Neg freq dep selection

[Prothama Manna]

Hello,

I have a quick question on negative frequency dependent selection.

initialize() {
initializeMutationRate(1e-7);
initializeMutationType("m1", 0.5, "f", 0.0); // neutral
initializeMutationType("m2", 0.5, "f", 0.1); // balanced
initializeGenomicElementType("g1", c(m1,m2), c(999,1));
initializeGenomicElement(g1, 0, 99999);
initializeRecombinationRate(1e-8);
}
1 early() { sim.addSubpop("p1", 500); }
10000 early() { sim.simulationFinished(); }
mutationEffect(m2) {
return 1.5 - sim.mutationFrequencies(p1, mut);
}

 I understand what we are changing here is the fitness effect when m2 becoming rare. I am a little confused about what does the 1.5 stand here? 

When exactly m2 is becoming beneficial in the population?

Best,

Prothama

[Ben Haller]

Hi Prothama!

The constant 1.5 is somewhat arbitrarily chosen, so that with a frequency of 0.0 (or infinitesimally larger) the mutation's fitness effect would be 1.5 - 0.0 == 1.5, and with a frequency of 1.0 (or infinitesimally smaller) the mutation's fitness effect would be 1.5 - 1.0 = 0.5.  (I quibble about infinitesimals here would of course with a frequency of 0.0 the mutation would be lost, and with a frequency of 1.0 it would be fixed.)  That produces a range of fitness effects from 0.5 to 1.5, where a frequency of 0.5 produces neutrality (1.5 - 0.5 == 1.0).  So an m2 mutation will begin to be beneficial when its frequency rises above 0.5.  But as I said, the constant 1.5 was somewhat arbitrarily chosen; this equation is merely an example, and many other functions, with other shapes, could be written that would also produce negative frequency-dependent selection, of different kinds, on a mutation.

I hope that helps.  Happy modeling!

Cheers,
-B.

Benjamin C. Haller
Messer Lab
Cornell University
 

Prothama Manna wrote on 4/25/24 4:57 PM:

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SLiM forward genetic simulation: http://messerlab.org/slim/
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