# The Widespread Abuse of Heritability

Together with evolution, heritability is perhaps one of the most misunderstood and abused concepts in biology.

Some white supremacists appeal to moderate to high estimates of heritability for phenotypic traits to justify genetic determinism, that genes explain between-group differences, the discrimination of ethnic groups or other malignant and pseudoscientific beliefs that are incompatible with science.

Some egalitarian dislikes scientific results regarding moderate to high heritability estimates because they believe that it indicate that the environment is unimportant in explaining the phenotype of individuals and latch onto single studies showing low heritability as if that meant that genes are less important.

As we shall see, both of these groups believe things that are flawed from a scientific standpoint. But before we discuss why and how this is, it might be beneficial to know something about what heritability actually is. Our definition of heritability will be unpacked and improved in several stages to facilitate understanding.

## Background to Heritability

Here is the most general and non-specific mathematical description of what heritability is.

(1) Heritability: a ratio of variances.

To unpack this statement, we need to know what a ratio is and what variance is.

A ratio can be explained in terms of a division. It has a numerator (above the division sign) and a denominator (below the division sign).

To understand variance, we need to understand what an arithmetic means (average) is. An arithmetic mean of a series of measurements is the sum of those measurements, divided by the number of measurements. If the measurements are: 5, 8, 2, 12, 7, 4, 5, 5, 4, 8, the arithmetic mean is the sum of these measurements (5 + 8 + 2 + 12 + 7 + 4 + 5 + 5 + 4 + 8 = 60), divided by the number of measurements (10). In this case, it is 6 (60/10).

Variance is a specific way to describe how far spread out measurements in a sample are from the arithmetic mean.

Here is how you construct the variance of the data in the sample ($s^{2}$). You start by taking the difference between a specific measurement (say, $x_{1}$) and the mean ($\overline {x}$).

$x_{1} - \overline {x}$

and then squaring it

$(x_{1} - \overline {x}) ^{2}$

Then this is done for all of the measurements and these are summed.

$(x_{1} - \overline {x}) ^{2} + (x_{2} - \overline {x}) ^{2} + ... + (x_{n} - \overline {x}) ^{2}$

This can be written in an equivalent way using sigma notation.

$\sum \limits_{x=1}^{n} (x_{n} - \overline {x}) ^{2}$

Finally, this is divided by the number of measurements.

$s^{2} = \sum \limits_{x=1}^{n} \frac{(x_{n} - \overline {x}) ^{2}}{N}$

When one is using the sample to infer something about the population, N – 1 is used instead of N to correct bias for small sample size.

For our sample, the variance is calculated like this:

$\frac{(5 - 6)^{2} + (8 - 6)^{2} + (2 - 6)^{2} + (12 - 6)^2 + (7 - 6)^{2} + (4 - 6)^{2} + (5 - 6)^{2} + (5 - 6)^{2} + (4 - 6)^{2} + (8 - 6)^{2}}{10} = 7.2$

So heritability is one variance divided by another. But variance of what?

(2) Heritability: the ratio of genotypic variance to phenotypic variance.

If the mathematics seemed to hard, you can think of variance as “variation” as a simplification. So heritability is the genotypic variation divided by the phenotypic variation. What does this mean in the biological context?

(3) Heritability: the amount of phenotypic variance (“variation”) that can be attributed to the genetic variance (“variation”).

As we saw, the variance is calculated by a bunch of measurements. In the biological context, these measurements come from different individuals. This means that heritability, on a fundamental level, is a population-level concept. It has nothing to do with a particular individual, but with a population (from which the sample was taken).

(4) Heritability: the amount of phenotypic variance (“variation”) in a particular population that can be attributed to the genetic variance (“variation”) in that specific population.

This is worth going into a bit more detail. Heritability tells you absolutely nothing about how much effect genes have on a certain trait in an individual. A high estimate of heritability for a trait does not mean that genes have a strong influence on that trait. It means that the variation in the trait is to a large degree influenced by the variation in genes. So there is a profound difference between heritability and inheritance.

Let us take an example. The heritability of height in industrialized western countries (e. g. Australia) is about 0.8, whereas in China it is 0.65. This does not mean that genes more strongly influence individuals in industrialized western countries than in China. What it means that, in Australia, the variation in height does not depend that much on environmental variation (most individuals are well-fed). In China, difference in nutritional status influences differences in height more than in Australia.

Another example is the number of fingers on one hand. We know that genetic causes of having a different number of fingers than five is extremely rare. In other words, the factor that accounts for almost all cases of having more or less than five finger is e. g. industrial accidents and other environmental factors. That means that the heritability of having five fingers on one hand is almost 0. Yet, we know that there are genetic influences on finger development.

In other words, a high estimate of heritability for a given trait does not mean that the genes strongly influence that trait. It just means that genetic variation accounts for a relatively high proportion of phenotypic variation. Similarly, a low estimate of heritability does not mean that genes are unimportant in the phenotype of a particular individual. It just means that variation is mostly due to environmental variation.

