So you think you can heritable?

What heritability actually means

Aug 07, 2025

Note: This post has a bunch of expandy-boxes with extra details, and an appendix about the “other heritability”. If you want to see those, go to dynomight.net/heritable.

The heritability wars have been a-raging. Watching these, I couldn’t help but notice that there’s near-universal confusion about what “heritable” means. Partly, that’s because it’s a subtle concept. But it also seems relevant that almost all explanations of heritability are very, very confusing. For example, here’s Wikipedia’s definition:

Any particular phenotype can be modeled as the sum of genetic and environmental effects:
Phenotype (P) = Genotype (G) + Environment (E).
Likewise the phenotypic variance in the trait – Var (P) – is the sum of effects as follows:
Var(P) = Var(G) + Var(E) + 2 Cov(G,E).
In a planned experiment Cov(G,E) can be controlled and held at 0. In this case, heritability, H², is defined as
H² = Var(G) / Var(P)
H² is the broad-sense heritability.

Do you find that helpful? I hope not, because it’s a mishmash of undefined terminology, unnecessary equations, and borderline-false statements. If you’re in the mood for a mini-polemic:

Phenotype (P) is never defined. This is a minor issue, since it just means “trait”.
Genotype (G) is never defined. This is a huge issue, since it’s very tricky and heritability makes no sense without it.
Environment (E) is never defined. This is worse than it seems, since in heritability, different people use “environment” and E to refer to different things.
When we write P = G + E, are we assuming some kind of linear interaction? The text implies not, but why? What does this equation mean? If this equation is always true, then why do people often add other stuff like G × E on the right?
The text states that if do you do a planned experiment (how?) and make Cov(G, E) = 0, then heritability is Var(G) / Var(P). But in fact, heritability is always defined that way. You don’t need a planned experiment and it’s fine if Cov(G, E) ≠ 0.
And—wait a second—that definition doesn’t refer to environmental effects at all. So what was the point of introducing them? What was the point of writing P = G + E? What are we doing?

Reading this almost does more harm than good. While the final definition is correct, it never even attempts to explain what G and P are, it gives an incorrect condition for when the definition applies, and instead mostly devotes itself to an unnecessary digression about environmental effects. The rest of the page doesn’t get much better. Despite being 6700 words long, I think it would be impossible to understand heritability simply by reading it.

Meanwhile, some people argue that heritability is meaningless for human traits like intelligence or income or personality. They claim that those traits are the product of complex interactions between genes and the environment and it’s impossible to disentangle the two. These arguments have always struck me as “suspiciously convenient”. I figured that the people making them couldn’t cope with the hard reality that genes are very important and have an enormous influence on what we are.

But I increasingly feel that the skeptics have a point. While I think it’s a fact that most human traits are substantially heritable, it’s also true the technical definition of heritability is really weird, and simply does not mean what most people think it means.

In this post, I will explain exactly what heritability is, while assuming no background. I will skip everything that can be skipped but—unlike most explanations—I will not skip things that can’t be skipped. Then I’ll go through a series of puzzles demonstrating just how strange heritability is.

What is heritability?

How tall you are depends on your genes, but also on what you eat, what diseases you got as a child, and how much gravity there is on your home planet. And all those things interact. How do you take all that complexity and reduce it to a single number, like “80% heritable”?

The short answer is: Statistical brute force. The long answer is: Read the rest of this post.

It turns out that the hard part of heritability isn’t heritability. Lurking in the background is a slippery concept known as a genotypic value. Discussions of heritability often skim past these. Quite possibly, just looking at the words “genotypic value”, you are thinking about skimming ahead right now. Resist that urge! Genotypic values are the core concept, and without them you cannot possibly understand heritability.

For any trait, your genotypic value is the “typical” outcome if someone with your DNA were raised in many different random environments. In principle, if you wanted to know your genotypic height, you’d need to do this:

Create a million embryonic clones of yourself.
Implant them in the wombs of randomly chosen women around the world who were about to get pregnant on their own.
Convince them to raise those babies exactly like a baby of their own.
Wait 25 years, find all your clones and take their average height.

