# Heritability in twins

Nature Genetics recently published a meta-analysis of virtually all twin studies over the last half century:

Tinca J C Polderman, Beben Benyamin, Christiaan A de Leeuw, Patrick F Sullivan, Arjen van Bochoven, Peter M Visscher & Danielle Posthuma. Meta-analysis of the heritability of human traits based on fifty years of twin studies. Nature Genetics 47,702–709 (2015) doi:10.1038/ng.3285.

One of the authors, Peter Visscher, is perhaps the most influential and innovative thinker in human genetics at this moment and this paper continues his string of insightful results. The paper examined close to eighteen thousand traits in almost three thousand publications, representing fifteen million twins. The main goal was to use all the available data to recompute the heritability estimates for all of these traits. The first thing they found was that the traits were highly skewed towards psychiatric and cognitive phenotypes. People who study heritability are mostly interested in mental function. They then checked to see if there was any publication bias where people only published results with high heritability. They used multiple methods but they basically checked if the predictions of effect size was correlated with sample size and they found none. Their most interesting result, which I will comment on more below was that the average heritability across all traits was 0.488, which means that on average genes and environment contribute equally. However, heritability does vary widely across domains where eye, ear, nose and throat function are most heritable, and social values were least heritable. The largest influence of shared environmental effects was for bodily functions, infections, and social values. Hence, staying healthy depends on your environment, which is why a child who may be stunted in their impoverished village can thrive if moved to Minnesota. It also shows why attitudes on social issues can and do change. Finally, the paper addressed two important technical issues which I will expand on below – 1) previous studies may be underestimating heritability and 2) heritability is mostly additive.

Heritability is the fraction of the variance of a trait due to genetic variance. Here is a link to a previous post explaining heritability although as my colleague Vipul Periwal points out, it is full of words and has no equations. Briefly, there are two types of heritability – broad sense and narrow sense. Broad sense heritability, $H^2 = Var(G)/Var(P)$, is the total genetic variance divided by the phenotypic variance. Narrow sense heritability $h^2 = Var(A)/Var(P)$ is the linear or additive genetic variance divided by the phenotypic variance. A linear regression of the standardized trait of the children against the average of the standardized trait of the parents is an estimate of the narrow sense heritability. It captures the linear part while the broad sense heritability includes the linear and nonlinear contributions, which include dominance and gene-gene effects (epistasis). To estimate (narrow-sense) heritability from twins, Polderman et al. used what is called Falconer’s formula and took twice the difference in the correlation of a trait between identical (monozygotic) and fraternal (dizygotic) twins ($h^2 =2 (r_{MZ}-r_{DZ})$). The idea being that the any difference between identical twins must be environmental (nongenetic), while the difference between dyzgotic twins is half genetic and environmental, so the difference between the two is half genetic. They also used another Falconer formula to estimate the shared environmental variance, which is $c^2 = 2 r_{DZ} - r_{MZ}$, since this “cancels out” the genetic part. Their paper then boiled down to doing a meta-analysis of $r_{DZ}$ and $r_{MZ}$. Meta-analysis is a nuanced topic but it boils down to weighting results from different studies by some estimate of how large the errors are. They used the DerSimonian-Laird random-effects approach, which is implemented in R. The Falconer formulas estimate the narrow sense heritability but many of the previous studies were interested in nonadditive genetic effects as well. Typically, what they did was to use either an ACE (Additive, common environmental, environmental) or an ADE (Additive, dominance, environmental) model. They decided on which model to use by looking at the sign of $c^2$. If it is positive then they used ACE and if it is negative they used ADE. Polderman et al. showed that this decision algorithm biases the heritability estimate downward.

If the heritability of a trait is mostly additive then you would expect that $r_{MZ}=2 r_{DZ}$ and they found that this was observed in 69% of the traits. Of the top 20 traits, 8 traits showed nonadditivity and these mostly related to behavioral and cognitive functions. Of these eight, 7 showed that the correlation between monozygotic twins was smaller than twice that of dizygotic twins, which implies that nonlinear genetic effects tend to work against each other. This makes sense to me since it would seem that as you start to accumulate additive variants that increase a phenotype you will start to hit rate limiting effects that will tend to dampen these effects. In other words, it seems plausible that the major nonlinearity in genetics is a saturation effect.

