Where's the heritability? Right where you'd expect—if you look close enough

Where's the heritability?

Where’s the heritability?

Biologists have at our disposal two major ways to assess how much genetics contributes to variation in the most interesting traits, or phenotypes, of our favorite study organisms—that is, the heritability of those phenotypes.
There’s what you might call the “top-down” approach, under a classic quantitative genetics framework, in which we can measure a whole bunch of individuals with known pedigree relationships, then use some form of linear regression to ask how well that known pedigree predicts the phenotype of each individual—the extent to which individuals with closer relationships have more similar phenotypes is the extent to which genes contribute to that phenotype.
Alternatively, we can use genetic marker data coupled with planned crosses between selected indivdiuals in a quantitative trait locus (QTL) study, or, if controlled crosses aren’t feasible, a genome-wide association (GWA) analysis. These are more “bottom-up” approaches, because they identify discrete pieces of the genetic code that individually explain some fraction of the total phenotype variation within the sample. Add up all the effects of all those individual pieces, and maybe account for some interactions between them, and you should find that you explain just as much of the phenotypic variation as you would with a top-down approach.
Except, it turns out, that doesn’t often happen.
When researchers have gone looking for specific genetic loci underlying traits for which we already have well-established, robust top-down estimates of heritability, they find that they loci they can detect using either QTL or GWA methods don’t account for some—and sometimes a lot—of the known heritability. The classic example is human height. Top-down (heh) methods give height a narrow-sense heritability—that is, the portion of heritable variation not due to interactions between loci or different variants at the same locus—of more than 80%. Yet studies looking for specific loci responsible for height have explained much less than that—sometimes as low as 5%.
Phenotypic variation, in other words, is left unexplained. This has made a lot of people very puzzled, and been widely regarded as a bad thing.
Geneticists call the difference between top-down and bottom-up heritability estimates “missing” heritability. There are many different reasons, none of them mutually exclusive, that QTL and GWA can’t account for all the heritability you’d think they ought to:

  • A lot of heritable variation is due to rare gene variants, which get missed in the sampling for GWA or QTL analyses.
  • A lot of variants underlying interesting phenotypes have small individual effects, which makes them hard to detect without really big samples.
  • Top-down methods may overestimate heritability, because they don’t properly account for interactions between loci.
  • There’s something else going on altogether, that neither top-down nor bottom-up methods are equipped to deal with—inheritance via epigenetic markers, or weird environmental effects.

The first three options essentially posit that bottom-up methods could find the missing heritability if they only had enough statistical power—big enough samples to detect subtle effects of rare variants, and to test for interactions between loci. A paper recently released online at Nature (and available at the preprint server arXiv) puts that proposition to the test, by assembling an very powerful QTL analysis of that unicellular laboratory workhorse, common yeast.
Massively multiplexed phenotyping
The authors, a team at Princeton and the University of Southern California led by Joshua Bloom, crossed a standard strain of laboratory yeast with a strain used in winemaking—strains with detectable phenotypic differences. Following a QTL approach, they collected high-density genotype data for the two parental strains and 1,008 offspring strains at more than 30,000 single-nucleotide polymorphism sites selected to differentiate between the two parental strains. (Given a 12.1Mb yeast genome, that’s a SNP every 400 bp or so across the whole genome, on average.) Then Bloom et al. measured some phenotypes for both parents and the offspring. Forty-six phenotypes, in fact.
How do you efficiently measure 46 phenotypes in more than 1,000 strains of yeast? The phenotypes in question are growth rates in various conditions—at high temperature, or on media at varying pH or doped with metal ions or other chemicals—relative to growth in control conditions. Bloom et al. used a robotic system to automatically apply standardized quantities of yeast cells to agar plates containing the various growth media. After a set growth period (48 hours), they could then image the plates with a scanner and use Image-J and the EBImage package in R to measure the size of colonies grown where the robot had placed cells.
Adding up the small effects
With the phenotypes measured, the team performed QTL analysis for each one, using the marker data to map loci that significantly accounted for variation in each growth-rate phenotype among the 1,008 offspring strains. They also estimated narrow-sense heritability using high-precision estimates of the relationships between all the offspring strains—estimated, again, from the SNP data. Then they compared the total variation explained by all the loci detected in the QTL analysis for each phenotype to the narrow-sense heritability estimated for that phenotype.

Bloom et al (2013), Figure 2a.

Relationship between narrow-sense heritability and phenotypic variation explained by QTL: pretty close to a slope of 1. Image from Bloom et al (2013), Figure 2a.

