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davidrpugh / population-ecology-approach

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Tracking average payoffs? #41

Closed davidrpugh closed 9 years ago

davidrpugh commented 9 years ago

@markeschaffer and @PaulSeabright

I am wondering if we should be tracking average payoffs of individuals carrying certain alleles? I ask because at the moment we are trying to differentiate natural selection pressure and sexual selection pressure. To differentiate these two types of selection pressure we need to measure them.

Seems to me that a good measure of natural selection pressure would be some function of the average individual payoff to adult females carrying A vs a alleles of the alpha gene. Similarly, it would seem that a measure of sexual selection pressure would be some function of the average family payoff of adult males carrying G vs g alleles of the gamma gene.

markeschaffer commented 9 years ago

If we're trying to track the direction of NS and SS pressure, we should skip payoffs and directly track changes in population shares. This is because (a) relative payoffs matter rather than absolute payoffs; (b) differences in average payoffs translate directly into changes in population shares via NS; (c) changes in pop shares via SS don't work via payoffs, so we'd miss the SS pressure.

How about tracking:

  1.  f^A(t)/f(t) – F^A(t)/F(t)  and similarly for a.
  2.  F^A(t+1)/F(t+1) – f^A()/f(t)  and similarly for a.
  3.  m^G(t)/m(t) – M^G(t)/M(t)  and similarly for g.

(1) will tell us which direction NS is pushing A.

(2) will tell us which direction SS is pushing A.

(3) will tell us which direction NS is pushing G.

NB: F(t)=2 and M(t)=1 for all t in the 1M2F model.

davidrpugh commented 9 years ago

@markeschaffer

Is there any other reason that we might want to track payoffs? If not, then I am going to close this issue. I will move the discussion on what/how to track NS vs SS to another thread.

markeschaffer commented 9 years ago

Sort of. The components, not average payoffs.

For example, we might want to know what share of adult A females are getting Pi_AA vs. Pi_Aa.

But maybe this should be embedded in a way of decomposing the difference between the average payoff received by A and a adult females.

davidrpugh commented 9 years ago

@markeschaffer

The way that we would track payoffs would be to track component payoffs. This way we could then compute whatever function of components (i.e.,the average) we want.

For the example you gave, it might be possible to back this share out without reference to the payoffs directly. The share of adult females getting Pi_AA is just twice the number of families with two A females divided by 2; the share of adult females getting Pi_Aa is just the sum of number of families where first female is A and second is a and the number of families where second female is A and first is a divided by 2.

davidrpugh commented 9 years ago

Looks like we can get everything we need without tracking payoffs.