Presentation plots

[davidrpugh]

@markeschaffer, @PaulSeabright

Below is a plot for the corner solution with G males and A females as well as an example that shows polymorphism in the alpha gene. The only difference between parameterizations in the two plots is the value of the e (which partially determines assortativity): high values of e generate a corner solution; low values of e generate polymorphism in alpha.

Note that the payoff structure does NOT satisfy returns to scarcity. Thus the plots demonstrate a minimal set of conditions necessary to generate polymorphism in alpha.

Multiple equilibria

GA Corner solution

ga Corner solution

Polymorphism with A and a alleles

Sweep for linear payoffs

Sweep for hierarchical payoffs

Feedback is much appreciated.

[markeschaffer]

This is great stuff btw. For payoffs 5 4 3.95 2 we have a few path plots to motivate and then param sweep fully characterises the equilibria. Then path plots for 5 4 3 2 and again param sweep fully describes equilibria. Then hierarchy and intuition behind its importance (total family payoffs matter for male). Then if time permits the decomp tells us about the forces driving the specific outcomes.

-------- Original message -------- Subject: Re: [population-ecology-approach] Presentation plots (#43) From: PaulSeabright notifications@github.com To: davidrpugh/population-ecology-approach population-ecology-approach@noreply.github.com CC: "Schaffer, Mark" M.E.Schaffer@hw.ac.uk

In that case I think it would be better to have three plots:

1. First plot shows corner solution with ga, say e=0.7 and MGA=0.5
2. Second plot shows that you can get corner solution with GA by keeping the same MGA=0.5 and setting e=0.9
3. Third plot shows you can get the GA corner solution by keeping e=0.7 and setting MGA=0.9

P

— Reply to this email directly or view it on GitHubhttps://github.com/davidrpugh/population-ecology-approach/issues/43#issuecomment-62024898.

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[PaulSeabright]

OK I'm going out now but will do this later on tonight and send to you to look at tomorrow morning

2014-11-06 19:48 GMT+01:00 markeschaffer notifications@github.com:

This is great stuff btw. For payoffs 5 4 3.95 2 we have a few path plots to motivate and then param sweep fully characterises the equilibria. Then path plots for 5 4 3 2 and again param sweep fully describes equilibria. Then hierarchy and intuition behind its importance (total family payoffs matter for male). Then if time permits the decomp tells us about the forces driving the specific outcomes.

-------- Original message -------- Subject: Re: [population-ecology-approach] Presentation plots (#43) From: PaulSeabright notifications@github.com To: davidrpugh/population-ecology-approach < population-ecology-approach@noreply.github.com> CC: "Schaffer, Mark" M.E.Schaffer@hw.ac.uk

In that case I think it would be better to have three plots:

1. First plot shows corner solution with ga, say e=0.7 and MGA=0.5
2. Second plot shows that you can get corner solution with GA by keeping the same MGA=0.5 and setting e=0.9
3. Third plot shows you can get the GA corner solution by keeping e=0.7 and setting MGA=0.9

P

— Reply to this email directly or view it on GitHub< https://github.com/davidrpugh/population-ecology-approach/issues/43#issuecomment-62024898>.

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We invite research leaders and ambitious early career researchers to join us in leading and driving research in key inter-disciplinary themes. Please see www.hw.ac.uk/researchleaders for further information and how to apply.

Heriot-Watt University is a Scottish charity registered under charity number SC000278.

— Reply to this email directly or view it on GitHub https://github.com/davidrpugh/population-ecology-approach/issues/43#issuecomment-62029745 .

Toulouse School of Economics, Manufacture des Tabacs, 21 allée de Brienne, 31015 Toulouse Cedex 6, France www.tse-fr.eu

Institute for Advanced Study in Toulouse www.iast.fr

Personal website:

http://paulseabright.com/

http://press.princeton.edu/titles/9169.html

[davidrpugh]

Agreed. Although, with the Wright-Bergstrom assortativity functions, hierarchy does not seem to be the driving force behind polymorphism (at least for alpha gene). In our original assortativity functions, we needed hierarchy to get any non-trivial polymorphisms as an equilibrium outcome.

[markeschaffer]

True, H not needed for poly in A. But last 3 plots show clearly that increasing H increases the range of e that supports poly in alpha. And extreme H can even generate double poly in alpha and gamma. Cool stuff.

-------- Original message -------- Subject: Re: [population-ecology-approach] Presentation plots (#43) From: "David R. Pugh" notifications@github.com To: davidrpugh/population-ecology-approach population-ecology-approach@noreply.github.com CC: "Schaffer, Mark" M.E.Schaffer@hw.ac.uk

Agreed. Although, with the Wright-Bergstrom assortativity functions, hierarchy does not seem to be the driving force behind polymorphism (at least for alpha gene). In our original assortativity functions, we needed hierarchy to get any non-trivial polymorphisms as an equilibrium outcome.

— Reply to this email directly or view it on GitHubhttps://github.com/davidrpugh/population-ecology-approach/issues/43#issuecomment-62030475.

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We invite research leaders and ambitious early career researchers to join us in leading and driving research in key inter-disciplinary themes. Please see www.hw.ac.uk/researchleaders for further information and how to apply.

Heriot-Watt University is a Scottish charity registered under charity number SC000278.

[davidrpugh]

Indeed. Very cool stuff...