The GMVH seems extremely plausible to me, but many people in my social circle disagree. I think they're letting their politics interfere with their reason; but, out of fear it is in fact I who am embarrassingly wrong, I'm going to test the GMVH by writing a simple evolution-simulation. Roughly:
simulate a population over time, where some genes can affect fitness variably depending on sex
after many generations, make some sort of graph from which I can eyeball each sex's fitness-variance
eyeball it, see if the variances are clearly different in the expected direction
Bias minimization
I want to minimize the ability of my preconceptions to taint my results. And there's the classic trap where you debug a program only until it produces the output you want/expect. So I'm going to try really hard to make this program produce a valid experimental result on the first try:
I'm going to litter the code with assertions to make sure it's simulating a reasonable, realistic scenario (e.g. "the individuals in each generation should not all share a parent"), so that I don't have to look at the results to notice something's fishy.
I'm going to put lots of printfs in my code, to print various things that might indicate something weird going on. I'll be sure to not print anything that I can see how it would correlate with whether the simulation supports the GMVH or not.
I'm probably going to fail, because nobody has ever written a nontrivial program that works correctly on the first try. So, after I run the program and get nonsense results, and fix it and re-run it and get nonsense results, etc., and then (of course) finally get the results I expected, I commit to spending at least 3x as long carefully debugging the program as the longest time it took me to resolve any previous issue. (If I give up at any point after the first not-obviously-nonsense run, this market will resolve NO.)
Program sketch
My program will probably look very-but-not-exactly like this one:
There is a population of 1000 organisms.
Each organism has:
1 "sex-gene," which is "A" or "B"
many "fitness-genes," each consisting of two numbers: "contribution to fitness-variance if I'm type A" and "... if I'm type B."
A "fitness," sampled from
Normal(mean=0, variance=sum(gene.fitnessVarianceContribution[o.type] for gene in o.fitnessGenes).
Each generation consists of 1000 samples from the following distribution:
Choose the parents: randomly choose an A-type from the previous generation, where each A's chance of being chosen is proportional to
2^fitness. Same for B, except proportional to (2.2)^fitness.Each of the offspring's genes is selected from one of the parents at 50-50-random.
...and then mutagenesis happens: 10 random fitness-variance-contributions are increased or decreased by a factor sampled from
LogNormal(0,0.1).
After 10,000 generations, make a histogram of all genes' fitness-variance-if-A. Make another histogram for fitness-variance-if-B. See if the histograms clearly represent different distributions.
I'm not sure I've chosen a good function from [each organism's genome] to [its expected number of offspring]; I fear that the exact program described above will lead to unrealistic scenarios where pretty much all the offspring come from only the "alpha" of each type, causing all genes to race for maximal variance. I might change it if I think of a more realistic-seeming model.
(I also might tweak the {population size, genome size, number of generations to run for} after further thought. And, though I could be argued out of this, I reserve the right to increase {genome size, number of generations} even after running the program, to increase resemblance to reality, where genomes and evolutionary-history are both very long.)
Correct my model!
If you create a market of the form "If the GMVH sim is re-run with $SOME_CHANGE, will the difference-in-variability be [larger/smaller]?", and I think your proposed change makes my model importantly more realistic --
(for example,
If the GMVH sim is re-run with a gene controlling offspring-sex-selection, will the difference-in-variability be lower?
)
-- then I will submit a M$200 NO limit-order at 50%, and, after resolving this market, I will implement your change and re-run the sim and tell you the results.
This means that, if you see an important error in my model, and you can predict which direction it will push my results, you can take my money.
(Offer only open while supplies last, "supplies" mostly being my willingness to implement various tweaks to my code.)
Market resolution
At some point before 2023-11-09, I'll run my sim several times, do the final "3x as long" debugging step, and then resolve this market:
YES if I eyeball the graph(s) and they clearly, consistently-across-the-several-runs, show type B having greater variance
NO if I think that, in ~half-or-more of the runs, a reasonable person could argue the graphed distributions are the same
N/A if I never write a sim that runs successfully without failing any of its copious assertions
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Resolved NO. The code ended up looking rather different from what the market-description described, downstream of the comments-discussion with Camille Perrin. (The market said the program would "probably look very-but-not-exactly like this one" -- we ended up on the improbable side of that, but I still think this is a fair resolution.)
My methodology was:
1. Debug the simulation with the sex-asymmetry off. Make sure evolution happens.
2. Run the simulation with the sex-asymmetry on, with various random seeds.
3. Plot the outputs. Eyeball them to see if the two fitness-distribution-curves were clearly different. They weren't: they all looked roughly like this:
Choose the parents: randomly choose an A-type from the previous generation, where each A's chance of being chosen is proportional to
2^fitness. Same for B, except proportional to (2.2)^fitness.
