Reasonable guess a priori, but I saw some data from GeneSmith at one point which looked like the interactions are almost always additive (i.e. no nontrivial interaction terms), at least within the distribution of today’s population. Unfortunately I don’t have a reference on hand, but you should ask GeneSmith if interested.
I think Steve Hsu has written some about the evidence for additivity on his blog (Information Processing). He also talks about it a bit in section 3.1 of this paper.
So I only briefly read through the section of the paper, but not really sure whether it applies to my hypothesis: My hypothesis isn’t about there being gene-combinations that are useful which were selected for, but just about there being gene-combinations that coincidentally work better without there being strong selection pressure for those to quickly rise to fixation. (Also yeah for simpler properties like how much milk is produced I’d expect a much larger share of the variance to come from genes which have individual contributions. Also for selection-based eugenics the main relevant thing are the genes which have individual contribution. (Though if we have precise ability to do gene editing we might be able to do better and see how to tune the hyperparameters to fit well together.))
Please let me know whether I’m missing something though.
(There might be a sorta annoying analysis one could do to test my hypothesis: On my hypothesis the correlation between the intelligence of very intelligent parents and their children would be even a bit less than on the just-independent-mutations hypothesis, because very intelligent people likely also got lucky in how their gene variants work together but those properties would unlikely to all be passed along and end up dominant.)
To clarify in case I’m misunderstanding, the effects are additive among the genes explaining the part of the IQ variance which we can so far explain, and we count that as evidence that for the remaining genetically caused IQ variance the effects will also be additive?
I didn’t look into how the data analysis in the studies was done, but on my default guess this generalization does not work well / the additivity on the currently identified SNPs isn’t significant counterevidence for my hyptohesis:
I’d imagine that studies just correlated individual gene variants with IQ and thereby found gene variants that have independent effects on intelligence. Or did they also look at pairwise or triplet gene-variant combinations and correlated those with IQ? (There would be quite a lot of pairs, and I’m not be sure whether the current datasets are large enough to robustly identify the combinations that really have good/bad effects from false positives.)
One would of course expect that the effects of the gene variants which have independent effects on IQ are additive.
But overall, except if the studies did look for higher-order IQ correlations, the fact that the IQ variance we can explain so far comes from genes which have independent effects isn’t significant evidence for the remaining genetically-caused IQ variation also comes from gene variants which have independent effects, because we were bound to much rather find the genes which do have independent effects.
(I think the above should be sufficient explanation of what I think but here’s an example to clarify my hypothesis:
Suppose gene A has variants A1 and A2 and gene B has B1 and B2. Suppose that A1 can work well with B1 and A2 with B2, but the other interactions don’t fit together that well (like badly tuned hyperparameters) and result in lower intelligence.
When we only look at e.g. A1 and A2, none is independently better than the other—they are uncorrelated to IQ. Studies would need to look at combinations of variants to see that e.g. A1+B1 has slight positive correlation with intelligence—and I’m doubting whether studies did that (and whether we have sufficient data to see the signal among the combinatorical explosion of possibilities), and it would be helpful if someone clarified to me briefly how studies did the data analysis. )
(Thanks. I don’t think this is necessarily significant evidence against my hypothesis (see my comment on GeneSmith’s comment.)
Another confusing relevant piece of evidence I thought I throw in:
Human intelligence seems to me to be very heavytailed. (I assume this is uncontrovertial here, just look at the greatest scientists vs great scientists.)
If variance in intelligence was basically purely explained by mildly-delterious SNPs, this would seem a bit odd to me: If the average person had 1000SNPs, and then (using butt-numbers which might be very off) Einstein (+6.3std) had only 800 and the average theoretical physics professor (+4std) had 850, I wouldn’t expect the difference there to be that big.
It’s a bit less surprising on the model where most people have a few strongly delterious mutations, and supergeniuses are the lucky ones that have only 1 or 0 of those.
It’s IMO even a bit less surprising on my hypothesis where in some cases the different hyperparameters happen to work much better with each other—where supergeniuses are in some dimensions “more lucky than the base genome” (in a way that’s not necessarily easy to pass on to offspring though because the genes are interdependent, which is why the genes didn’t yet rise to fixation). But even there I’d still be pretty surprised by the heavytail.
The heavytail of intelligence really confuses me. (Given that it doesn’t even come from sub-critical intelligence explosion dynamics.)
If each deleterious mutation decreases the success rate of something by an additive constant, but you need lots of sequential successes for intellectual achievements, then intellectual formidability is ~exponentially related to deleterious variants.
Yeah I know that’s why I said that if a major effect was through few significantly deleterious mutations this would be more plausible. But i feel like human intelligence is even more heavitailed than what one would predict given this hypothesis.
If you have many mutations that matter, then via central limit theorem the overall distribution will be roughly gaussian even though the individual ones are exponential.
(If I made a mistake maybe crunch the numbers to show me?)
