ClippingStyle->None,ViewPoint->{1,-2,1.5},AxesEdge->{Automatic,{1,-1},Automatic},ColorFunction->Function[{x,y,z},GrayLevel[10*(z-0.9)]],ColorFunctionScaling->False],
Plot3D[λ/.{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.3/.c->0.1,{am,0.04285-0.0025,0.04285+0.0025},{sm,0.14285-0.0025,0.14285+0.0025},PlotRange->{0.98,1}]]

{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.9/.c->0.1

Show[Plot3D[λ/.{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.9/.c->0.1,{am,0.85,0.95},{sm,0.951,1.05},PlotRange->{0.9997,1.0002},ClippingStyle->None,ViewPoint->{1,-2,1.5},AxesEdge->{Automatic,{1,-1},Automatic},ColorFunction->Function[{x,y,z},GrayLevel[1500 (z-0.9994)]],ColorFunctionScaling->False],
Plot3D[λ/.{s->(SuperStar[s]),a->(SuperStar[a])}/.subESS/.u->1/.b->1/.k->0.9/.c->0.1,{am,0.9-0.0025,0.9+0.0025},{sm,1-0.0025,1+0.0025}]]

Sup Mat Figure 12.2.3-Accessory proteins-predictions

k=1/3;

Plot[{-((c k)/(-1+k))}/.k->1/3,{c,0,1}]

Show[Plot[{-(((2^k) c u)/((-1+k) (4-4 u+(2^k) u)))}/.u->1/4,{c,0,1}],
Plot[{-(((2^k) c u)/((-1+k) (4-4 u+(2^k) u)))}/.u->1/2,{c,0,1},PlotStyle->{Dashing[{.025}]}],
Plot[{-(((2^k) c u)/((-1+k) (4-4 u+(2^k) u)))}/.u->3/4,{c,0,1},PlotStyle->{Dashing[{.012}]}]
]

