Study of the k>1 case

Name of this file: Cuaderno20120425T143135.m

Definitions

P=@(a,s,k,nx,ny) (1+(1+a*s.^-(nx-k*ny))./(1+a*s.^-(ny-k*nx))).^-1;

nx=1:.1:30;
nx=repmat(nx,[length(nx) 1]);

Plot

a=.01;
s=2;
k=1.5;
imagesc(P(a,s,k,nx,nx’))
set(gca,’YDir’,’normal’)

 

Indeed, we can have different things.

New figure for robustness in stickleback

Name of this file: Cuaderno20120418T134813.m

I realized that I did not include the robustness with respect to changing parameter a in the symmetric cases, so I include it.

fig_pap_robustezstickleback(1,[0 0 0])

 

New supplementary figure for the number of fish to count

Name of this file: Cuaderno20120416T194643.m

It will now go in a separate figure.

fig_pap_ncontar(1)

 

New summary figure

Name of this file: Cuaderno20120416T192437.m

I remove the blue arrow, because Gonzalo thought it was a bit misleading.

fig_pap_resumen_ecn(1)

 

New summary figure

Name of this file: Cuaderno20120413T102318.m

I add the arrow with “optimal decision making”

fig_pap_resumen_ecn(1)

ans =
175.1096
ans =
221.1096
ans =
233.1096
ans =
245.1096
ans =
257.1096

 

New summary figure (two versions, again)

Name of this file: Cuaderno20120412T110105.m

I reduce the size of the equation. I keep the other version to facilitate comparison.

Without the equation:

fig_pap_resumen(1)

ans =
177.0702
ans =
223.0702
ans =
235.0702
ans =
247.0702
ans =
259.0702

 

With the equation

fig_pap_resumen_ecn(2)

ans =
711.0084
ans =
757.0082
ans =
769.0082
ans =
781.0082
ans =
793.0082
ans =
805.0082

 

New summary figure (two options)

Name of this file: Cuaderno20120412T104920.m

I have added the descriptions of the three rules, and the equation.

Without the equation:

fig_pap_resumen(1)

ans =
177.0653
ans =
223.0653
ans =
235.0653
ans =
247.0653
ans =
259.0653

 

With the equation

fig_pap_resumen_ecn(2)

ans =
711.0072
ans =
757.0070
ans =
769.0070
ans =
781.0070
ans =
793.0070
ans =
805.0070

 

Shape of isoprobability lines

Name of this file: Cuaderno20120411T174105.m

We want to see if isoprobability lines for high n are straight in all the plane, or only in the transition zone.

Define model

P=@(a,s,k,nx,ny) (1+(1+a*s.^-(nx-k*ny))./(1+a*s.^-(ny-k*nx))).^-1;
a=100;
s=5;
k=.5;

Plot model

nx=0:.1:100;
nx=repmat(nx,[length(nx) 1]);
imagesc(P(a,s,k,nx,nx’))
axis image

 

Plot in logarithmic

imagesc(log10(P(a,s,k,nx,nx’)))
axis image

 

So isolines are straight also in the saturated regions.

Figure with the robustness of the fit for ants

Name of this file: Cuaderno20120403T174921.m

fig_pap_robustezhormigas(1,0)

a_opt =
2.5119
s_opt =
1.0700
k_opt =
0.5300
prand_opt =
0.3900

 

New main text figure for stickleback

Name of this file: Cuaderno20120403T160434.m

I have changed the symmetric case to 1-1, and have changed the titles of the lower row.

fig_pap_stickleback(1)