(initially misunderstood what you mean where i thought complete nonsense.)
I don’t understand what you’re trying to say. Can you maybe rephrase again in more detail?
Suppose people’s probability of solving a task is uniformly distributed between 0 and 1. That’s a thin-tailed distribution.
Now consider their probability of correctly solving 2 tasks in a row. That will have a sort of triangular distribution, which has more positive skewness.
If you consider e.g. their probability of correctly solving 10 tasks in a row, then the bottom 93.3% of people will all have less than 50%, whereas e.g. the 99th percentile will have 90% chance of succeeding.
Conjunction is one of the two fundamental ways that tasks can combine, and it tends to make the tasks harder and rapidly make the upper tail do better than the lower tail, leading to an approximately-exponential element. Another fundamental way that tasks can combine is disjunction, which leads to an exponential in the opposite direction.
When you combine conjunctions and disjunctions, you get an approximately sigmoidal relationship. The location/x-axis-translation of this sigmoid depends on the task’s difficulty. And in practice, the “easy” side of this sigmoid can be automated or done quickly or similar, so really what matters is the “hard” side, and the hard side of a sigmoid is approximately exponential.
Is the following a fair paraphrasing of your main hypothesis? (I’m leaving out some subtleties with conjunctive successes, but please correct the model in that way if it’s relevant.):
“”″ Each deleterious mutation multiplies your probability of succeeding at a problem/thought by some constant. Let’s for simplicity say it’s 0.98 for all of them.
Then the expected number of successes per time for a person is proportional to 0.98^num_deleterious_mutations(person).
So the model would predict that when Person A had 10 less deleterious mutations than person B, they would on average accomplish 0.98^10 ~= 0.82 times as much in a given timeframe. ”″”
I think this model makes a lot of sense, thanks!
In itself I think it’s insufficient to explain how heavytailed human intelligence is—there were multiple cases where Einstein seems to have been able to solve problems multiple times faster than the next runner ups. But I think if you use this model in a learning setting where success means “better thinking algorithms” then if you have 10 fewer deleterious mutations it’s like having 1⁄0.82 longer training time, and there might also be compounding returns from having better thinking algorithms to getting more and richer updates to them.
Not sure whether this completely deconfuses me about how heavytailed human intelligence is, but it’s a great start.
I guess at least the heavytail is much less significant evidence for my hypothesis than I initially thought (though so far I still think my hypothesis is plausible).
Reasonable guess a priori, but I saw some data from GeneSmith at one point which looked like the interactions are almost always additive (i.e. no nontrivial interaction terms), at least within the distribution of today’s population. Unfortunately I don’t have a reference on hand, but you should ask GeneSmith if interested.
@towards_keeperhood yes this is correct. Most research seems to show ~80% of effects are additive.
Genes are actually simpler than most people tend to think
I think Steve Hsu has written some about the evidence for additivity on his blog (Information Processing). He also talks about it a bit in section 3.1 of this paper.
Thanks.
So I only briefly read through the section of the paper, but not really sure whether it applies to my hypothesis: My hypothesis isn’t about there being gene-combinations that are useful which were selected for, but just about there being gene-combinations that coincidentally work better without there being strong selection pressure for those to quickly rise to fixation.
(Also yeah for simpler properties like how much milk is produced I’d expect a much larger share of the variance to come from genes which have individual contributions. Also for selection-based eugenics the main relevant thing are the genes which have individual contribution. (Though if we have precise ability to do gene editing we might be able to do better and see how to tune the hyperparameters to fit well together.))
Please let me know whether I’m missing something though.
(There might be a sorta annoying analysis one could do to test my hypothesis: On my hypothesis the correlation between the intelligence of very intelligent parents and their children would be even a bit less than on the just-independent-mutations hypothesis, because very intelligent people likely also got lucky in how their gene variants work together but those properties would unlikely to all be passed along and end up dominant.)
Thanks for confirming.
To clarify in case I’m misunderstanding, the effects are additive among the genes explaining the part of the IQ variance which we can so far explain, and we count that as evidence that for the remaining genetically caused IQ variance the effects will also be additive?
I didn’t look into how the data analysis in the studies was done, but on my default guess this generalization does not work well / the additivity on the currently identified SNPs isn’t significant counterevidence for my hyptohesis:
I’d imagine that studies just correlated individual gene variants with IQ and thereby found gene variants that have independent effects on intelligence. Or did they also look at pairwise or triplet gene-variant combinations and correlated those with IQ? (There would be quite a lot of pairs, and I’m not be sure whether the current datasets are large enough to robustly identify the combinations that really have good/bad effects from false positives.)
One would of course expect that the effects of the gene variants which have independent effects on IQ are additive.
But overall, except if the studies did look for higher-order IQ correlations, the fact that the IQ variance we can explain so far comes from genes which have independent effects isn’t significant evidence for the remaining genetically-caused IQ variation also comes from gene variants which have independent effects, because we were bound to much rather find the genes which do have independent effects.