It seems GMVH is already baked in this assumption? (It would be interesting to see this closer to first principles, say from the higher parental investment of one sex. But I do not know how to do that on the level of the simulation).
It seems GMVH is already baked in this assumption?
Ah, the GMVH isn't that males have higher variance in numbers of offspring, but rather that they have higher variance in traits.
What is the motivation behind this assumption? (The fitness distributions).
Two:
It's a simple distribution, which limits experimenter-degrees-of-freedom.
It captures what I think is the GMVH-relevant male-female asymmetry: males can have many more kids. (Or, somewhat rephrased: the reproductive benefit for being alpha male is much higher than for being alpha female.)
I predict you will eventually write a simulation that follows the specification.
However I doubt it provides evidence one way or the other,since a detractor could easily claim the simulation specs are written to support the hypothesis (as evidenced from the choice of genotype-to-fitness model, directly involving variance, and nothing else; and mating selection model).
@CamillePerrin Oh, sure, I'd never wave this simulation at somebody else to convince them. I want it as evidence for me.
[bounty retracted; see below]
Bounty: M$100 for each time you (or anybody else!) point out a way in which my model deviates from reality in ways that dis/favor the GMVH, such that after you point it out, I agree the deviation clearly pushes the sex-variance-difference in a particular direction.
(I don't see how my genotype-to-fitness model or mating selection model are biased; agreed they deviate from reality, but the sign of the effect isn't clear to me. Maybe you were just pointing them out as experimenter-degrees-of-freedom that somebody could point at as things I might have carefully chosen to give the GMVH the best possible shot.)
Wait! This is Manifold! That bounty stands for any comment you've already started typing, but in general, replace that bounty with: I'll bet M$200 NO in any market of the form "If the GMVH sim is re-run with $SOME_CHANGE, will the difference-in-variability be [larger/smaller]?"
(details on eagerness-to-be-corrected added to market description)
@OptimizationProcess If the simulation would not convince somebody else (somewhat informed about the topic), why would it convince you?
And there are ~infinitely many changes to the model that might increase or decrease fit with your hypothesis, yet the only ones that matter is the ones that are close to reality. To me, the correct thing to bounty is therefore someone pointing out deviation from how fitness and mating actually works in the world.
"If the simulation would not convince somebody else (somewhat informed about the topic), why would it convince you?"
I believe that most well-informed people (rightly!) don't trust experimenters not to subconsciously p-hack. I trust myself pretty well along that axis, but I don't see a way to credibly signal that skill to others (even assuming I do, in fact, have it).
"the correct thing to bounty is therefore someone pointing out deviation from how fitness and mating actually works in the world."
Here's a list of deviations I've thought of between my model and reality: in the real world...
animals are mostly diploid, not haploid
genomes are much larger
populations are much larger
population size varies over time
populations have small-world-network-ish structure
fitness is enormously polygenic in ways that are unfathomably complicated and vary across time and space
which parent each gene comes from isn't independent
individuals tend to have kids with mates they've had kids with with before
generations aren't discrete, they overlap with each other
parental investment exists
differential parental investment exists
...in complicated, varying, culture-dependent ways
females are rate-limited producing offspring, males ~aren't
All of these seem (to varying degrees) plausibly important, but fixing all of them would require more programmer-time and more CPU-time than I'm willing to devote.
Is there some obvious-to-you heuristic that I'm missing, for identifying which issues are worth solving and which aren't?
Or are you claiming that this whole project is mere streetlight-searching, that the results of this sim don't have even one half of a bit of mutual information with the GMVH?
@OptimizationProcess First, I would totally do the sim anyway: 1/ its going to be interesting, if only for the programming.
2/ always a chance for truly unexpected results, orthogonal to original hypothesis
Additionally, suppose you get a clear positive/negative result w/r/t the hypothesis. Regardless of relation to real world, it still a result on how a given (relatively simple) fitness and mating mechanism can/cannot give rise to different distributions, which is interesting in itself. Especially if you can implement some of the factors from your list, and see if the results change.
Regarding what factor is important or not - it's likely there is already discussion in the literature - cited in the papers proposing/opposing the hypothesis. But I haven't read it, and I have no special insight into what might turn out important or not. Sounds like a whole-ass research plan, though, write a grant :D
I also don't think I have the ability to accurately record small increments like "half a bit" of evidence for any theory - so this would not move the needle one way or another.
@CamillePerrin Okay! I'll just keep searching under this streetlight, then. 😛
Many thanks for your consultation! I found it quite valuable.