Since you can’t / shouldn’t do that, you’ll never know your genotypic height. But that’s how it’s defined in principle—the average height someone with your DNA would grow to in a random environment. If you got lots of food and medical care as a child, your actual height is probably above your genotypic height. If you suffered from rickets, your actual height is probably lower than your genotypic height.

Comfortable with genotypic values? OK. Then (broad-sense) heritability is easy. It’s the ratio

heritability = var[genotype] / var[height].

Here, var is the variance, basically just how much things vary in the population. Among all adults worldwide, var[height] is around 50 cm². (Incidentally, did you know that variance was invented for the purpose of defining heritability?)

Meanwhile, var[genotype] is how much genotypic height varies in the population. That might seem hopeless to estimate, given that we don’t know anyone’s genotypic height. But it turns out that we can still estimate the variance using, e.g., pairs of adopted twins, and it’s thought to be around 40 cm². If we use those numbers, the heritability of height would be

heritability ≈ (40 cm²) / (50 cm²) ≈ 0.8.

People often convert this to a percentage and say “height is 80% heritable”. I’m not sure I like that, since it masks heritability’s true nature as a ratio. But everyone does it, so I’ll do it too. People who really want to be intimidating might also say, “genes explain 80% of the variance in height”.

Of course, basically the same definition works for any trait, like weight or income or fondness for pseudonymous existential angst science blogs. But instead of replacing “height” with “trait”, biologists have invented the ultra-fancy word “phenotype” and write

heritability = var[genotype] / var[phenotype].

The word “phenotype” suggests some magical concept that would take years of study to understand. But don’t be intimidated. It just means the actual observed value of some trait(s). You can measure your phenotypic height with a tape measure.

On meaning

Let me make two points before moving on.

First, this definition of heritability assumes nothing. We are not assuming that genes are independent of the environment or that “genotypic effects” combine linearly with “environmental effects”. We are not assuming that genes are in Hardy-Weinberg equilibrium, whatever that is. No. I didn’t talk about that stuff because I don’t need to. There are no hidden assumptions. The above definition always works.

Second, many normal English words have parallel technical meanings, such as “field”, “insulator”, “phase”, “measure”, “tree”, or “stack”. Those are all nice, because they’re evocative and it’s almost always clear from context which meaning is intended. But sometimes, scientists scientists redefine existing words to mean something technical that overlaps but also contradicts the normal meaning, as in “salt”, “glass”, “normal”, “berry”, or “nut”. These all cause confusion, but “heritability” must be the most egregious case in all of science.

Before you ever heard the technical definition of heritability, you surely had some fuzzy concept in your mind. Personally, I thought of heritability as meaning how many “points” you get from genes versus the environment. If charisma was 60% heritable, I pictured each person has having 10 total “charisma points”, 6 of which come from genes, and 4 from the environment:

  Genes       ★★★☆☆☆
  Environment ★☆☆☆
  Total       ★★★★☆☆☆☆☆☆

If you take nothing else from this post, please remember that the technical definition of heritability does not work like that. You might hope that if we add some plausible assumptions, the above ratio-based definition would simplify into something nice and natural, that aligns with what “heritability” means in normal English. But that does not happen. If that’s confusing, well, it’s not my fault.

Intermission

Not sure what’s happening here, but it seems relevant.

Heritability puzzles

So “heritability” is just the ratio of genotypic and phenotypic variance. Is that so bad?

I think… maybe?

How heritable is eye color?

Close to 100%.

This seems obvious, but let’s justify it using our definition that heritability = var[genotype] / var[phenotype].

Well, people have the same eye color, no matter what environment they are raised in. That means that genotypic eye color and phenotypic eye color are the same thing. So they have the same variance, and the ratio is 1. Nothing tricky here.

How heritable is speaking Turkish?

Close to 0%.

Your native language is determined by your environment. If you grow up in a family that speaks Turkish, you speak Turkish. Genes don’t matter.

Of course, there are lots of genes that are correlated with speaking Turkish, since Turks are not, genetically speaking, a random sample of the global population. But that doesn’t matter, because if you put Turkish babies in Korean households, they speak Korean. Genotypic values are defined by what happens in a random environment, which breaks the correlation between speaking Turkish and having Turkish genes.

Since 1.1% of humans speak Turkish, the genotypic value for speaking Turkish is around 0.011 for everyone, no matter their DNA. Since that’s basically constant, the genotypic variance is near zero, and heritability is near zero.

