When we talk of "close" or "distant" relatives, we are rarely thinking in terms of how far away they live. We are usually referring to the degree of familial closeness, which we all have a feel for but which most of us might have trouble describing in any numerical way.

Usually exactness is not needed. Sometimes, however, it can have big practical consequences. Suppose, for example, that your great-uncle says in his will that all his estate should go to his "closest living relative." How do you calculate who is that lucky person?

There is a precise way of doing this in terms of genetics. Moreover, it is an easy calculation for what I will term a "simple" family, by which I mean one in which there has been no within-family breeding, such as uncles marrying cousins or aunts in one family marrying brothers in another.

Here's the procedure: for any two people in a family, let's call them Mark and Sally, draw the family tree. Take it backward in time, enough generations to reach all of Mark and Sally's common ancestors. For instance, if Mark and Sally are brother and sister, you need go back only one generation, to their parents. If they are first cousins, you must go back as far as their grandparents.

Now, starting with Mark and a value of 1, go back through the generations until you reach one of Mark and Sally's common ancestors. For each generation that you go back, multiply the starting value of 1 by 1/2. So, for example, to get to a grandparent who is a common ancestor of Mark and Sally, the "score" from Mark to grandfather would be 1/2 x 1/2 = 1/4.

Now come forward through the generations from grandfather to Sally, each time multiplying the score to date by 1/2. Since we have to come forward two generations, the final score will be 1/4 x 1/2 x 1/2 = 1/16. This is a measure of the "family closeness" of Mark and Sally, because of a shared grandfather. If Mark and Sally are first cousins, however, they will also share a grandmother. We go through exactly the same procedure for that grandparent, and again find a contribution of 1/16 to the family closeness of Mark and Sally. We now add these contributions, 1/16 + 1/16 = 1/8, and obtain a final answer: first cousins share 1/8 of their genetic material, which is a numerical measure of their family closeness. This is an average figure, because actual inheritance will depend on the way in which genes are distributed over offspring. It is, however, as good a measure as you can get to describe the closeness of relatives in a family.

If Mark and Sally are brother and sister, then going back a generation from Mark to their mother and forward a generation to Sally gives 1/2 x 1/2 = 1/4. Doing the same thing for their father gives another 1/4. Adding these, we find that Mark and Sally share 1/4 + 1/4 = 1/2 of their genetic material. In a specific way, you are four times as close to your brother or sister as you are to any of your first cousins. This led J.B.S. Haldane to make the statement, at first sight perplexing but genetically sound, "I would lay down my life for two brothers or eight cousins."

The same principle applies to any relations. I invite you to check for yourself that a half-brother is as close a relative to you (1/4 shared genetic material) as an uncle, while a great-aunt is as close to you as a first cousin (1/8 shared genetic material).

Most societies, without going through explicit calculations, recognize that inbreeding is likely to have harmful effects on the offspring and have evolved rules of society that discourage it. Thus the marriage of brothers and sisters, with 1/2 shared genetic material, is usually forbidden (the pharaohs of ancient Egypt formed a genetically undesirable exception, with offspring often afflicted by feeble-mindedness). The marriage of first cousins (1/8 shared genetic material) is usually discouraged, while marriage of second cousins (only 1/32 shared genetic material) is freely permitted.

There is what may at first seem like a catch in this method of calculation. Each of us has two parents, four grandparents, eight great-grandparents, and so on. Continue back for thirty generations, and this doubling process indicates that each of us then had more than a billion ancestors. Thirty generations takes us back in time five or six thousand years; but five thousand years ago the total human population was only about a hundred million. We are forced to conclude that we all, though we may not know it, share common ancestors. According to the rules I have provided, all these common ancestors must be included in the calculation because they all contribute to shared genetic material.

Fortunately, the doubling process operates even more strongly to weaken the genetic linkage of individuals. If two people possess a common ancestor as close as five generations back, the two will only share 1/1000 of their genetic material. Ten generations reduce that number to one-millionth. For all practical purposes, those shared remote ancestors can be ignored in determining the closeness of family relationships.

I ought to make one other point. Sometimes, reading about the great apes, you come across a statement like "chimpanzees are closer to humans than any other animals, and have 98 percent of their DNA in common with humans." The only carrier of genetic material in humans is DNA, yet we have asserted that brothers and sisters share only 50 percent of their genetic material. Should we conclude that a chimp is closer to you than your own brother?

There is no contradiction here. The 50 percent shared by a brother and a sister is of genetic material that carries specifically human traits. Much as you might wish it were otherwise, and much as his appearance and behavior might seem to contradict the fact, Great-uncle Fred is far more closely related to you than he is to any gorilla or chimpanzee.

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