Tuesday, December 24, 2013

More than All

Imagine there are two islands, widely separated. Imagine there is some easily quantifiable difference between the two islands, say average height. The inhabitants of Island A are noticeably talleer (on average) than than the inhabitants of Island B. Finally, imagine that we wish to determine to what extent the difference is genetic, and what extent it is environmental.
We might initially guess that about half the difference is environmental (say, due to differences in diet) and about half genetic, and might consider the possibility that the difference is all genetic or all environmental to be the extreme cases. But that would be a mistake: it's quite possible that the environmental and genetic factors tend to work in opposite directions, and so the observed difference could be "more than all" due to one or the other. Making the simplifying assumption that all environmental differences act through diet, and that there are no synergistic effects between the genes and the diet, we could determine the answer we seek by equalizing the diets. If the difference in heights in our new experimental population is smaller than the previous difference but keeps the same sign, we can conclude that indeed the factors act in the same direction, and can calculate what fraction of the previous difference was genetic and what fraction was environmental.
But it could be that after we equalize the diets, the difference becomes even larger than before. In that case, the previous difference was more than 100% genetic, with environmental differences acting in the opposite direction. Conversely, it could be that after equalizing the diets, the previously "tall" island is now the "short" island. In that case, the previous difference was more than 100% environmental, with genetic effects working in the opposite direction.
Of course, we can't actually perform this kind of experiment. It is unethical and impractical.
The point is, where there are multiple factors at play, a 100% factor isn;t necessarily the whole story. It isn't even necessarily the most important factor. If one factor is is by itself responsible for 100% of an observed effect, that only means that the other factors taken as an aggregate cancel each other out. It does not mean they are insignificant by themselves. It is even possible that the 100% factor is not the most important factor.

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