How heritable is speaking English?

Perhaps 30%. Probably somewhere between 10% and 50%. Definitely more than zero.

That’s right. Turkish isn’t heritable but English is. Yes it is. If you ask an LLM, it will tell you that the heritability of English is zero. But the LLM is wrong and I am right.

Why? Let me first acknowledge that Turkish is a little bit heritable. For one thing, some people have genes that make them non-verbal. And there’s surely some genetic basis for being a crazy polyglot that learns many languages for fun. But speaking Turkish as a second language is quite rare, meaning that the genotypic value of speaking Turkish is close to 0.011 for almost everyone.

English is different. While only 1 in 20 people in the world speak English as a first language, one in seven learn it as a second language. And who does that? Educated people.

Most people say educational attainment is around 40% heritable (though we'll return to this later). My guess is that speaking English as a second language is similar. But since there's a minority of native speakers (where genes don't really matter), I'm dropping my estimate to 30%.

Say there’s an island where genes have no impact on height. How heritable is height among people on this island?

0%.

There’s nothing tricky here.

Say there’s an island where genes entirely determine height. How heritable is height?

100%.

Again, nothing tricky.

Say there’s an island where neither genes nor the environment influence height and everyone is exactly 165 cm tall. How heritable is height?

It’s undefined.

In this case, everyone has exactly the same phenotypic and genotypic height, namely 165 cm. Since those are both constant, their variance is zero and heritability is zero divided by zero. That’s meaningless.

Say there’s an island where some people have genes that predispose them to be taller than others. But the island is ruled by a cruel despot who denies food to children with taller genes, so that on average, everyone is 165 ± 5 cm tall. How heritable is height?

0%.

On this island, everyone has a genotypic height is 165 cm. So genotypic variance is zero, but phenotypic variance is positive, due to the ± 5 cm random variation. So heritability is zero divided by some positive number.

Say there’s an island where some people have genes that predispose them to be tall and some have genes that predispose them to be short. But, the same genes that make you tall also make you semi-starve your children, so in practice everyone is exactly 165 cm tall. How heritable is height?

∞%. Not 100%, mind you, infinitely heritable.

To see why, note that if babies with short/tall genes are adopted by parents with short/tall genes, there are four possible cases.

If a baby with short genes is adopted into random families, they will be shorter on average than if a baby with tall genes is adopted into random families. So genotypic height varies. However, in reality, everyone is the same height, so phenotypic height is constant. So genotypic variance is positive while phenotypic variance is zero. Thus, heritability is some positive number divided by zero, i.e. infinity.

(Are you worried that humans are “diploid”, with two genes (alleles) at each locus, one from each biological parent? Or are you worried that when multiple people raise a kid they all tend to have thoughts on the merits of semi-starvation? If so, please pretend people on this island reproduce asexually. Or, if you like, pretend that there’s strong assortative mating so that everyone in the population either has all-short or all-tall genes and only breeds with other people with the same genes. Also, don’t find the hypothetical.)

Say there are two islands. They all live the same way and have the same gene pool, except people on island A have some gene that makes them grow to be 150 ± 5 cm tall, while on island B they have a gene that makes them grow to be 160 ± 5 cm tall. How heritable is height?

It’s 0% for island A and 0% for island B, and 50% for the two islands together.

Why? Well on island A, everyone has the same genotypic height, namely 150 cm. Since that’s constant, genotypic variance is zero. Meanwhile, phenotypic height varies a bit, so phenotypic variance is positive. Thus, heritability is zero.

For similar reasons, heritability is zero on island B.

But if you put the two islands together, half of people have a genotypic height of 150 cm and half have a genotypic height of 160 cm, so suddenly (via math) genotypic variance is 25 cm². There’s some extra random variation so (via more math) phenotypic variance turns out to be 50 cm². So heritability is 25 / 50 = 50%.

Say there’s an island where neither genes nor the environment influence height. Except, some people have a gene that makes them inject their babies with human growth hormone, which makes them 5 cm taller. How heritable is height?

0%.