It was a pretty good match.
Across all 46 phenotypes, QT loci accounted for a median of 88% of narrow-sense heritability. (The full range ran from 72% to 100%.) The authors attribute that score to the high statistical power afforded by a panel of 1,008 offspring strains; when they repeated QTL estimation using only 100 lines, the QTLs that exceeded the significance threshold consistently explained less variation. Consistent with that observation is the fact that, across all traits, a large majority of detected QTLs had small individual effects.
Bloom et al (2013), Figure S3

Most QTLs, across all traits, have small effects. Image from Bloom et al (2013), Figure S3

Elusive interactions
That accounts for at least one of the possible reasons heritability might go missing. To tackle another, Bloom et al. examined the difference between broad-sense heritability—the total variation explained by genetics—and narrow-sense heritability, the proportion of attributable to simple additive effects of individual loci. That difference is an estimate of the variation explainable by interactions between two or more loci—and the yeast cross offspring provided a big enough sample to actually test for pairwise interactions between QT loci.
However, this search didn’t turn up much. Bloom et al. found interactions for only about half the phenotypes (24), in spite of the fact that almost all 46 had some difference between broad- and narrow-sense heritability estimates. Where interactions were detectable, there were only a few, and most of them explained a small proportion of the difference between broad- and narrow-sense heritability. Where’s the rest of the interaction variation? The authors suggest that even their great big dataset still lacks statistical power; and speculate that there may be many cases where more than two loci are interacting.
We’ve gotta have more power!
So Bloom et al. found some—in many cases quite a lot—of the missing heritability, in loci of small effect. In yeast. A study system that makes it relatively easy to create thousands of offspring lines in a test cross, and phenotype them all in a highly controlled, massively replicated fashion. How other organisms that aren’t single-celled could we use in that kind of experiment? Not a lot; off the top of my head, maybe Caenorhabiditis elegans, maybe some plant species. And these would present substantial logistical challenges compared to what Bloom et al. managed.
That leaves those of us who don’t study such organisms to speculate about how well this result applies to orchids, or maize, or giant squid, or humans. It doesn’t help that it’s hard to know whether the phenotypes Bloom et al. measured, while unquestionably an impressive sampling, are a good reflection of the genetic architecture of quantitative phenotypes in general. We know they lack one effect that may often be important in humans and other vertebrates: dominance, when two different variants at the same diploid locus interact in non-addtive ways. The yeast strains Bloom et al. examine are haploid—which simplifies a lot of their analysis, but also means that dominance effects are absent a priori
Still, this seems to be the takeaway: if your candidate loci don’t account for all your heritability, you probably haven’t looked closely enough. If you’re interested in identifying specific loci underlying disease risk, you’ve probably got a lot more phenotyping to do, to dig into that big pile of small-effect variants. If you’re mainly interested in predicting evolutionary responses within natural populations, maybe you’re better off building rigorous estimates of broad- and narrow-sense heritability than identifying lists of loci.
In other words, maybe we should stop worrying, and learn to tolerate (if not love) missing heritability.
For another reaction to the paper, check out the preprint review at Haldane’s Sieve. I found the online-early release at Nature thanks to a tweet from senior author Leonid Kruglyak.
Bloom, J.S., Ehrenreich, I.M., Loo, W.T., Lite, T.-L.V. & Kruglyak, L. 2013. Finding the sources of missing heritability in a yeast cross. Nature. doi: 10.1038/nature11867. ArXive: 1208.2865.
Macgregor, S., Cornes, B.K., Martin, N.G. & Visscher, P.M. 2006. Bias, precision and heritability of self-reported and clinically measured height in Australian twins. Human Genetics 120: 571–80. doi: 0.1007/s00439-006-0240-z
Manolio, T. a, Collins, F.S., Cox, N.J., Goldstein, D.B., Hindorff, L. a, Hunter, D.J., et al. 2009. Finding the missing heritability of complex diseases. Nature 461: 747–53. doi: 10.1038/nature08494.
Rockman, M. V. 2012. The QTN program and the alleles that matter for evolution: all that’s gold does not glitter. Evolution 66: 1–17. doi: 10.1111/j.1558-5646.2011.01486.x.
Yang, J., Benyamin, B., McEvoy, B.P., Gordon, S., Henders, A.K., Nyholt, D.R., et al. 2010. Common SNPs explain a large proportion of the heritability for human height. Nature Genetics 42: 565–9. doi: 10.1038/ng.608.

About Jeremy Yoder

Jeremy B. Yoder is an Assistant Professor of Biology at California State University Northridge, studying the evolution and coevolution of interacting species, especially mutualists. He is a collaborator with the Joshua Tree Genome Project and the Queer in STEM study of LGBTQ experiences in scientific careers. He has written for the website of Scientific American, the LA Review of Books, the Chronicle of Higher Education, The Awl, and Slate.
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