Many non-scientists have a great interest in heritability, but lack the science education and/or cognitive ability to understand modern techniques like Genome-wide Complex Trait Analysis (GCTA), so this post is a quick attempt to explain it. Full Disclosure: I have virtually no formal science training beyond high school but this is just an oversimplified explanation.
GCTA gives a measure of the squared correlation between additive genotype and phenotype. The reason it’s so confusing is that you can’t directly correlate a phenotype with a genotype if you haven’t found the genes that code for that phenotype, and thus you can’t determine if someone is genetically high on a given trait.
So for example, you can’t determine if someone’s genetic IQ matches their actual IQ, if you don’t know if they have the genes for IQ. Since a correlation, by definition, is how close the rank order of two variables (i.e. genetic IQ and actual IQ) agree, it can’t be directly calculated if one of said variables (i.e. genetic IQ) can’t be ranked. It would be like trying to calculate the correlation between height and weight, but all the weights were reported in a language you didn’t speak.
To sidestep this problem, GCTA was invented by a scientist of East Asian heritage. In GCTA, instead of ranking everyone in your sample from highest to lowest on each trait, you simply randomly assign people to pairs, and for each pair, calculate the genetic distance and the phenotype distance. So for example, if the people who differ by 100 single nucleotide polymorphisms (SNPs), on average, differ by one standard deviation in IQ, and if people who differ by one standard deviation in IQ differ, on average, by 39 SNPs, then perhaps it can be inferred that (in this sample) the correlation between genetic IQ and actual IQ is whatever number when squared and multiplied by 100, equals 39.
That number is 0.62
This is because in a bivariate normal distribution, the slope of the standardized regression line equals the correlation between two variables, so if a genetic difference of 100 SNPs regresses to a one standard deviation difference in IQ, then one standard deviation must be only 62% as extreme as 100 SNPs and if a one standard deviation difference in IQ regresses to a 39 SNP difference, then 39 must be only 62% as extreme as one standard deviation.
Once we have the correlation of say 0.62 between additive genotype and phenotype , we square it to get the amount of variation explained which in this example would be 0.38 (the real number is probably much higher, and even higher still for broad-sense heritability).
Of course what very few people realize is that heritability is technically NOT the percentage of the phenotypic variation explained by genes, it’s the percentage explained by genes when environment is held constant or allowed to vary randomly.
Pumpkin Person 
most SNPs are binary so a binary matrix is a good model.
the problem is that the probability such matrices are invertible goes to 1 as the matrix increases in size even when rare SNPs are included as long as they have frequency > 1%.
if you have N SNPs and N people you can almost always “predict” their phenotype PERFECTLY using their binary SNP genotype vectors.
uh drrrr.
Of course what very few people realize is that heritability is technically NOT the percentage of the phenotypic variation explained by genes, it’s the percentage explained by genes when environment is held constant or allowed to vary randomly.
if by that you mean the % explained for a given population within a give range of environments then yes. otherwise no.
if e is the same for everyone, rather than the range of e, the h^2 = 1.
if by “allowed to vary randomly” you mean the subjects are selected at random then yes. but the range of environments for the randomly sampled population is always restricted. that is, no studies have been done on the population of the whole world.
h^2 is a measure of the variance in e just as much as it is a measure of the variance in g.
Ross,
You should join the Prometheus society.
ross?
Yes., Ross. You should join. Then Pumpkin will stop arguing with you.
the only other guy who calls me “ross” is the frequent commenter on lion’s blog, destructure.
guy.
idk who “ross” is.
Use the breeder’s equation, or read this recent Cochran post:
https://westhunt.wordpress.com/2016/04/19/such-a-thing/
BTW you don’t understand what high heritability means. High heritability means that environment has less of a role, and all the twin studies prove that. And that also proves that IQ has a mostly genetic component, which GWAS and GCTA have proven.
*” Since a correlation, by definition, is how close the rank order of two variables (i.e. genetic IQ and actual IQ) agree, it can’t be directly calculated if one of said variables (i.e. genetic IQ) can’t be ranked. It would be like trying to calculate the correlation between height and weight, but all the weights were reported in a language you
didn’t speak.
To sidestep this problem, GCTA was invented by a scientist of East Asian heritage. In GCTA, instead of ranking everyone in your sample from highest to lowest on each trait, you simply randomly assign people to pairs, and for each pair, calculate the genetic distance and the phenotype distance. So for example, if the people who differ by 100 single nucleotide polymorphisms (SNPs), on average, differ by one standard deviation in IQ, and if people who differ by one standard deviation in IQ differ, on average, by 39 SNPs, then perhaps it can be inferred that (in this sample) the correlation between genetic IQ and actual IQ is whatever number when squared and multiplied by 100, equals 39.”
That number is 0.62″*
Wow, I assume genetic IQ varies with individual? In that case, that is amazingly low. dz=h^2S definitely very interesting!
Pumpkin, can you do a post on people with ADHD-PI? I’m pretty sure I have it, although I haven’t been formally diagnosed.