The most striking result was that the average heritability across all of the traits was about 0.5. Is an average value of 0.5 obvious or deep? I honestly do not know. When I told theoretical neuroscientist Fred Hall this result, he thought it was obvious and should be expected from maximum entropy considerations, which would assume that the distribution of $h^2$ would be uniform or at least symmetric about 0.5. This sounds plausible but as I have asserted many times – biology is the result of an exponential amplification of exponentially unlikely events. Traits that are heritable are by definition those that have variation across the population. Some traits, like the number of limbs, have no variance but are entirely genetic. Other traits, like your favourite sports team, are highly variable but not genetic even though there is a high probability that your favourite team will be the same as your parent’s or sibling’s favourite team. Traits that are highly heritable include height and cognitive function. Personality on the other hand, is not highly heritable. One of the biggest puzzles in population genetics is why there is any variability in a trait to start with. Natural selection prunes out variation exponentially fast so if any gene is selected for, it should be fixed very quickly. Hence, it seems equally plausible that traits with high variability would have low heritability. The studied traits were also biased towards mental function and different domains have different heritabilities. Thus, if the traits were sampled differently, the averaged heritability could easily deviate from 0.5. Thus, I think the null hypothesis should be that the $h^2 = .5$ value is a coincidence but I’m open to a deeper explanation.

A software tool to investigate these results can be found here. An enterprising student could do some subsampling of the traits to see how likely 0.5 would hold up if our historical interests in phenotypes were different.

Thanks go to Rick Gerkin for suggesting this topic.

## 5 thoughts on “Heritability in twins”

1. Thanks, Carson!

Do you think the “most contributions are additive” result is surprising or not? What would you have predicted for the % that are additive prior to this paper?

And does the high amount of additivity make most future work in biomedical research easier (because linear systems are easier to model) or harder (because there may not be many interactions that are both not yet known, but really important)?

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2. that is an interesting post, and i think i saw that paper discussed elsewhere recently. (visscher of course is well known, even by me; tho i’more the Limiting pathway type of zuk and lander). i think from my skim that the ‘saturation’ effect is on track (basically correct) but i think the nonlinearities are both the most interesting and even relevant—this is why even tho supposedly humans share like 90 or 99 percent of their dna with chimpanzees, we aren’t chimpanzees). i’d add one can look at https://www.unz.com where r. khan of gnxp (gene expression blog ) to see some related articles (khan i think was fired by the NYT’s) . i’m more into the stuff from the netherlands on using the ‘central manifold theorem’ used by H Haken (synergetics) —either boomsma or broomsa–there are 2—; a related one was used by kenneth wahlstein (canada, was at UNC greensboro) in BBS (brain behav scis long ago). there are also the various ‘principles of least action’ (which govern my life—they may be used in and required by the us constitution) (stella and hirsch (israel) , nick barton and rhouani—now head of a university in iran), etc. in pop genetics.

i sometimes wonder whether one of the problems i have remembering all these formulas is ‘environmental’. people i know have never heard of anything, they know more about saying ‘reading marx’s capital’ or getting out of jail or thrown out of their relatives house, where to buy c-k and where i live. i’m close to making a 911 call.

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3. @Rick It’s been known since the time of Fisher and Wright that heritable genetic variants should be additive because we inherit individual genes and not full genotypes. Thus any gene that survives selection should have some benefit on its own. However, that is not to say that biology is not full of nonlinearities, it’s just that most of the nonlinearities are already fixed. Hence, it is likely that we mostly inherit additive variants but every once in a while either by genetic drift or a bottleneck or some other mechanism, some nonlinear combination gets fixed.

@Ishi It’s not at all obvious or necessary that the difference between humans and chimps or even rats needs to be nonlinear. 1% of the genome is still 30 million nucleotides. Animal breeding experiments have shown that additive variants can get you multiple standard deviation increases in many phenotypes.

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4. i’d agree that it is neither obvious nor neccesary for nonlinearty to be involved; but i find that to be the most interesting or ‘aesthetic’ possibility—i dislike alot of models which can fit any curve just adding more epicycles. thats why i mentioned the arxiv economics paper—which has the exact same. in my view, kind of logic. a maximum entropy argument fairly well explains economic inequality—and the gini coefficient is also .5 to a first approximation if one goes through the details. but economists who use ‘merit’, genes, opportunity get the same number from a non-entropic argument. that also has to me somewhat weirder even ‘metaphysical’ implications.
i also think the preference for a particular line of thinking or theory (another example is chomsky’s view of language versus rumelghart/clintion/clark/elman connectionist ones—innate or learned) is based on extra-scientific factors ( ideological ones), both environmental and temperamental/personality based (eg 5 factor model or WEIRD people (western educated industrialized rich democratic ones) . ‘men only see what they look at and they only look at what they already have in mind’ (frederick celine, noted french nazi sympathizer and author).

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