When someone tells you that height is 80% heritable, does that mean:
a) 80% of the reason you are the height you are is due to genes
b) 80% of the variation within the population on the trait of height is due to variation of the genes
The answer is of course b. Unfortunately in the 5 years I've been blogging the conception of heritability has been rather difficult to get across, and I regularly have to browbeat readers who conflate the term with a. That is, they assume that if I say that a trait is mostly heritable I mean that its development is mostly a function of genes. In reality not only is that false, it's incoherent. Heritability is addressing the population level correlation between phenotypic variation and genotypic variation. In other words, how well can genetic variation work as a proxy for phenotypic variation? What proportion of the phenotypic variation can be accounted for by genotypic variation? The key terms here are population level and variation (or technically, variance). We are not usually talking about individuals; and we are restricting our discussion to traits which vary within the population.
In contrast, consider the number of fingers you have on your hand. I assume you have five. How is this specified? Is it a particular diet? Do you enter into an activity which shapes your digital morphology so that it is canalized toward five fingers? Of course not. You have five fingers because there is a genetic program which specifies five fingers during your development as a fetus. There is no variation on this trait in humans aside from a few outliers, to be human is to have five fingers. Additionally, those without five fingers are assumed to be abnormal, they're mutants, not wild type. Of course you could cut off fingers so that the environment would have an impact on the number you manifested (I know someone who had two fingers cut off in an accident at work), but this is pretty rare in the modern age. For the trait of five fingers we can say with a high degree of confidence that for any given individual it is mostly a function of genes. It isn't incoherent to say this, there is no real variation on the trait despite a wide variation in diet and lifestyle. Even malnutrition doesn't really alter the fact that you'll develop five fingers, it's a robust trait. The number of fingers you have on your hand isn't heritable, it's inherited.
Now on to heritability. Heritability is generally used in reference to continuous or quantitative traits. For example, height, I.Q., fingerprint ridge count and so on all exhibit continuous quantitative distributions. Heritability comes out of the tradition of statistical genetics which emerged in the late 19th century to analyze normal variation before Mendelian assumptions came to into play. While someone with three fingers is abnormal, someone who is two inches shorter than the mean is simply deviated along the normal distribution of height. Heritable traits are often subject to the independent action of numerous variables of small effect, so they naturally are subject to the central limit theorem and exhibit an approximate Gaussian distribution (the "Bell Curve"). The investigations of heritable traits is often an exploration of the nature of the variation of those traits. What proportion of the variation is genetic, environmental or an interplay between the two? The easiest way to do this is plot the values of offspring as a function of the mean of the parental values. In short if the trait is highly heritable one would see a strong linear relationship and the slope would approach the value of 1.0. As the relationship between parental and offspring values decreases the line of best fit (the regression) would start to approach 0, at which point the parental values had no bearing on the offspring values. Of course there are complications with this. For example, what about traits (e.g., height) where males and females exhibit different distributions? What about traits which exhibit strong "maternal effect" due to the impact on the fetus of the mother's health during gestation? Of course there is the problem of gene-environment correlation between parents and offspring, e.g., the environmental heterogeneity is not random but tracks the genotypes so as to exaggerate the putative relationship between genes and outcome. Heritability is a term that needs to be used with care, nuance and subtly. In laboratory or agricultural environments where organisms can be bred in strictly controlled circumstances so as to eliminate most of the variation in non-genetic inputs one can increase heritabilities so that a maximal proportion of the variation is due to genetic variation (though this doesn't always eliminate all the noise, as some of it occurs during development and might be the result of random infections of the mother and alterations in the fetal environment). Obviously this is a more difficult proposition when speaking of humans, necessitating the ubiquitous twin studies where as much of the shared environment is controlled as possible.
Going back to height, I noted that in developed countries it is 80% heritable. What if I told you that the heritability was lower in non-developed countries? That probably wouldn't surprise, consider the environmental stochasticity and the greater variation in nutrient intake; it makes logical sense environmental inputs would form a greater proportion of the variation. But please note that again we are speaking about population level variations in the trait! Consider the following assertion: height is more due to environment in Third World countries than in First World countries. This might seem natural when comparing 80% heritability in the First World in height to 60% in the Third World. But the reason that heritability is so high in the First World is that sufficient nutrition exists so that it is no longer a component of variation! In other words, the greater environmental inputs result in greater heritability! Lower or more erratic environmental inputs inputs (e.g., a famine during a critical developmental period) lead to lower heritability as genetic factors cede ground to environmental parameters. Obviously when thinking about it logically the length of one's bones are contingent upon nutritional factors, so even if heritability is high it makes no sense to say that height is "mostly genetic." The increased heritabilities of traits as individuals age are not due to them becoming "more genetic," rather, the non-genetic components of variation seem to drop out or attenuate over time (perhaps this is the outcome of gene-environment correlation as particular genotypes "seek out" particular environments).
