What a tangled web we weave...
...when first we practice to conceive!
Sorry about that. You know, for a professional geneticist, I sure don't talk much about genetics in here. Not surprising, really-it's too much like work. But I've been dying to use that title for months now....
I got to thinking about my ethnic heritage after watching a scene in the movie Porco Rosso, in which we find that one of the main characters has a grandmother who is one-quarter Italian, and so is accepted (for the convenience of the bad guys) as being Italian himself. Traditionally, I've thought of myself as half Irish and half Swedish; but neither nationality shows up in my appearance, unless you look really hard and notice that about one in 20 of my beard hairs is red. So, I estimate that I have, at most, eight or nine chromosomes (out of 46) from each nationality, and that the rest of my chromosomes are generic, who-knows-where European. (However, my Y chromosome is almost certainly Irish, because if you scan straight up the male line you'll surely find an Irishman after several generations.)
Usually, people don't bother to divide their ancestry up more finely than quarters (thus making the distinction at the grandparents' generation), but once in a while you'll meet someone particularly proud of her pedigree, who identifies herself as being one-eighth [what have you]. The character in Porco Rosso was one-sixteenth Italian. How far back can we reliably go? Should we even bother to try to find out whether we're, say, 1/128 Tibetan?
We usually assume that we have, in addition to our two parents, four grandparents, eight great-grandparents, 16 great-great-grandparents, and so on: with each additional generation removed in ancestry we double the number of ancestors in that generation. Naturally, we can't do that forever. For example, thirty generations back we would each have to have 230, or over a billion (109), great-to-the-twenty-eighth grandparents-and even if we lump all the people on earth together into one population, there weren't that many people on earth 600 years ago. In other words, we're all slightly inbred: some individuals within those myriads of progenitors appear in our family tree more than once. And the average amount of inbreeding depends on the size of the population. A very isolated population, like those on certain Pacific islands, is highly inbred, by necessity; and even a large interbreeding population (think of the world's largest cities) has a significant amount of inbreeding.
Measuring the average consanguinity (a fancy term for inbreeding) in populations is very difficult, because even to make an educated guess, it is necessary to assume that everyone chooses mates at random-and of course that assumption is never true. Modern transportation is beginning to overcome the problem of geographical separation, but even where lots of people live within walking distance of one another, as in Manhattan, many reproductive barriers still exist: economic class, race, education and a host of other factors. So, the question you're dying to ask-"How closely are my spouse and I related, on average?"-is not answerable to any reasonable degree of accuracy in the general case.
Nonetheless, a careful survey of a very large number of families within a population may yield a pretty good guess. Prof. Lynn Jorde at the University of Utah recently carried out an extensive study of the inbreeding of about 300,000 Mormons, in order to assess whether close inbreeding was associated with increased child mortality.
At this point I'd like to dispel a myth: Mormons are not more inbred, overall, than the American population at large. Their population is large enough, and receives enough genetic inflow from outside, that two Mormons chosen at random might as well be from anywhere in the USA. Utah Mormons make such a good subject for studies of human genetics because they have large families and because they keep immaculate genealogical records.
(On the other hand, Mormons in isolated populations are as inbred as you'd expect a small isolated group to be. A few places in southern Utah clearly suffer from a deficiency in hybrid vigor. Probably not coincidentally, these same pockets of inbreeding also happen to encompass most of the few remaining practitioners of polygamy. Another aside: I recall distant suburb of Salt Lake City at which everyone likes to poke fun-with good reason, in my opinion. I used to joke that the only source of genetic diversity in this suburb was the incredibly high mutation rate from all the toxic metals in the mine tailings that everyone there lived on.)
Anyway, in order to explain the results of Prof. Jorde's survey, I have to make a slight technical digression. Geneticists usually express the extent of inbreeding using the coefficient of inbreeding, represented by the letter f (for "familiality"). The actual definition of f is a bit complicated for this discussion; suffice it to say that f is proportional to, but generally not equal to, the probability that a given rare recessive disease will show up in an inbred individual. Below I have tabulated values of the inbreeding coefficient for the offspring of matings between various types of relatives. As a general rule, f decreases by a factor of four for each additional generation between the related parents and their common ancestors.