(5) Heritability: the amount of phenotypic variance (“variation”) in a particular population that can be attributed to the genetic variance (“variation”) in that specific population, but not a measure of the relative influence of genes on the phenotype of an individual compared to environment.

There is a crucial element still missing here, namely environment. As we saw with height, estimates of heritability for a phenotypic trait varies depending on the environment.

(6) Heritability: the amount of phenotypic variance (“variation”) in a particular population in a given environment that can be attributed to the genetic variance (“variation”) in that specific population in that given environment, but not a measure of the relative influence of genes on the phenotype of an individual compared to environment.

An estimate of heritability is only valid for the particular population in the particular environment where the data came from.

Imagine two populations of flowers. One, let’s call it A, has an average of 10 cm stalk and all of them are between 9 and 11 cm. The other population, B, has an average of 4 cm stalk and all of them are between 3 and 5 cm. Assume that the heritability of stalk length in each population is 1. That means that all the variation in length is due to genetic variation. But, as it happens, population A has big lamps over their location, whereas population B does not. So, clearly, heritability of a phenotypic trait within groups tells you nothing about the causes of the variation between groups.

Heritability: the amount of phenotypic variance (“variation”) in a particular population in a given environment that can be attributed to the genetic variance (“variation”) in that specific population in that given environment, but not a measure of the relative influence of genes on the phenotype of an individual compared to environment and is not informative about between-group differences.

So this brings us to a robust and clear definition of heritability.

## Examples of abuse or misuse of heritability

I will be looking at a few examples where people are either abusing heritability for their morally questionable ideological goals, researchers who despite knowing more about heritability still misuse it and will finish with an example of an egalitarian who, despite being almost entirely correct, still manages to misunderstand not only heritability, but also the difference between heritability and genetic mapping. The space devoted to each example should not be seen as proportional to the moral or scientific severity of the misuse. On the contrary, the most absurd abuses are the easiest to debunk.

1. In general, the concept of heritability is abused mostly by white nationalists, white supremacists, racists and neo-Nazis. Most treatments of heritability that I have read written by individuals of these groups is horribly flawed, often both mathematically and scientifically.

It is easy to find abuses of heritability in topics posted at the Stormfront forum. It is the world’s largest hate forum with assorted white nationalist, white supremacists, racists and neo-Nazis inhabitants. I won’t link to specific posts on Stormfront out of principle, but a web search of the topic title or quotes can be easily done.

In the hate-filled crackpot thread “Anti’s why do you Believe negro’s are our equals?”, the user MattwhiteAmerica posted (#71, top post on page 8) some text that talked about on heritability that made the following ridiculous claims:

As environments become more equal, the “remaining differences in intelligence are increasingly determined by differences in genes” (Herrnstein, 1994, p. 91) and the heritability of intelligence increases. Thus, as the egalitarians make the environments of blacks and whites more equal, the remaining IQ differences between blacks and whites will become more controlled by genes and therefore more intractable.15

This is false for a number of reasons. First, heritability is not informative about between-group differences in a trait. Second, if environmental variation that influences variation in IQ test scores is eliminated, this will reduce the overall variation in IQ test scores and so weaken any white supremacist argument about race and IQ. Third, as a high heritability of IQ test scores does not imply that the influence of genes on IQ test scores is large. Remember, heritability is just a ratio of variances, not about individual development. Fourth, both the influence of genes and genetic variation does not make something more resistant to change. Genes play a large role in certain diseases like phenylketonuria, but the difference between people with PKU and without PKU can be reduced by simple environmental interventions (e. g.phenylalanine free diet). The exists influences of genetic variation on variation in IQ test scores, but these estimates are only valid for a particular population in a particular environment. We also know that environmental interventions can increase IQ as the reaction range is something like 15-20 points.

2. A paper called “Thirty Years of Research on Race Differences in Cognitive Ability” in Psychology, Public Policy, and Law back in 2005 by Rushton and Jensen claims that a moderate heritability of IQ test scores within groups imply that the difference between groups is 50% due to genes. As we have seen, this is wrong. Heritability is not informative about in group differences, as it is possible to have a heritability of 1 for a trait within a group, yet attribute all variation between groups to environmental variation. Second, heritability says nothing about the relative merit of genes in explaining phenotypic variation, only the relative merit of genetic variation as an explanation. Despite understanding more about heritability than the average white supremacist, Rushton and Jensen still make this flawed argument.

3. Rushton and Jensen in a 2010 paper called “Race and IQ: A Theory-Based Review of the Research in Richard Nisbett’s Intelligence and How to Get It” continues to incorrectly interpret heritability.

Brain size is also highly heritable. An MRI study of 112 extended twin families found heritabilities of 82% for whole-brain gray matter volume, 87% for wholebrain white matter volume, 86% for IQ, and 100% for the relation between them (Posthuma et al. [117]). An MRI study of 46 pairs of twins found a high heritability for many specific connections within the brain, including myelin sheath, the fatty “insulation” that coats the axons and increases the speed of neural transmission

Heritability is not the same as heritable. Heritability is the proportion of phenotypic variation in a particular population and environment that can be attributed to genetic variation in that population and environment. It says nothing about how much of a character is caused by genes or how much genetic influences is inherited. Finally, it is genes, not phenotypes, that are inherited.

