Mind the residual!

One of the important things to remember in life is that even after accounting for “all factors” often you can’t account for much. By “life” I do not mean mathematics or physics, two domains where this does not hold. In biology by contrast this is something you always have to keep in mind. I like to say that genes matter, but they’re not everything. As a specific illustration, an old friend with a background in elegans research observed that even with isogenic lines with controlled environmental conditions you can only account for half the variation in some traits which are clearly biologically caused. In plainer language, if you have inbred genetically homogeneous organisms in uniform conditions you’re still going to have variation because of randomness. A side effect of the mysterious aspect of all this is that the “environmental” component is often totally outside of our control (at least conscious).

I’ve been thinking a little about this because of the divergent developmental paths of my two children. To a good approximation my son is in the interval of one to two standard deviations above the norm in size, while my daughter is one to two standard deviations below.* To our knowledge there hasn’t been any difference in environmental input, and they began life at about the same weight and length. The divergence began within the first few weeks, as he gained an inordinate amount of weight in his first week. Height is a quantitative trait which looks to be about 80 to 90 percent heritable in Western societies. That means that 80 to 90 percent of the variation within the population can be accounted for in variation of genes in the population. I suspect many people would be surprised by such a wide range in size in offspring despite the high heritability of height, but correlation in height for full siblings is only ~0.50.

Let’s assume that our offspring end up one standard deviation above and below the norm in adult.** What’s the probability of this, assuming these two particular parents? Well, the mid-parent expected value is ~1/3 above the mean. Therefore my son is ~2/3 standard deviation units above expectation, and my daughter is ~1 & 1/3 below. The probability that my son would be as long as he is is about ~25% (i.e., 25 percent chance his particular length, or longer). For my daughter’s height I get 9%. So the chance of having two children which are this far apart in size is about 2%, 1 out of 50. It’s not common, but, it’s not exactly vanishingly rare.

This sort of insight can be extrapolated to any quantitative trait. Imagine for example that a couple has a tall, intelligent, and good looking offspring. The chance of replicating this is not particularly good.*** It is the nature of things for there to be diversity within families. From what I know about height and intelligence the variation within families for quantitative traits is probably about the same as the variation within the population (in standard deviation units).  Of course the average within families may differ a great deal from the average within the population, but  that is a different issue altogether.****

* Averaging over time, and also taking into account imprecision at this age in measurement.

** I have yet to find a correlation statistic for predicting infant/toddler height to adulthood. Please tell if you know. More precisely the “double from height at age two” is an expected value. I want the error.

*** Yes, I’m aware of the genetic correlation between these traits, but it’s not incredibly high.

**** I know of a family where one brother became a Rhodes Scholar, while the other went on to graduate from a moderately selective private college. In another family the second brother wouldn’t be too shabby, but he was labelled the “dumb one.”

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