This foggy-headedness has been a huge pain in the ass my entire life. I’m the son of two PHDs, yet I barely made it thru college, and I’m working a menial job. I don’t read often. When I try to, the words on the page are only that–words on the page. I can’t visualize what I’m reading. This is very problematic: I’m a visual, as opposed to sequential, learner. Not seeing it = not getting it. These fellow-sufferers describe it well:
http://www.psychforums.com/attention-deficit-hyperactivity/topic27892.html
Reading aloud helps tremendously, I’ve found.
I’m undergoing neuropsych testing on the second of June. Should I happen to take an I.Q. test, I’ll post the results.
I don’t know enough about ADHD to post about it, but after you’re tested in June, you could write a guest post discussing your test results and/or diagnosis
So for example, if the people who differ by 100 single nucleotide polymorphisms (SNPs), on average, differ by one standard deviation in IQ, and if people who differ by one standard deviation in IQ differ, on average, by 39 SNPs, then perhaps it can be inferred that (in this sample) the correlation between genetic IQ and actual IQ is whatever number when squared and multiplied by 100, equals 39.
That number is 0.62.
that’s an interesting idea and a good example of the concept, but i don’t think that’s how it’s actually done, the reason being that differences between unrelated people aren’t that large.
but the general idea is that people who are closer together genetically are closer together phenotypically, and that some measure of this tendency allows for an estimation of h^2 for the entire population.
but genetic distance may be the so-called “hamming distance” or anything you like as long as it satisfies the criteria for a metric.
this is why i think extrapolation to 0 genetic distance may be the best way of estimating h^2. there’s nothing ambiguous about a genetic distance of 0, and MZTs, or clones, are part of the “gold standard” and DISPOSITIVE study which i’ve detailed many times before. that is, a study which would close this never ending argument about nature vs nurture and would likely surprise and disappoint both sides.
that’s an interesting idea and a good example of the concept,
I’m glad you find it mathematically sound. I was trying to think of ways one could determine a correlation if all they knew were differences between pairs of people and that was my solution.
but i don’t think that’s how it’s actually done, the reason being that differences between unrelated people aren’t that large.
I agree they probably don’t do it that way, but I don’t know why you think the differences aren’t large enough since the numbers I used in my example are numbers I actually heard in Steve Hsu’s youtubes though it’s possible I misunderstood.
this is why i think extrapolation to 0 genetic distance may be the best way of estimating h^2. there’s nothing ambiguous about a genetic distance of 0, and MZTs, or clones, are part of the “gold standard” and DISPOSITIVE study which i’ve detailed many times before. that is, a study which would close this never ending argument about nature vs nurture and would likely surprise and disappoint both sides.
Unfortunately that study is unlikely to ever be done, but GCTA using pairs of individuals in different countries sounds like a very feasible study.
oh and i guess that i just don’t know…
from the HBD perspective…
the spanish are world masters for 150 years, because what it takes to be a weltmeister for that sesqui-century is an EXTREME nobility…an “i don’t give a fuck…fuck you!” attitude.
and i guess i just don’t know.
never done heroin, but thank you jews for lou reed.
I was at a book fair recently and the Spaniards were the most noble of all the booksellers. They were offering several Don Quixote first editions, and also a few Arabic and Jew writings, such that it would give HBD Chick a tingle.
Why were they next to the Swedes and their boring Scandinavian cousins, I really don’t know. It could have been worse if they were with a group of American or Brit Proles.
peepeee has put blinders on her blog.
she might claim that she must, her “mission statement” is curtailed.
maybe.
i wish that…i was born a thousand years ago….i wish that…i’d sailed the darkened seas…from this land here to that…
or i wish peepee would grok SECRETARIAT’S BELMONT.
what pee pee will never get…
every death is a point…a point made…
an exclamation point!
who was dying in droves 100 years ago?
april 1916 motherfuckers?
ireland said fuck you to the UK!
august 2014 to november 2018 is the centenary of the most significant event…ever…
since the resurrection.
And each slow dusk a drawing-down of blinds.
MOTHERFUCKERS!
it’s both funny and DIAGNOSTIC of the hereditists how much of a problem SECRETARIAT is for their world view.
…he is moving like a TREMENDOUS MACHINE..but SECRETARIAT is all alone…an unbelievable, an amazing performance…by this miracle horse…
so if you have a subject who is jamming up against the maximum…
and ca 15 generations later you can’t improve on him…
give up?
that would be the rational decision.
but shoe would just breed using SNP scores, and make a “cheetah”-horse.
whatever mofo.
the ceiling is
SECRA
MOTHERFUCKING
TARIAT!
or rather…
SECRE
MOTHERFUCKING
TARIAT!
whatever the spelling the hereditists must deal with:
1. breeding is always better than engineering
2. breeding has a limit
3. that limit is NOT a cheetah-horse.
4. MOST of the SDs of the very best will NOT be from G. they will be from E.
(that is, if the P = G + E model is followed.)
if you have a subject who is jamming up against the maximum…
The very idea of a maximum is fascinating. We tend to think of the bell curve as extending infinitely, but of course no matter how big the population is, certain phenotypes might be virtually impossible..
make it 3. make it 3 and a 1/2….
it happened 43 years ago, before i was born, and before peepee was born…
come on mofos.
FOLD!
your hand has become increasingly less likely to win as the years have gone by.
make it 3. make it 3 and a 1/2….