Ultimately the major problem here in talking about quantitative traits and their heritable component is the imperfect mapping of statistical terminology with conventional descriptive language. That makes sense insofar as humans seem to be unequipped with much "innate statistics," at least beyond general notions of means, medians and modes. In any case, the key point is to be cautious with language, look closely at the meaning of the terms, and remember that "common sense" interpretations of scientific terms can sometimes lead one astray.
Note: I ignored details like heritability in the "narrow sense" vs. "broad sense," or "additive genetic variance," to keep the post intelligible. But anyone interested in the topic should obtain a copy of D.S. Falconer's Introduction to Quantitative Genetics. The math is at a relatively low level but hits all the major issues.
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Thanks! I actually learned something today :)
Option a, the common sense idea about what percentage of a trait is caused by genes, is arguably meaningless as you imply by referring to incoherence. The arithmetic breaks down when considering a causal factor that is necessary but not sufficient for the development of a trait. If you remove this factor, the trait vanishes so it looks like it is 100% causal. But if you remove all factors but this one, the trait will again be absent so we are back down to 0% causality. Perhaps we can talk about percentages within the undisturbed nexus of causes, but measuring that looks rather tricky! Better still we could define traits relative to each other to invoke relevant comparisons...
But there is an asymmetry in logic worth pointing out. If a trait is not heritable then genes may or may not be influential, but if our trait is heritable then there must be SOME causal contribution from genes. Correlating variances can reveal something about causes just not everything.
Thanks for a very interesting post!
The arithmetic breaks down when considering a causal factor that is necessary but not sufficient for the development of a trait. If you remove this factor, the trait vanishes so it looks like it is 100% causal.
exactly. perhaps part of the issue is the mental model of using the genome as analogous to the phenotypic outcome. that is, each fragment of the genome maps onto some outcome of the phenotype in an intuitive way. you mix these genomic contributions with environmental contributions in various proportions and you get various phenotypic outcomes.
of course the problems is that the genome is a digital system which encodes complex instructions which don't operate via analogy. it's more like a computer program where every line of code may be necessary and so equally important to the execution of a particular developmental step. in this model the genes responsible for the heritability of the trait are among the least important, if you remove them (or lose function) you simply change the quantitative value by a small increment. in contrast there are a many genes which would simply result in the total irrelevancy of the trait because of developmental problems (e.g., bone diseases which make any attempt to measure height trivial).
Thanks for the excellent post. I believe I have heard much before, but it bears repeating often since us laymen don't think about it much and tend to forget the logic behind.
I think you meant to say digital vs analog function.
Hmm. AFAIU gene regulation has analog (and stochastic!) elements in it. A similar description could be that it is a partly algorithmic system where most every part counts.
Another analogy to draw out the major point of Ben's and your logic could perhaps be a factory production chain (or similar systems of differential equations). At any specific time there is with high probability a more or less local bottleneck which looks important. But removing any other part could block or change the system quite as much (or, not coincidentally, more for those DE system).
Just a quick thought to say: great post; and, in my searches for trying to find a good explanation of this issue (i.e., one that I can pass along to others), one of the best explanations is in Alan Templeton's new Pop.Gen Book: Population Genetics and Microevolutionary Theory. This book provides a truly novel approach to population genetics, check it out...
man, you're the second person to recommend templeton's book! i guess i'll have to get it ;-) (there aren't many used copies that are cheap yet)
Great post! I had never really taken the time to think about the semantics of the statement "x is 80% heritable". I appreciate the lesson. :)
great explanation. I was reading Genome by Matt Ridley and on the chapter on intelligence (chapter 6) this sentence stood out:
"If IQ is fifty per cent heritable individually, then some genes must influence it. But it is impossible to tell how many".