Offspring of f
Siblings 0.25 (= 1/4)
1st cousins 0.062 (= 1/16)
2nd cousins 0.016 (= 1/64)
3rd cousins 0.0039 (= 1/256)
4th cousins 0.00098 (= 1/1024)
5th cousins 0.00024 (= 1/4096)
Prof. Jorde found that the mean value of f, averaged over all the subjects, was about 0.0004. We can take this value as a fairly good estimate of the average inbreeding among Americans at large. An f of 0.0004, or 1/2500, falls somewhere between the fourth-cousin and fifth-cousin levels in the table. However, the mean is not a very good descriptive summary of these data, because a first-cousin marriage, for example, adds far more to the total average than a union between distant relatives. One first-cousin union in every 156 marriages is sufficient to produce a mean f of 0.0004 in the absence of any other inbreeding. In fact, 1,048 of the 303,675 study subjects, or about 1 in 290, were the offspring of such unions, and additional 1,129 were descended from second-cousin marriages. Thus, the observed inbreeding was mostly the product of a few unions between fairly close relatives, and not the result of universal marriage among fourth or fifth cousins. A more relevant figure might be the median value of f between random pairs of individuals, since this would be the dividing line between the top and bottom halves of the distribution of values across all random pairs. The median f will definitely be smaller than the mean. The bottom line is that if you don't know your spouse to be a relative, chances are that he or she is not closely related enough to worry about. (Nonetheless, I should point out that parents more distantly related than third cousins were scored as unrelated, so the quoted mean is probably an underestimate.)
As I mentioned, finding the mean inbreeding coefficient was not actually the point of this study. Rather, it was to examine whether more highly inbred individuals suffered greater childhood mortality (defined as death before 16 years of age) than offspring of distantly related or unrelated parents. Offspring of first-cousin marriages were found to have a 70% greater risk of childhood mortality (95% C.I. = [52%, 91%]) than offspring of unrelated parents. More distant relationships between parents were not associated with significantly elevated mortality. Still, these results might be construed as a gentle warning to "kissing cousins." (For the record, I do not oppose first-cousin marriages. Let 'em kiss, says I. Any group that uses Charles Darwin as its poster boy gets my respect. But they should know of the slightly increased danger to their children.)
Here I'd like to change the subject just a bit: Have you ever heard someone claim to have a one-third heritage? "I'm one-third Japanese." How on earth do they figure that? At first I assumed that such a person just doesn't know anything about genetics (or mathematics), but it occurred to me that it might be possible to explain a 1/3 (or 2/3, or 1/6, etc.) contribution to a person's ancestry, if we use some creative pedigree building.
Consider the following four-generation pedigree. (As usual for human pedigrees, circles indicate women, squares are men, vertical lines indicate descent with a horizontal line at the top between the parents.)
Here, the single person in the fourth generation, Inbred Jed, is the offspring of first cousins. His parents share one set of grandparents-the individuals in the first generation labeled C and D. As a result, Jed has only six great-grandparents! It is tempting to conclude that if any two of Jed's great-grandparents were, say, Russian, then Jed would be exactly one-third Russian. That's exactly what I believed at first-but I soon realized I was wrong. You can think about it this way: Jed really does have eight great-grandparents, but two of them-C and D-are counted twice. Consequently, these two individuals hand down a double dose of genes; they each contribute one-fourth to Jed's genome, whereas the other grandparents contribute the usual one-eighth. Alas, inbreeding doesn't really help us with this question.
We need to find a way to add up 1/2, 1/4, 1/8, etc., to equal 1/3, for these numbers (of the form 1/(2n)) represent the fraction of heritage accounted for by each parent, grandparent, great-grandparent, etc. As it happens, the number 1/3 cannot be expressed as a finite sum of fractions of the form 1/(2n). However, 1/3 can be approximated to any degree of accuracy using the infinite sum
1/3 = 1/4 + 1/16 + 1/64 + 1/256 + ...
