Tracking natural vs sexual selection

[davidrpugh]

As suggested by @markeschaffer in issue #41 ...

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:

f^A(t)/f(t) – F^A(t)/F(t)

and similarly for a.

F^A(t+1)/F(t+1) – f^A()/f(t)

and similarly for a.

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]

@markeschaffer

I have already sketched interactive plots for 1 and 2 above. We can look at them and discuss the next time that we meet.

Regarding 3, am I correct that the total number of male children is the same as the total number of female children (i.e., because exactly half of the total number of children produced are of each gender)? Also, we are not currently tracking the number of male children by genotype.

[markeschaffer]

On your second point – yes, you are correct. The sex ratio at birth is 1:1.

Because the distribution of male children m(t) is identical to the distribution of adult males M(t+1), there's no need to track both.

[davidrpugh]

@markeschaffer

Just to confirm for number 3 above we want to compute

m^G(t)/m(t) - M^G(t)/M(t) = M^G(t+1) / M(t+1) - M^G(t) / M(t) = M^G(t+1) - M^G(t)

and similarly for g.

[markeschaffer]

Yes, that's right.

[davidrpugh]

@markeschaffer

I think we have sorted female selection pressure, but I am confused about how we should be tracking selection pressure for gamma gene. We should talk about this later this week.

[davidrpugh]

@markeschaffer

Thinking about how to implement our formulas for male selection pressure got me to thinking about how to compute the total number of children. I think that the total number of children in a time period is just twice the total number of female children. The total number of female children is just the sum of the number of female children across genotypes.

Do you concur?

[davidrpugh]

@markeschaffer

Also, is the number of male children carrying G allele just the sum of the number of female children carrying GA genotype and the number of female children carrying the Ga genotype? I think this is correct so long as the distribution of male and female children must be the same.

[markeschaffer]

Yes, that’s right. And the distribution across genotypes of male and female children will also be identical.

[markeschaffer]

Yes, that’s right.

[davidrpugh]

@markeschaffer and @PaulSeabright

I agree that we should be talking about selection pressure on alpha and gamma genes (instead of females and males). However, shouldn't part of the natural (and sexual) selection pressure on say alpha come from the females and part from the males? Currently the natural selection pressure for the alpha gene is entirely determined by females (similarly the selection pressure for gamma is entirely determined by males).

[markeschaffer]

Great point. In fact, can think of hitchhiking effects. Gamma hitchhikes on female children into the next gen of families. And alpha hitchhikes on the males.

So do we want measures for overall pressure that we can decompose into direct and hitchhiking effects?

-------- Original message -------- Subject: Re: [population-ecology-approach] Tracking natural vs sexual selection (#42) 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

@markeschafferhttps://github.com/markeschaffer and @PaulSeabrighthttps://github.com/PaulSeabright

I agree that we should be talking about selection pressure on alpha and gamma genes (instead of females and males). However, shouldn't part of the natural (and sexual) selection pressure on say alpha come from the females and part from the males? Currently the natural selection pressure for the alpha gene is entirely determined by females (similarly the selection pressure for gamma is entirely determined by males).

— Reply to this email directly or view it on GitHubhttps://github.com/davidrpugh/population-ecology-approach/issues/42#issuecomment-60928607.

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[davidrpugh]

@markeschaffer @PaulSeabright

We want to have measures of selection pressure for individual genes. I think these measures need to decompose as follows:

• sexual selection:
  • female contribution
  • male contribution
• natural selection:
  • female contribution: natural selection outside the family unit (i.e., within the entire population).
  • male contribution: natural selection within the family unit.

We would them plot sexual selection and natural selection pressure on alpha and gamma genes decomposed by gender on two subplots; a third subplot would then plot the total (net) selection pressure by aggregating the natural and sexual selection components.

[markeschaffer]

OK … to fix ideas, let’s look at the 2 sexual selection components for gamma:

Females: ln { F^G(t+1) / f^G(t) } – ln { F^g(t+1) / f^g(t) }

Males: ln { m^G(t) / M^G(t) } – ln { m^g(t) / M^g(t) }

And the distributions of genotypes for male and female children are identical, right?

So m^G(t) = f^G(t) m^g(t) = f^g(t)

And that suggests total sexual selection pressure for gamma is going to be the sum of male and female pressure, namely

Total SS (gamma): ln { F^G(t+1) / M^G(t) } – ln { F^g(t+1) / M^g(t) }

The same for NS (females) / IFC (males), this time for alpha:

Females: ln { f^A(t) / F^A(t) } – ln { f^a(t) / F^a(t) }

Males: ln { M^A(t+1) / m^A(t) } – ln { M^a(t+1) / m^a(t) }

Total NS (alpha): ln { M^A(t+1) / F^A(t) } – ln { M^A(t+1) / F^a(t) }

This looks too good to be true. And also a little odd. Is it easily interpretable?

[markeschaffer]

Typo in previous version in the last line (last big A should be a little a), corrected below.

Am writing out the full set of total NS and SS eqns for alpha and gamma:

Total SS (alpha): ln { F^A(t+1) / M^A(t) } – ln { F^a(t+1) / M^a(t) }

Total NS (alpha): ln { M^A(t+1) / F^A(t) } – ln { M^a(t+1) / F^a(t) }

Total SS (gamma): ln { F^G(t+1) / M^G(t) } – ln { F^g(t+1) / M^g(t) }

Total NS (gamma): ln { M^G(t+1) / F^G(t) } – ln { M^g(t+1) / F^g(t) }

And you can see that if you now added the two alpha effects and rearrange terms, you get

Total SS+NS (alpha): ln { F^A(t+1) / F^A(t) } + ln { M^A(t+1) / M^A(t) }

• [ ln { F^a(t+1) / F^a(t) } + ln { M^a(t+1) / M^a(t) } ]

…which makes sense. It’s all in adults and add the female and male effects.

And similarly for total SS+NS (gamma).

Too good to be true….

[davidrpugh]

@markeschaffer

I will go ahead and implement these measures and then regenerate the plots as discussed in issue #43.

[markeschaffer]

That's a lot of measures: 12 in total. Are you thinking of something like this? (a) male, female, total SS for alpha; (b) m, f, total NS for alpha; (c) total SS, total NS, total total for alpha; and similarly for gamma? Lots of plots to choose from but we won't have time for very many in the presentation.