Isn't this at variance (no pun indented) with heritability being a population statistic? It is meaningless to say that that 50% of IQ in an individual is inherited.
It's inevitable that people will do this though, they intuitively relate statements about heritability to their own experience to try to test them or interpret what they might mean personally, or to people they know. They'll do it even when they know that's not what it means.
I would argue it's better to have to keep browbeating and have people continue to be interested in and trying to learn and understand the subject, unless they just refuse to accept the correction. But now that you've posted this excellent lecture, you can just keep referring us back to it to keep us on the straight and narrow path to enlightenment :)
I know that's not your stated purpose, which is to get informed comment, you want quality not quantity and I am very sympathetic to that, but don't underestimate the educational value of what you are doing or what it is worth - it's huge, and people who engage will want dialogue now and again, it's human nature.
Your posts uses a lot of jargon, and it rambles a bit. There are also quite a few links to extraneous data. If you are writing for a general audience of non-biologists, then you need to simplify your concepts and organize them better.
Then again, maybe you are writing for a more sophisticated audience, but then why explain ideas they should already understand? Maybe you don't care whether people understand what you are saying. Maybe you are just taking your education out for a walk. I guess that is okay, too.
Razib, you are dead right, in my opinion:
Following that wisdom, in this quote,
I would suggest you phrase it as the lower environmental variation results in greater heritability, and higher environmental variation lead to lower heritability. That is what you mean, right?
i've been a laymen reading about genetics for years and was always carrying the implicit folk interpretation heritable in my head. thanks for the correction and making it explicit what you guys really mean.
Jeff, Razib's obviously writing for an audience that's heard these terms a lot but isn't involved in their use day-to-day, and so is probably a bit fuzzy on what they mean exactly -- as several commenters have already stated.
Maybe you don't care about giving the obvious, charitable interpretation when someone doesn't spell their motives out precisely. Maybe you are just being an asshole. I guess that is OK too.
the lower environmental variation results in greater heritability, and higher environmental variation lead to lower heritability.
well, would have to add "proportion." mebee genetic architecture would matter as well. in any case, my intent was to indicate that better nutrition (more non-genetic input) means that only genes matter in terms of variance. in fact, it seems likely that beyond a certain input level environmental variation wouldn't matter, there's only so much calcium and other nutrients you need to build bones. poorer median nutrition would mean genes matter less (the variance would increase here too is my assumption, though that isn't spelled out).
Then again, maybe you are writing for a more sophisticated audience, but then why explain ideas they should already understand?
"sophisticated" audiences often exhibit distributions of knowledge in particular areas. now, seeing as you found my elementary statistical term "jargon" (i'm really not going to elaborate on what a variance is, on one level it is pretty intuitive) of course it would be greek to you, but those terms map across many disciplines. so it's a common currency i can use with people in other areas who haven't ever thought of things in a genetic context.
This seems to depart from the use of these terms as defined for laymen by scientists like Dawkins (admittedly not a geneticist), who defines genes by their potential differentiation from other genes:
So if there is no allele for four fingers or some other non-five fingered phenotype, how can we say that five fingers is a feature determined genetically?
The code metaphor for gene activity is useful to a point, but it seems to break down where organization is concerned. In order for a code to be meaningful, there must be someone on the receiving end with a key, or codebook. If you tap out instructions to me in morse code, and I don't know morse code, nothing is going to happen. It seems that the only sense in which other molecules in a cell "know" the genetic code is in building proteins. But organisms are not just lumps of proteins, they are complexly organized structures. This seems to be something operating outside the coding/decoding metaphor.
This seems to depart from the use of these terms as defined for laymen by scientists like Dawkins (admittedly not a geneticist), who defines genes by their potential differentiation from other genes:
evolutionary biologists tend to use a different definition of "gene" than molecular biologists. a molecular geneticist might be interested in a specific gene and its functional role. they might "knock out" that gene and generate mutants which then exhibit loss of some function, but the gene itself may be fixed. evolutionary biologists are obviously more interested in variation, and i believe dawkins tends to use g.c. williams conception that a gene is simply a stretch of the genome which lasts long enough to be subject to selection (i.e., it isn't broken up by recombination). broadly interpreted dawkins' definition is covered by five fingers because there are mutants which deviate from the norm. but it isn't a heritable trait because there isn't a normal range of variation, just outliers.
