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Quantitative Traits

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Siblings vary One of the most curious things to people is that siblings can vary a great deal in their traits. Sometimes, this is not simply due to environment. Height is a predominantly genetic characteristic in terms of its heritability within the population, but the correlation between siblings is only 0.50 in terms of the trait value. The standard deviation in IQ among siblings is only a bit less than the standard deviation among the general population.

And yet with a quantitative trait where most of the variation is due to genes of small effect this seems peculiar. Though genetics is not “blending,” it seems that inheritance should be closer to blending when it comes to thousands of genes combining to account for the variation on one trait.

Andrew Oh-Wilke brings up the objection below:

Because if there are really 5,000-10,000 loci, the law of averages is going to kick in with a vengeance and similarly regression to the mean should be huge, but while IQ breeds fairly true, IQ variation between fairly closely related individuals is often quite significant. If children inherit randomly from both parents and there are really 5,000-10,000 loci that matter, all of which have very small effects, IQ differences between siblings ought to be really, really slight and rare, because the 5,000-10,000 random trials for the large number of low effect SNPs should average out between full siblings almost completely. But, while full siblings are definitely correlated, there are routinely meaningful magnitude sibling IQ differences. When no one inherited factor has an impact of more than say 0.02%, that shouldn’t happen.

Siblings vary

Siblings vary

The short answer is that segregation maintains variance. I allude to this in my Slate piece on grandparents. Siblings may be expected to be 50% identical in terms of their genetic state due to parental contribution, but in reality there is variation around this value. I have two siblings who are 41% identical. The standard deviation around 50% is about 3%.

For the deeper and more explicit formalism in relation to quantitative traits and polygenetic inheritance, you could get a copy of Introduction to Quantitative Genetics (I do recommend this of course). But Alan Rogers published a paper from 1983 which touches upon most of the major issues in a clear manner, Assortative mating and the segregation variance:

Feldman and Cavalli-Sforza (Theoret. Pop. Biol. (1979), 15, 276-307; (1981), 19, 370-377) have emphasized the role of the segregation variance in models of assortative mating for continuous characters. This note examines its behavior in the context of a general additive model. Using known results concerning the effects of assortative mating and selection on genic variance and correlations among uniting gametes it is shown that the effects of these processes on segregation variance will be small if the effective number of loci is large. Thus models in which the segregation variance remains constant are approximate descriptions of the behavior of characters determined by many loci.

Basically he’s saying that contra what some had modeled, segregation variance is rather constant across generations if the genetic variance is on a highly polygenic trait. Naturally this means polygenic traits exhibit segregation variance.

Screenshot 2016-05-15 10.39.25 Rogers shows through some algebra that the segregation variance is a function of the additive genetic variance (the first term after 1/2), and, (1 – f). Therefore if f ~0, the segregation variance is about the same as the additive genetic variance, which to me aligns intuitively with why there is roughly the same standard deviation across groups of siblings and the general population in IQ (though the former is smaller than the latter).

Screenshot 2016-05-15 10.45.41 Rogers shows that f is a function of variance at the locus (weighted across all the loci) and f i, which is the correlation between uniting gametes. If the correlation between gametes is very high (in the context of this paper he is focused on phenotypes and assortative mating), then variance will naturally be low, as there is not going to be genetic variation at that locus in that individual. Basically, f measures deviation from Hardy-Weinberg equilibrium. In a random mating population then f is small, so the segregation variance and additive genetic variance will be of similar magnitude.

 
Razib Khan
About Razib Khan

"I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. If you want to know more, see the links at http://www.razib.com"