We can convert the fractions on the right side of this equation easily into ancestral generations, if we assume no inbreeding (at least in portions of the pedigree from which we inherit the particular ethnicity we're interested in). Each term in the infinite sum is just 1/4 of the term before it. Similarly, the share that one ancestor has in our heritage at a given generation in our family tree is 1/4 that of an ancestor two generations below that. Because we have four grandparents, one grandparent will account for the 1/4 term; and from here we need exactly one ancestor from every other generation above the grandparental one. One great-great-grandparent will take care of the 1/16 term (because we have 16 great-great-grandparents), and so on.
So, a person who has one pure Italian grandparent, one pure Italian great-great-grandparent, one pure Italian great-great-great-great-grandparent, etc., will be very close to 1/3 Italian. (Of course, we can't count any two progenitors within the same line of descent: if you have one pure Italian grandfather, you can't add his parents, who must be Italian, to your tally of Italian heritage as well.) The genetic survey I described above suggests that there's really no point in going much past the great-to-the-sixth grandparent stage, since the average inbreeding in the population will likely swamp out the tiny contributions of such distant ancestors.
One last genetic thought: you might think that if we go all the way back, we should all we essentially 100% inbred. Whether or not you believe the story of Adam and Eve, there must have been a first Homo sapiens sapiens, right? Not necessarily. A large population can evolve from one species to another as a group, if speciation occurs by gradual modification of genes. Additionally, as I alluded to a while back, mutations (and other means of modifying the genome) tend to counteract inbreeding by slowly increasing genetic diversity (here I'm assuming no significant natural selection). The level of inbreeding 40,000 years ago may not have much impact on the present.
Okay, if we aren't all descended from Adam and Eve, just whom are we descended from? It is possible to estimate something called the "effective population size" from our current level of genetic diversity. Basically, the effective population size is the number of individuals in a hypothetical population of stable size, assuming random mating, that would contain the same level of diversity that humanity as a whole actually does contain. Because our population has been rapidly expanding, the effective population size (which, remember, assumes a unchanging number of people) is much smaller than the actual size. In other words, explosive growth in numbers does little to add overall diversity. What would you guess is our effective population size? Would you believe, about ten thousand? Amazing, but true. We have not one Adam and Eve, but approximately five thousand of each.
Sorry about that. You know, for a professional geneticist, I sure don't talk much about genetics in here. Not surprising, really-it's too much like work. But I've been dying to use that title for months now....
I got to thinking about my ethnic heritage after watching a scene in the movie Porco Rosso, in which we find that one of the main characters has a grandmother who is one-quarter Italian, and so is accepted (for the convenience of the bad guys) as being Italian himself. Traditionally, I've thought of myself as half Irish and half Swedish; but neither nationality shows up in my appearance, unless you look really hard and notice that about one in 20 of my beard hairs is red. So, I estimate that I have, at most, eight or nine chromosomes (out of 46) from each nationality, and that the rest of my chromosomes are generic, who-knows-where European. (However, my Y chromosome is almost certainly Irish, because if you scan straight up the male line you'll surely find an Irishman after several generations.)
Usually, people don't bother to divide their ancestry up more finely than quarters (thus making the distinction at the grandparents' generation), but once in a while you'll meet someone particularly proud of her pedigree, who identifies herself as being one-eighth [what have you]. The character in Porco Rosso was one-sixteenth Italian. How far back can we reliably go? Should we even bother to try to find out whether we're, say, 1/128 Tibetan?
We usually assume that we have, in addition to our two parents, four grandparents, eight great-grandparents, 16 great-great-grandparents, and so on: with each additional generation removed in ancestry we double the number of ancestors in that generation. Naturally, we can't do that forever. For example, thirty generations back we would each have to have 230, or over a billion (109), great-to-the-twenty-eighth grandparents-and even if we lump all the people on earth together into one population, there weren't that many people on earth 600 years ago. In other words, we're all slightly inbred: some individuals within those myriads of progenitors appear in our family tree more than once. And the average amount of inbreeding depends on the size of the population. A very isolated population, like those on certain Pacific islands, is highly inbred, by necessity; and even a large interbreeding population (think of the world's largest cities) has a significant amount of inbreeding.
