What you thought you understood about the meaning of heritability

A quick comment by a colleague about how she teaches students to think about the meaning and limitations of the concept of heritability led me to explore her example of coming to speak the language of one’s country of origin.

Consider English-speaking families in the USA and families that have children when they immigrate to the USA from a place where English is not spoken.  We know that language “runs in the family” in that children will speak the language of their families.  Of course, we suspect that is all about the environment parents provide for the children, but let us examine the heritability of English-speakingness anyway.

We can conduct a classic twin study of 10-year olds to estimate heritability by comparing the similarity of identical (monozygotic or MZ) twins and fraternal (dizygotic or DZ) twins.  What we would expect to find is that if one twin speaks English so does the other, whether MZ or DZ.   And if one twin doesn’t speak English neither does the other, again whether MZ or DZ.  No math is needed to conclude that the heritability is zero.  Notice that this result holds even if the twins in some immigrant families have gone to schools that enable them to become bilingual but the twins from other families have not learned English, at least not by age 10.

Suppose however that we go back to the foundations of heritability estimation as it is conceived of in trials of plant varieties grown in a number of locations.  Growing in a number of locations for humans requires the thought experiment that identical twins are separated and raised one in an English-speaking family and one in a non-English-speaking family.  (Perhaps they could be raised in different countries.)

Suppose that the data looked like Table 1, where 1 = speaks English at 10 y.o., 0 = does not.

Table 1

raised in an English-speaking family raised in a non-English-speaking family
Twin pair 1 1 0
Twin pair 2 1 1
Twin pair 3 1 0

The heritability estimate for the data in Table 1 is .25.

(The math are as follows: Means for the twin pairs = .5, 1., .5.  Variance of those means = 1/18.  Variance for the trait over the whole data set = 2/9.  Heritability = ratio of those variances. [Any statistician worrying about sample versus population variance can simply imagine that this pattern in the data is repeated many times so that the two estimates converge.])

Why is the estimate not zero this time?  After all, nothing changed about the way the world works in relation to language acquisition.   We might suspect that the data point for Twin Pair 2 raised in a non-English-speaking family is recorded incorrectly and should be 0.  But suppose we have asked for this to be checked and it is correct.  What needs to be understood is that the estimate of 0 from the original twin study corresponds to a partial snapshot of the phenomenon compared to the separated twins study, as indicated in Table 2.

Table 2

raised in an English-speaking family raised in a non-English-speaking family
MZ or DZ twin pair 1 raised together 1 n.a.
MZ or DZ twin pair 2 raised together n.a. 0
MZ or DZ twin pair 3 raised together Etc. Etc.

What does it mean that the heritability estimate is not zero?  If the data were from plants not people (and the trait was some plant trait!), then non-zero heritability means that the breeder could expect to increase the average value of the trait in the population by selectively breeding the variety that has higher average value across the locations (i.e., the Twin Pair 2 variety).   The plant breeder might be curious about the factors underlying the observed trait values, but would not have to discover those factors before proceeding.

But these are human data; selective breeding is not possible.  So the next way to look at the non-zero heritability would be to investigate what the underlying factors are.  It turns out, once a sociologist looked deeper at the twins in their families that, for twin-pair 2, the twin raised in a non-English-speaking family watched a lot of English-language TV and learned English even though it wasn’t spoken by the family.

Watching a lot of English-language TV sounds like an environmental factor, so how do we understand that factor resulting in non-zero heritability? From the plant breeder’s point of view, we now have to make sure that the locations have that factor—the families need to have TV with English-language shows and let the child view them—if the heritability value is still to lead us expect to increase the average value of the trait in the population by selectively breeding the variety that has higher average value across the locations.  In short, understanding non-zero heritability does not require that we have exposed underlying genetic factors.

Four objections might arise:

  1. Given that selective breeding is not possible, why then are we interested in heritability for humans?   Answer: There is no need to be.
  2. Is the analysis of Table 1 correct given that being raised in a non-English-speaking family is not being raised in the same location if some children can watch a lot of English-language TV and others can’t?  Answer: We don’t know that the others couldn’t watch English-language TV.  But, even if that were the case, it was through analysis of the data that we decided to look more deeply at the families (locations).  If we had known in advance what all the relevant underlying factors were we wouldn’t have bothered with the twin study.
  3. It is possible that all the twins were allowed to watch English-language TV in the non-English-speaking families, but only in Twin Pair 2 did the twin learn English by the age of 10.  The underlying factor is no longer having English-language TV to watch, but choosing to watch it and learning from that.   That no longer sounds like an environmental factor.  Response: a. From the plant breeder’s point of view, nothing has changed; the label is unimportant; b. From the human sociologist’s point of view, the situation has become more interesting: What leads a child to choose to watch and learn from the English-language TV when it is not spoken in the family?  This is an interesting question, but not one that demands that the factors we investigate are genetic.
  4. What if we learned that, contra the twin study described at the start, DZ twins are less similar than MZ twins in choosing to watch and learn from English-language TV in the non-English-speaking families?  That is, the heritability estimate is non-zero.  Answer: We shouldn’t be any more likely to search for underlying genetic factors than we would based on the non-zero estimate based on Table 1 (which, as noted earlier, is a complete not partial snapshot of the situation).

The impulse to look for the underlying factors is understandable if we are interested in changing the situation (in this case, to produce English-language speakers even in non-English-speaking families).  What heritability estimation does not warrant is taking values of heritability as an indication that the factors to look for are genetic.  Indeed, heritability estimation is a snapshot of a situation at one point of time, so it does not warrant a subsequent search for underlying factors at all.

When breeders use the estimates to make predictions about advances under selection they know from experience that the outcomes do not always match the predictions.  If they care enough about the discrepancy, they might go on to investigate a) the underlying genetic factors and how they are getting recombined through bi-parental matings (unless they are cloning offspring); b) the underlying environmental factors to see whether they are truly reproducing the locations from generation to generation; and c) the ways that those genetic and environmental factors combine to influence the trait.

A clear understanding that heritability does not measure the relative influence of genetic versus environmental factors may lead us not to teach students to think about the meaning and limitations of the concept of heritability through human examples that involve modifying underlying factors.  (The classic case of this approach involves not language learning, but the high heritability human trait height.  One points to the increase in average height of Japanese from the pre-WWII to the post-WWII generation and suggests that changes in the quality of diet led to the change.  The problem with this approach is that it invites us to imagine that the explanation is probably genetic factors if we encounter a trait in which there is a large average difference between groups but no obvious single environmental factor explains the difference.)

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