Variation And Structure In Populations—Explaining Human Biodiversity
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Sometimes the schoolmaster in me comes out and has to be aired.  This happened the other day in conversation with some friends (intelligent, well-educated over-50s) both of whom knew about Nicholas Wade’s book A Troublesome Inheritance.John Derbyshire On Nicholas Wade’s A TROUBLESOME INHERITANCE—A Small, But Significant, Step For Race Realism

Both my friends came out with the kinds of shallow objections you’ll hear from people who don’t think much about human variation.  “But don’t we all come from Africa?” and “Aren’t our differences just skin deep?” and so on.  One even brought up the old Jared Diamond chestnut: “Why not define races by blood group—a Type A race, a Type O race, and so on?”

That was when schoolmaster mode kicked in.  My explanation didn’t come out altogether coherent, and I’m pretty sure I saw eyes glazing over around one minute in, but I gave it my best impromptu shot.

Improving this little educational exercise in my head later, I came up with the following, to which you are welcome.


Start with a dataset, which you can visualize as a Venn diagram—a big circle containing lots of dots.  The circle is the set; the dots are its elements.  Or:  The circle is a population, the dots are its members.

The dots are all the same kind of thing—all apples, all oranges, all something.  Each one is gifted with attributes characteristic of that thing.  Let’s say, for example, that shape is an attribute, and comes in two varieties:  triangular or square.a big circle containing lots of dots

When an attribute has only a finite number of varieties like this, it’s called a qualitative trait.  So shape—triangular or square—is a qualitative trait.

A qualitative trait may have more than two varieties.  I could declare that each dot, as well as being either triangular or square, is either red, yellow, green or blue.  In other words the dots have the trait color, and it comes in four varieties.

Let’s add another trait.  This one is a quantitative trait: it can vary across a range.  The obvious one is size.  Let’s give each dot a size (defined by area) between one square inch and ten square inches.  Size can be any number in that range.  It might be 7.4908316 square inches, or pi square inches.

I’ll add a second quantitative trait for symmetry.  Suppose that each dot emits a pure note when touched, a pitch, between 256 Hz and 880 Hz—from Middle C to A above the treble staff, more or less.  Again, the pitch might be any number in that range.  It’s another quantitative trait.

Now every one of my dots has four traits: two qualitative (shape and color), two quantitative (size and pitch).

For purposes of some inquiry I’m undertaking, I might divide up my population on one trait.  I might, for example, be interested in the shape division, treating triangles and squares as different sub-populations.  Sometimes this is useful, but it’s not very interesting (except apparently to Jared Diamond.)

Things get interesting when I notice patterns among the traits.  I might notice that most, or even all, of the square dots are blue or yellow; or that big red or blue triangular dots, with few exceptions, emit higher notes than small yellow or green square ones.  Certain traits may seem to “travel together.”

If the population is small, these patterns are likely just random.  If the population is in millions, though, and blue triangles are 50 percent bigger, on average, than yellow squares, and emit lower pitches, that’s a significant pattern.  There is structure in my population.

At that point my scientific curiosity, if I have any, is awakened.  What’s the underlying reason for that pattern?  What causes it?  Why are traits “traveling together” like that?

I speculate, and discuss my speculations with colleagues.  I form hypotheses and test them by further observation or experiment.  I try to untangle correlation and causation.  I publish my results, and hope others will be able to duplicate them.  I do science.

Or if I am a seasoned science journalist I might go round among researchers in the field, read their papers, discuss their speculations and hypotheses, add a couple of my own, and publish a book …


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