True, people with that gene will tend be taller. And the gene is causing them to be taller. But if babies are adopted into random families, it’s the genes of the parents that determine if they get injected or not. So everyone has the same genotypic height, genotypic variance is zero, and heritability is zero.

Suppose there’s an island where neither genes nor the environment influence height. Except, some people have a gene that makes them, as babies, talk their parents into injecting them with human growth hormone. The babies are very persuasive. How heritable is height?

We’re back to 100%.

The difference with the previous scenario is that now babies with that gene get injected with human growth hormone no matter who their parents are. Since nothing else influences height, genotype and phenotype are the same, have the same variance, and heritability is 100%.

Suppose there’s an island where neither genes nor the environment influence height. Except, there are crabs that seek out blue-eyed babies and inject them with human growth hormone. The crabs, they are unstoppable. How heritable is height?

Again, 100%.

Babies with DNA for blue eyes get injected. Babies without DNA for blue eyes don’t. Since nothing else influences height, genotype and phenotype are the same and heritability is 100%.

Note that if the crabs were seeking out parents with blue eyes and then injecting their babies, then height would be 0% heritable.

It doesn’t matter that human growth hormone is weird thing that’s coming from outside the baby. It doesn’t matter if we think human growth hormone should be semantically classified as part of “the environment”. It doesn’t matter that heritability would drop to zero if you killed all the crabs, or that the direct causal effect of the relevant genes has nothing to do with hight. Heritability is a ratio and doesn’t care.

What good is heritability?

Heritability can be high even when genes have no direct causal effect. It can be low even when there is a strong direct effect. It changes when the environment changes. It even changes based on how you group people together. It can be larger than 100% or even undefined.

Even so, I’m worried people might interpret this post as a long way of saying heritability is dumb and bad, trolololol. So I thought I’d mention that this is not my view.

Say a bunch of companies create different LLMs and train them on different datasets.Some the resulting the LLMs are better at writing fiction than others. Now I ask you, “What percentage of the difference in fiction writing performance is due to the base model code, rather than the datasets or the GPUs or the learning rate schedules?”

That’s a natural question. But if you put it to an AI expert, I bet you get a funny look. You need code and data and GPUs to make an LLM. None of those things can write fiction by themselves. Experts would prefer to think about one change at a time: Given this model, changing the dataset in this way changes fiction writing performance this much.

Similarly, for humans, I think what we really care about is interventions. If we changed this gene, could we eliminate a disease? If we educate children differently, can we make them healthier and happier? No single number can possibly contain all that information.

But heritability is something. I think of it as saying how much hope we have to find an intervention by looking at changes in current genes or current environments.

If heritability is high, then given current typical genes, you can’t influence the trait much through current typical environmental changes. If you only knew that eye color was 100% heritable, that means you’re not to change your kid’s eye color by reading to them, or putting them on a vegetarian diet, or moving to higher altitude. But it’s conceivable you could do it by putting electromagnets under their bed or forcing them to communicate in interpretive dance.
If heritability is high, that also means that given current typical environments you can influence the trait through current typical genes. If the world was ruled by an evil despot who forced red-haired people to take pancreatic cancer pills, then pancreatic cancer would be highly heritable. And you could change the odds someone gets pancreatic cancer by swapping in existing genes for black hair from other people.
If heritability is low, that means that given current typical environments, you can’t cause much difference through current typical genetic changes. If we only knew that speaking Turkish was ~0% heritable, that means that doing embryo selection won’t much change the odds that your kid speaks Turkish.
If heritability is low, that also means that given current typical genes, you might be able change the trait through current typical environmental changes. If we only know that speaking Turkish was 0% heritable, then that means there might be something you could do to change the odds your kid speaks Turkish, e.g. moving to Turkey.

But be careful. Just because heritability is high doesn’t mean that changing genes is easy. And just because heritability is low doesn’t mean that changing the environment is easy, or even possible. Heritability could be low because things are just random.

But heritability doesn’t say anything about non-typical environments or non-typical genes. If an evil despot is giving all the red-haired people cancer pills, perhaps we could solve that by intervening on the despot. And if you want your kid to speak Turkish, it’s possible that there’s some crazy genetic modifications that would turn them into unstoppable Turkish learning machine.

Heritability has no idea about any of that, because it’s just an observational statistic based on the world as it exists today.