Measuring the average consanguinity (a fancy term for inbreeding) in populations is very difficult, because even to make an educated guess, it is necessary to assume that everyone chooses mates at random-and of course that assumption is never true. Modern transportation is beginning to overcome the problem of geographical separation, but even where lots of people live within walking distance of one another, as in Manhattan, many reproductive barriers still exist: economic class, race, education and a host of other factors. So, the question you're dying to ask-"How closely are my spouse and I related, on average?"-is not answerable to any reasonable degree of accuracy in the general case.
Nonetheless, a careful survey of a very large number of families within a population may yield a pretty good guess. Prof. Lynn Jorde at the University of Utah recently carried out an extensive study of the inbreeding of about 300,000 Mormons, in order to assess whether close inbreeding was associated with increased child mortality.
At this point I'd like to dispel a myth: Mormons are not more inbred, overall, than the American population at large. Their population is large enough, and receives enough genetic inflow from outside, that two Mormons chosen at random might as well be from anywhere in the USA. Utah Mormons make such a good subject for studies of human genetics because they have large families and because they keep immaculate genealogical records.
(On the other hand, Mormons in isolated populations are as inbred as you'd expect a small isolated group to be. A few places in southern Utah clearly suffer from a deficiency in hybrid vigor. Probably not coincidentally, these same pockets of inbreeding also happen to encompass most of the few remaining practitioners of polygamy. Another aside: I recall distant suburb of Salt Lake City at which everyone likes to poke fun-with good reason, in my opinion. I used to joke that the only source of genetic diversity in this suburb was the incredibly high mutation rate from all the toxic metals in the mine tailings that everyone there lived on.)
Anyway, in order to explain the results of Prof. Jorde's survey, I have to make a slight technical digression. Geneticists usually express the extent of inbreeding using the coefficient of inbreeding, represented by the letter f (for "familiality"). The actual definition of f is a bit complicated for this discussion; suffice it to say that f is proportional to, but generally not equal to, the probability that a given rare recessive disease will show up in an inbred individual. Below I have tabulated values of the inbreeding coefficient for the offspring of matings between various types of relatives. As a general rule, f decreases by a factor of four for each additional generation between the related parents and their common ancestors.
Offspring of f
Siblings 0.25 (= 1/4)
1st cousins 0.062 (= 1/16)
2nd cousins 0.016 (= 1/64)
3rd cousins 0.0039 (= 1/256)
4th cousins 0.00098 (= 1/1024)
5th cousins 0.00024 (= 1/4096)
Prof. Jorde found that the mean value of f, averaged over all the subjects, was about 0.0004. We can take this value as a fairly good estimate of the average inbreeding among Americans at large. An f of 0.0004, or 1/2500, falls somewhere between the fourth-cousin and fifth-cousin levels in the table. However, the mean is not a very good descriptive summary of these data, because a first-cousin marriage, for example, adds far more to the total average than a union between distant relatives. One first-cousin union in every 156 marriages is sufficient to produce a mean f of 0.0004 in the absence of any other inbreeding. In fact, 1,048 of the 303,675 study subjects, or about 1 in 290, were the offspring of such unions, and additional 1,129 were descended from second-cousin marriages. Thus, the observed inbreeding was mostly the product of a few unions between fairly close relatives, and not the result of universal marriage among fourth or fifth cousins. A more relevant figure might be the median value of f between random pairs of individuals, since this would be the dividing line between the top and bottom halves of the distribution of values across all random pairs. The median f will definitely be smaller than the mean. The bottom line is that if you don't know your spouse to be a relative, chances are that he or she is not closely related enough to worry about. (Nonetheless, I should point out that parents more distantly related than third cousins were scored as unrelated, so the quoted mean is probably an underestimate.)
As I mentioned, finding the mean inbreeding coefficient was not actually the point of this study. Rather, it was to examine whether more highly inbred individuals suffered greater childhood mortality (defined as death before 16 years of age) than offspring of distantly related or unrelated parents. Offspring of first-cousin marriages were found to have a 70% greater risk of childhood mortality (95% C.I. = [52%, 91%]) than offspring of unrelated parents. More distant relationships between parents were not associated with significantly elevated mortality. Still, these results might be construed as a gentle warning to "kissing cousins." (For the record, I do not oppose first-cousin marriages. Let 'em kiss, says I. Any group that uses Charles Darwin as its poster boy gets my respect. But they should know of the slightly increased danger to their children.)