4. For good measure, let us look at some misunderstandings of heritability made by an egalitarian. Back in May 2005, Stephanie Zvan wrote a blog post for Scientific American called The Politics of the Null Hypothesis. My overall impression is that the text is tightly argued and an intellectually impressive piece of popular science. Because of that, there is some legitimate room for simplification and the mistakes that I will be discussing are not that prominent and does not to any greater extent undermine the general arguments or conclusions that Zvan makes.

Still, it is worth correcting them for completeness. They are generally divided into two groups of errors: (1) thinking that heritability is about how much phenotypic variation is caused by genes (as opposed to genetic variation) and (2) confusing heritability studies with genetic mapping.

No one is pretending BGI Hong Kong doesn’t exist or that it isn’t looking for genes associated with variability in IQ scores. No one is issuing fatwas to stop them or even protesting their work. Some people are questioning IQ as a proxy for intelligence, but no one is saying the work shouldn’t go forward until a better proxy is found. Similarly, no one is pretending that Paul Thompson isn’t doing some fascinating work in brain imaging and variability in brain structure.

BGI Hong Kong uses genome-wide association studies (GWAS). That means that they are looking at variation in single-nucleotide polymorphisms (SNPs) associated with variation in phenotypic trait (such as IQ). In other words, they are not looking for genes associated with variability in IQ scores, but variation in SNPs associated with variation in IQ scores.

What is in dispute is the likelihood that genes will be found that account for any significant fraction of the variability found in human intelligence and whether the current literature on the topic is sufficient to predict that

Here Zvan confuses two different research questions: (i) what the heritability of IQ is and (ii) the problem of the missing heritability. Do not confuse estimates of heritability with genetic mapping studies. Knowing that something exist and finding the exact location are two different things.

Zvan is not alone in this as Jerry Coyne made the same mistake when he decided to share his views about medical psychiatry, which I criticized in my article Why Jerry Coyne is Wrong about Medical Psychiatry.

Heritability of IQ is about what proportion of phenotypic variations in IQ that can be explained by genetic variation (in a particular population and environment). In general, heritability of IQ is 0.5-0.7 (but remember the qualifiers in the previous sentence).

The problem of the missing heritability, on the other hand, is the problem that the SNPs found by GWAS usually only account for a tiny fraction of this heritability. But this does not mean that the heritability studies where wrong. It just mean that the variation in phenotype does not come primarily from variation in additive alleles. One of the most prominent explanations for the missing heritability is genetic interactions, which is not at all investigated in GWAS. There is almost no controversy that in-group variation in IQ is influenced by genetic variation. The controversy is where this heritability can be found.

Instead, these studies rely on degree of relatedness (usually between identical and fraternal twins) as a measure of shared genes. This sounds reasonable, and to a degree it is. However, unless researchers can measure or control for the way genes unrelated to intelligence interact with the environment, these studies can’t tell us how much variation in brain structure is due to shared genes that code for intelligence and shared genes that code for something else, such as illness that limits time in school. Until these studies are designed to look for genetic influences in addition to environmental influences, these studies are useless for their intended purpose

There are problems and limitations with twin studies, and confounders include prenatal hormonal influences and correlation between environment in the adoptive family. After all, it is not an equal probability that the adoptive family will live in Somalia and Sweden. However, the particular objection to twin studies that Zvan is making here is confused. This is because heritability estimates the proportion of phenotypic variation that can be attributed to genetic variation in a given population in a given environment. Heritability studies are not trying to find “genes that cause intelligence” (in which case the objection that they need to control for other genes that indirectly reduce adult IQ by influencing environmental exposure would make sense). There is nothing that says that the genetic variation identified in a particular population/environment is directly causative of the variation in phenotypic traits. That is for studies in functional genomics to decide. The coverage of the arguments made by Shalizi is very good, though. They are worth reading by everyone.

Despite the fact that these studies do not and cannot tell us that there is a genetic component to the variation in IQ, we still see genetic triumphalism like this 2009 article in The Economist.

Heritability studies can tell and do tell us that some of the variation in IQ can be attributed to genetic variation (but not about genes per se). To be sure, these studies have important limitations, but they are not as large as to eliminate or strongly reduce non-zero heritability of the trait completely.

Visscher, P. M., Hill, W. G., & Wray, N. R. (2008). Heritability in the genomics era – concepts and misconceptions. [10.1038/nrg2322]. Nat Rev Genet, 9(4), 255-266.

Brooker, R. J. (2011). Genetics: Analysis and Principles. New York: McGraw-Hill, Fourth edition.

Passer, M., Smith, R., Holt, N., Bremner, A., Sutherland, E., & Vliek, M. (2009). Psychology: The Science of Mind and Behavior. New York: McGraw-Hill Education.

#### Emil Karlsson

Debunker of pseudoscience.