(I think the above should be sufficient explanation of what I think but here’s an example to clarify my hypothesis:
Suppose gene A has variants A1 and A2 and gene B has B1 and B2. Suppose that A1 can work well with B1 and A2 with B2, but the other interactions don’t fit together that well (like badly tuned hyperparameters) and result in lower intelligence.
When we only look at e.g. A1 and A2, none is independently better than the other—they are uncorrelated to IQ. Studies would need to look at combinations of variants to see that e.g. A1+B1 has slight positive correlation with intelligence—and I’m doubting whether studies did that (and whether we have sufficient data to see the signal among the combinatorical explosion of possibilities), and it would be helpful if someone clarified to me briefly how studies did the data analysis.
)
(Thanks. I don’t think this is necessarily significant evidence against my hypothesis (see my comment on GeneSmith’s comment.)
Another confusing relevant piece of evidence I thought I throw in:
Human intelligence seems to me to be very heavytailed. (I assume this is uncontrovertial here, just look at the greatest scientists vs great scientists.)
If variance in intelligence was basically purely explained by mildly-delterious SNPs, this would seem a bit odd to me: If the average person had 1000SNPs, and then (using butt-numbers which might be very off) Einstein (+6.3std) had only 800 and the average theoretical physics professor (+4std) had 850, I wouldn’t expect the difference there to be that big.
It’s a bit less surprising on the model where most people have a few strongly delterious mutations, and supergeniuses are the lucky ones that have only 1 or 0 of those.
It’s IMO even a bit less surprising on my hypothesis where in some cases the different hyperparameters happen to work much better with each other—where supergeniuses are in some dimensions “more lucky than the base genome” (in a way that’s not necessarily easy to pass on to offspring though because the genes are interdependent, which is why the genes didn’t yet rise to fixation). But even there I’d still be pretty surprised by the heavytail.
The heavytail of intelligence really confuses me. (Given that it doesn’t even come from sub-critical intelligence explosion dynamics.)
If each deleterious mutation decreases the success rate of something by an additive constant, but you need lots of sequential successes for intellectual achievements, then intellectual formidability is ~exponentially related to deleterious variants.
Yeah I know that’s why I said that if a major effect was through few significantly deleterious mutations this would be more plausible. But i feel like human intelligence is even more heavitailed than what one would predict given this hypothesis.If you have many mutations that matter, then via central limit theorem the overall distribution will be roughly gaussian even though the individual ones are exponential.(If I made a mistake maybe crunch the numbers to show me?)(initially misunderstood what you mean where i thought complete nonsense.)
I don’t understand what you’re trying to say. Can you maybe rephrase again in more detail?
Suppose people’s probability of solving a task is uniformly distributed between 0 and 1. That’s a thin-tailed distribution.
Now consider their probability of correctly solving 2 tasks in a row. That will have a sort of triangular distribution, which has more positive skewness.
If you consider e.g. their probability of correctly solving 10 tasks in a row, then the bottom 93.3% of people will all have less than 50%, whereas e.g. the 99th percentile will have 90% chance of succeeding.
Conjunction is one of the two fundamental ways that tasks can combine, and it tends to make the tasks harder and rapidly make the upper tail do better than the lower tail, leading to an approximately-exponential element. Another fundamental way that tasks can combine is disjunction, which leads to an exponential in the opposite direction.
When you combine conjunctions and disjunctions, you get an approximately sigmoidal relationship. The location/x-axis-translation of this sigmoid depends on the task’s difficulty. And in practice, the “easy” side of this sigmoid can be automated or done quickly or similar, so really what matters is the “hard” side, and the hard side of a sigmoid is approximately exponential.
Thanks!
Is the following a fair paraphrasing of your main hypothesis? (I’m leaving out some subtleties with conjunctive successes, but please correct the model in that way if it’s relevant.):
“”″
Each deleterious mutation multiplies your probability of succeeding at a problem/thought by some constant. Let’s for simplicity say it’s 0.98 for all of them.
Then the expected number of successes per time for a person is proportional to 0.98^num_deleterious_mutations(person).
So the model would predict that when Person A had 10 less deleterious mutations than person B, they would on average accomplish 0.98^10 ~= 0.82 times as much in a given timeframe.
”″”
I think this model makes a lot of sense, thanks!
In itself I think it’s insufficient to explain how heavytailed human intelligence is—there were multiple cases where Einstein seems to have been able to solve problems multiple times faster than the next runner ups. But I think if you use this model in a learning setting where success means “better thinking algorithms” then if you have 10 fewer deleterious mutations it’s like having 1⁄0.82 longer training time, and there might also be compounding returns from having better thinking algorithms to getting more and richer updates to them.
Not sure whether this completely deconfuses me about how heavytailed human intelligence is, but it’s a great start.
I guess at least the heavytail is much less significant evidence for my hypothesis than I initially thought (though so far I still think my hypothesis is plausible).