Sup Mat Figure 12.2.4 - Accessory proteins - Branching

arraya={{0,0},{1,0.8},{2,4.396014573622383},{3,3.670654899895629},{4,3.670654899895629},{5,3.670654899895629},{6,3.670654899895629},{7,3.670654899895629},{8,3.670654899895629},{9,3.670654899895629},{10,3.670654899895629},{11,3.670654899895629},{12,3.670654899895629},{13,3.670654899895629},{14,4.088113165850723},{15,4.088113165850723},{16,4.088113165850723},{17,4.088113165850723},{18,4.088113165850723},{19,4.088113165850723},{20,4.088113165850723},{21,4.088113165850723},{22,4.088113165850723},{23,4.088113165850723},{24,4.088113165850723},{25,4.088113165850723},{26,4.088113165850723},{27,4.088113165850723},{28,4.088113165850723},{29,4.088113165850723},{29,4.413773609333341},{30,4.088113165850723},{30,4.413773609333341},{31,4.088113165850723},{31,4.413773609333341},{32,4.088113165850723},{32,4.413773609333341},{33,4.088113165850723},{33,4.413773609333341},{34,4.088113165850723},{34,4.413773609333341},{35,4.088113165850723},{35,4.413773609333341},{36,4.088113165850723},{36,4.413773609333341},{37,4.413773609333341},{37,0.773381859526961},{38,4.413773609333341},{38,0.773381859526961},{39,4.413773609333341},{39,0.48826184658685756},{40,4.413773609333341},{40,0.48826184658685756},{41,4.413773609333341},{41,0.48826184658685756},{42,4.413773609333341},{42,0.48826184658685756},{43,4.413773609333341},{43,0.48826184658685756},{44,4.413773609333341},{44,0.48826184658685756},{45,4.413773609333341},{45,0.48826184658685756},{46,4.413773609333341},{46,0.48826184658685756},{47,4.413773609333341},{47,0.48826184658685756},{48,4.413773609333341},{48,0.48826184658685756},{49,4.413773609333341},{49,0.48826184658685756},{50,4.413773609333341},{50,0.48826184658685756},{51,4.413773609333341},{51,0.48826184658685756},{52,4.413773609333341},{52,0.20795947442342827},{53,4.413773609333341},{53,0.20795947442342827},{54,4.413773609333341},{54,0.20795947442342827},{55,4.413773609333341},{55,0.20795947442342827},{56,4.413773609333341},{56,0.20795947442342827},{57,4.413773609333341},{57,0.20795947442342827},{58,0.20795947442342827},{58,4.607662798320281},{59,0.20795947442342827},{59,4.607662798320281},{60,0.20795947442342827},{60,4.607662798320281},{61,0.20795947442342827},{61,4.607662798320281},{62,0.20795947442342827},{62,4.607662798320281},{63,0.20795947442342827},{63,4.607662798320281},{64,0.20795947442342827},{64,4.607662798320281},{65,0.20795947442342827},{65,4.607662798320281},{66,0.20795947442342827},{66,4.607662798320281},{67,0.20795947442342827},{67,4.607662798320281},{68,0.20795947442342827},{68,4.607662798320281},{69,0.20795947442342827},{69,4.607662798320281},{70,0.20795947442342827},{70,4.607662798320281},{71,0.20795947442342827},{71,4.607662798320281},{72,0.20795947442342827},{72,4.607662798320281},{73,0.20795947442342827},{73,4.607662798320281},{74,0.20795947442342827},{74,4.607662798320281},{75,0.20795947442342827},{75,4.607662798320281},{76,0.20795947442342827},{76,4.607662798320281},{77,0.20795947442342827},{77,4.607662798320281},{78,0.20795947442342827},{78,4.607662798320281},{79,0.20795947442342827},{79,4.607662798320281},{80,0.20795947442342827},{80,4.607662798320281},{81,0.20795947442342827},{81,4.607662798320281},{82,0.20795947442342827},{82,4.607662798320281},{83,0.20795947442342827},{83,4.607662798320281},{84,0.20795947442342827},{84,4.607662798320281},{85,0.20795947442342827},{85,4.607662798320281},{86,0.20795947442342827},{86,4.607662798320281},{87,0.20795947442342827},{87,4.607662798320281},{88,0.20795947442342827},{88,4.607662798320281},{89,0.20795947442342827},{89,4.607662798320281},{90,0.20795947442342827},{90,4.607662798320281},{91,0.20795947442342827},{91,4.607662798320281},{92,0.20795947442342827},{92,4.607662798320281},{93,0.20795947442342827},{93,4.607662798320281},{94,0.20795947442342827},{94,4.607662798320281},{95,0.20795947442342827},{95,4.607662798320281},{96,0.20795947442342827},{96,4.607662798320281},{97,0.20795947442342827},{97,4.607662798320281},{98,0.20795947442342827},{98,4.607662798320281},{99,0.20795947442342827},{99,4.607662798320281},{100,0.20795947442342827},{100,4.607662798320281},{101,0.20795947442342827},{101,4.607662798320281},{102,0.20795947442342827},{102,4.607662798320281},{103,0.20795947442342827},{103,4.607662798320281},{104,0.20795947442342827},{104,4.607662798320281},{105,0.20795947442342827},{105,4.607662798320281},{106,0.20795947442342827},{106,4.607662798320281},{107,0.20795947442342827},{107,4.607662798320281},{108,0.20795947442342827},{108,4.607662798320281},{109,0.20795947442342827},{109,4.607662798320281},{110,0.20795947442342827},{110,4.607662798320281},{111,0.20795947442342827},{111,4.607662798320281},{112,0.20795947442342827},{112,4.607662798320281},{113,0.20795947442342827},{113,4.607662798320281},{114,0.20795947442342827},{114,4.607662798320281},{115,0.20795947442342827},{115,4.607662798320281},{116,0.20795947442342827},{116,4.607662798320281},{117,0.20795947442342827},{117,4.607662798320281},{118,0.20795947442342827},{118,4.607662798320281},{119,0.20795947442342827},{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ListPlot[{arrays}]