Down the line

By Razib Khan | November 2, 2008 3:22 am

My discussion with Jim Manzi on epistasis generated a lot commentary. It’s a complex topic, as I said there are different ways to define epistasis, and evolutionarily its effect on trait value might be different from its effect on fitness. Finally, I think it is important that epistatic and additive genetic variation can convert from one to the other; and over the long term it is this heritable variation which is the “stuff of evolution,” so to speak. But a friend recommended that I post a figure from Genome-wide association analysis identifies 20 loci that influence adult height.

One figure does not an argument make, but the cumulative impact of these data will resolve to some extent disputes about the efficacy of interaction effects. I say to some extent because evolutionary biology is predicated on variation, and I will not be surprised if one finds it difficult to fruitfully generalize about the ubiquity of particular processes across the whole of deep time & the tree of life.

  • Darth Quixote

    Manzi’s factory analogy is flawed. Once the optimal genome is attained, it is immediately broken up in the next generation by recombination. This is why the increase in a trait induced by selection is determined by the narrow-sense heritability: the proportion of the trait variance accounted for by the straight line (or plane, or hyperplane) fitted by weighted least squares to the genotypic values (the entries in what Manzi calls the “look-up table”). If, as Manzi would have it, the slope of this line is zero, then evolution is impossible. If the fitness of the optimal factory cannot be predicted at all from a linear approximation, then the fitness advantage of its descendants will decay by half each generation.
    The narrow-sense heritability need not be high in order to account for the paleontological record of evolution. In fact, it might not even have to be statistically distinguishable from zero. But countless selection experiments have shown that the narrow-sense heritability for most traits is typically well north of zero.
    If a biometrical study estimates that the narrow-sense heritability of some trait (height, IQ, or what have you) is 0.80, then this very roughly amounts to the assertion that the correlation between actual trait value and estimated trait value from a linear function of allele counts is 0.80^0.5 = 0.89. I personally do not think this a ridiculous conclusion; the surface of trait value in genotype space can be quite rugged and still admit very good predictability from a linear approximation.
    Admittedly, most biometrical studies employ models that are certainly false; they lack the degrees of freedom to estimate epistatic components of variance. But the conclusion of high narrow-sense heritability cannot easily be discounted. Suppose that the MZ correlation is 0.80 and the DZ correlation 0.40. The simplest possible model fitting these data is that the trait is determined entirely by additive genetic effects, with no influence of shared environment; this is so because MZ twins share twice as much of their genome identical by descent, relative to DZ twins. Such a model gives a narrow-sense heritability of 0.80. It is in principle possible, however, that the narrow-sense heritability is zero. Suppose that the entire MZ correlation is accounted for by non-additive interactions between alleles at the same locus (dominance) and environmental effects. Then, if you set the proportion of trait variance attributable to intra-locus non-additive interactions equal to ~0.5 and the proportion of trait variance attributable shared environment to ~0.3, you get exactly the same fit as the additive model. A genome-phenome map giving rise to such parameters, however, is truly pathological. One way to realize such a map is, at all loci, to set the allele frequency to 0.5 and to give the heterozygote the highest trait value. Other realizations depend on an even more grotesquely balanced combinations.
    In any case we have the evidence from selection experiments telling us that, across a variety of organisms and traits, that the narrow-sense heritability is typically some nontrivial value greater than zero.
    Some good reads:

  • Darth Quixote

    then the fitness advantage of its descendants will decay by half each generation.
    Whoops. It should be “the fitness of its descendants will decay by at least a factor of 0.75 each generation.”


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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at


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