Razib, now I'm confused. Are you saying that to a geneticist there's a gene for five fingers? That doesn't seem right. What would you be "knocking out" in that case? The number of fingers? Perhaps I'm not looking at it the right way, but doesn't this imply an infinite number of alleles? That is, if there are no specific alleles in the homo sapiens population for four fingers, or seven, or anything but five fingers, what do you get when you "knock out the gene"? Zero fingers? Five thumbs? Twenty pinkies?
I was under the impression that morphology shared by a species could not be accounted for by gene expression, and that this was one of the remaining mysteries of molecular biology. Is that an obsolete impression?
i had a long response, but really i think you just need to consider that dawkins' definition there isn't all encompassing. e.g., he is talking about variation within species (his reference to alleles and individuals). it would be totally irrelevant then to a biologist studying the differences on genes between species where the two species might have alternative fixed variants.
and to be clear about my early examples
1) there are a an x number of genes which are implicated in the development of five fingers. all of these genes are functionally fixed (that is, there isn't functional variation on them, because there's no variation on the trait).
2) there are an x number of genes which are implicated in the normal variation of height. these genes exhibit polymorphism which is responsible for this variation. but, there are also an x number of genes are implicated in the development of bones and their lengthening, and these genes are functionally fixed (disrupting any of these genes makes the variational influence of the first set of genes moot).
Thanks Razib, for clarifying.
I'm still curious to see if I understand correctly that to a geneticist there really is a gene (or set of genes) for 5 fingers. It seems to me "five fingers" isn't really a trait, but rather a series of traits that can't be separated fully from each other, or from the structure of the organism as a whole. For example, there are variations in finger lengths, but generally the pinky is notably smaller than the others. And the muscle and tendon relationships among fingers aren't universal (e.g. not being able to move the pinky independently of the ring finger).
In other words it's not just "build such and such a phalange and repeat five times;" there's variation in each digit. So the gene for this trait would have to account for all these sub-traits as well.
Isn't it true that what we might identify as a trait might sometimes be invisible to the genome? We could say, for example, that having seven holes our head is common to all primates, but I don't think there's any genetic relationship between eyes, ears, nostrils and mouth.
I know that all kinds of crazy mutants can be generated by playing with genes, but there must be a finite number of phenotypes, since there are a finite number of protein-building pieces of chromosome. So how do we know what's a "trait," designed by gene activity, and what's just a spandrel, except in those cases where there is experimental evidence (i.e. knocking out genes in fruit flies, etc.) This is why defining genes as choices between alleles seems on much more solid ground to me.
In other words it's not just "build such and such a phalange and repeat five times;"
actually, that's almost exactly what it is. having more than five fingers in humans can be caused by a single mutation that changes the regulation of a gene important in development, essentially so that the developmental program is changed from "make five fingers" to "make six".
http://www.gnxp.com/blog/2006/12/how-to-make-extra-finger.php
P-ter,
The fact that a regulatory gene adds a mutant digit doesn't really demonstrate a "normal" gene for five fingers. It seems more likely that instead of changing the instruction from "make five fingers" to "make six," the mutation causes a single digit to be made twice. After all, "make six fingers" is a pretty vague direction. Are we to add a pinky? A ring finger?
Likewise, the observation that the mutant gene is expressed in the hands/paws doesn't tell us anything specific about the genetic program. We have a phenotypic difference between five and six fingers, with one gene differing between them, but what is responsible for the original five?
Something tells the embryo to branch out at the ends of its limbs, with five branches at each location. But it can't be a single instruction; "five" has no inherent meaning to molecules. We might be tempted to say there is something "emergent" about the five, like the 6 tines of a snowflake, but as you point out, there are too many cases of polydactly to make that plausible. Snowflake "blueprints," based on laws of lattice formation, are immutable, and biological blueprints are not. And yet the alternative that the digits are built individually of each other seems counterintuitive, and wasteful at the very least.
So it continues to seem problematic to me to consider "five fingers" as a genotypic trait.
chris,
read about the role of "morphogens" in determining cell fate in development
http://en.wikipedia.org/wiki/Morphogen
it's likely that an initial signal sets the number of cells that will become fingers, and later differentiation occurs. The trait "five fingers" is not due to a single gene, but rather a developmental pathway (made up of multiple genes). the difference between six and five fingers, however, can be due to a single gene.