Here I'd like to change the subject just a bit: Have you ever heard someone claim to have a one-third heritage? "I'm one-third Japanese." How on earth do they figure that? At first I assumed that such a person just doesn't know anything about genetics (or mathematics), but it occurred to me that it might be possible to explain a 1/3 (or 2/3, or 1/6, etc.) contribution to a person's ancestry, if we use some creative pedigree building.
Consider the following four-generation pedigree. (As usual for human pedigrees, circles indicate women, squares are men, vertical lines indicate descent with a horizontal line at the top between the parents.)
Here, the single person in the fourth generation, Inbred Jed, is the offspring of first cousins. His parents share one set of grandparents-the individuals in the first generation labeled C and D. As a result, Jed has only six great-grandparents! It is tempting to conclude that if any two of Jed's great-grandparents were, say, Russian, then Jed would be exactly one-third Russian. That's exactly what I believed at first-but I soon realized I was wrong. You can think about it this way: Jed really does have eight great-grandparents, but two of them-C and D-are counted twice. Consequently, these two individuals hand down a double dose of genes; they each contribute one-fourth to Jed's genome, whereas the other grandparents contribute the usual one-eighth. Alas, inbreeding doesn't really help us with this question.
We need to find a way to add up 1/2, 1/4, 1/8, etc., to equal 1/3, for these numbers (of the form 1/(2n)) represent the fraction of heritage accounted for by each parent, grandparent, great-grandparent, etc. As it happens, the number 1/3 cannot be expressed as a finite sum of fractions of the form 1/(2n). However, 1/3 can be approximated to any degree of accuracy using the infinite sum
1/3 = 1/4 + 1/16 + 1/64 + 1/256 + ...
We can convert the fractions on the right side of this equation easily into ancestral generations, if we assume no inbreeding (at least in portions of the pedigree from which we inherit the particular ethnicity we're interested in). Each term in the infinite sum is just 1/4 of the term before it. Similarly, the share that one ancestor has in our heritage at a given generation in our family tree is 1/4 that of an ancestor two generations below that. Because we have four grandparents, one grandparent will account for the 1/4 term; and from here we need exactly one ancestor from every other generation above the grandparental one. One great-great-grandparent will take care of the 1/16 term (because we have 16 great-great-grandparents), and so on.
So, a person who has one pure Italian grandparent, one pure Italian great-great-grandparent, one pure Italian great-great-great-great-grandparent, etc., will be very close to 1/3 Italian. (Of course, we can't count any two progenitors within the same line of descent: if you have one pure Italian grandfather, you can't add his parents, who must be Italian, to your tally of Italian heritage as well.) The genetic survey I described above suggests that there's really no point in going much past the great-to-the-sixth grandparent stage, since the average inbreeding in the population will likely swamp out the tiny contributions of such distant ancestors.
One last genetic thought: you might think that if we go all the way back, we should all we essentially 100% inbred. Whether or not you believe the story of Adam and Eve, there must have been a first Homo sapiens sapiens, right? Not necessarily. A large population can evolve from one species to another as a group, if speciation occurs by gradual modification of genes. Additionally, as I alluded to a while back, mutations (and other means of modifying the genome) tend to counteract inbreeding by slowly increasing genetic diversity (here I'm assuming no significant natural selection). The level of inbreeding 40,000 years ago may not have much impact on the present.
Okay, if we aren't all descended from Adam and Eve, just whom are we descended from? It is possible to estimate something called the "effective population size" from our current level of genetic diversity. Basically, the effective population size is the number of individuals in a hypothetical population of stable size, assuming random mating, that would contain the same level of diversity that humanity as a whole actually does contain. Because our population has been rapidly expanding, the effective population size (which, remember, assumes a unchanging number of people) is much smaller than the actual size. In other words, explosive growth in numbers does little to add overall diversity. What would you guess is our effective population size? Would you believe, about ten thousand? Amazing, but true. We have not one Adam and Eve, but approximately five thousand of each.