IN 1977, a book editor suggested that I write up the history of my family, and I accepted the proposition not only eagerly but with a sense of urgency. My two grandmothers were both nearly ninety. I had heard some of their stories, in bits and pieces -of how they had got out of Russia because of the Revolution and started life over again in the United States, and of what their life had been before-but I had never heard the whole story. One afternoon, as I was studying some genealogical material they had given me, I noticed a possible connection between two Ukrainian families, the Adamoviches and the Vitovts, which would have meant that my mother's and father's forebears had been related to each other in the seventeenth century. I had heard that the Genealogical Society of Utah-a branch of the Church of Jesus Christ of Latter-day Saints-had the most voluminous genealogical archives in the world, and I wrote to ask if the society could be of help in confirming this connection, and if anything had been written about the overlapping of pedigrees in general. A few weeks later, an amazing paper by Robert C. Gunderson, called "Connecting Your Pedigree Into Royal, Noble, and Medieval Families," came in the mail. Gunderson, who heads the Genealogical Society's Royalty Identification Unit, has calculated that if you kept multiplying by two the progenitors of a person born today-doubling his parents, their parents, etc.-the person would have (based on an average generation length of twenty-five years) something like two hundred and eighty-one trillion forebears alive at the time of Charlemagne. Each person's pedigree, in other words, experiences a sort of retrogressive population explosion.
     Obviously, there were nowhere near that many people around in 800 A.D., or at any other time. What prevents the theoretical population explosion from taking place is another phenomenon, which Gunderson delightfully calls "pedigree collapse." Pedigree collapse is caused by cousins marrying cousins-:-both intentional mating between close cousins and random mating between distant ones who don't know that they are related. Close-cousin marriage has happened much more often than is generally supposed. In tribal societies, the exogamic restriction is usually applied not to all one's blood relatives but only to those in one's kinship group. In a patrilineal society, for instance, there is nothing to stop one from marrying a matrilineal cousin or uncle; in fact, such a match is often esteemed. The ideal is to marry out, but not too far out. In Japan, which has one of the world's highest consanguinity rates, arranged marriages between first cousins have been going on for centuries; and surveys made in the nineteen-six ties in southern India found that up to a third of the marriages among the Sudras . of Andhra Pradesh were between first cousins and that the proportion of uncle-niece matings might have been as high as twelve per cent.
     "If we could only get into God's memory, we would find that eighty per cent of the world's marriages have been with at least second cousins," the British social theorist Robin Fox told me recently. "In a population of between three and five hundred people, after six generations or so there are only third cousins or closer to marry. During most of human history, people have lived in small, isolated communities of about that size, and have in fact probably been closer to the genetic equivalent of first cousins, because of their multiple consanguinity. In nineteenth-century rural England, for instance, the radius of the average isolate, or pool of potential spouses, was about five miles, which was the distance a man could comfortably walk twice on his day off, when he went courting- his roaming area by daylight. Parish registers bear this out. Then the bicycle extended the radius to twentyfive miles. This was a big shakeup." Even in today's much more mobile English society-according to an estimate in Fox's book "Kinship and Marriage"-the average isolate for any given individual, which is "to some extent determined by the previous marriage choices of his ancestral consanguines," varies from about nine hundred people to just over two thousand.
      Elevated consanguinity has not been a feature only of rural populations. Jewish people have tended to maintain themselves, throughout history, as an endogamous religious isolate. Marriage between close kin of various types is permitted in Jewish law, and such alliances are still common in groups like the Haddanites, of Israel, whose first-cousin marriage rate was recently determined to be fifty-six per cent. In most of the world's upper classes, cousin intermarriage has been frequent, in order to keep wealth and power in the family, or because of a dearth of other acceptable mates. Consanguineous marriage has been particularly common in royal houses, the extreme cases being the Egyptian Pharaohs and the Incan kings, who had to marry their own sisters. In spite of the Catholic Church's ban on marriage within the fourth degree of relationship (third cousins), which lasted from 1550 to 1917, most of the people sitting on the thrones of Europe have been cousins of one sort or another, with their pedigrees in varying stages of collapse. The pedigree of Alfonso XIII of Spain (1886-1941), for instance, collapsed almost immediately: because of cousin intermarriage, he had only eight great-great-grandparents instead of the usual sixteen.
     Each time cousins marry, a duplication will occur in the pedigrees of their descendants because as cousins they already occupy a slot in them. The farther back one traces any person's genealogy, the greater the rate of duplication, until finally, when cousin intermarriage begins to predominate, the shape of the pedigree, in theory, stops expanding, and begins to narrow. Each person's complete family tree, in other words, is shaped more or less like a diamond. In the beginning, it expands upward from the person in an inverted triangle. At some point, hundreds of years back, the rate of expansion reaches its maximum and the pedigree starts to narrow, eventually coming to a point at a theoretical first couple. Whether one such couple existed, and, if so, where and when, cannot be known, of course; the answers to these questions require, among other things, a subjective judgment about when we became human, and the notion that a primordial couple are the mother and father of us all begins to seem like a romantic oversimplification when one considers that most of our complement of genes had evolved before we separated from the apes and that we share ninety-nine and a half per cent of our evolutionary history with chimpanzees.
     "Beginning about 200,000 to 300,000 years ago, forms of humans appear that might be called Homo sapiens, with a skull size comparable to that of modern man," the geneticists Walter F. Bodmer and Luigi Cavalli-Sforza write in their book "Genetics, Evolution, and Man." One "reasonable hypothesis," based on a comparative study of skull metrics in widely distributed ancient and aboriginal populations and on present geographic variations in the frequency of certain genes, holds that "the subspecies Homo sapiens sapiens may have expanded from a nuclear area (perhaps in Western Asia) to all of the world during a period perhaps 30 to 40 thousand years ago," replacing or mixing with earlier human populations, and initiating the rapid cultural change of the late Paleolithic. That is about as specific as anybody can be about our ultimate ancestors with out taking a religious leap of faith.
     The demographer Kenneth W. Wachter has created a simple probability model for the progenitors of an English child born in 1947. The child would have more than sixty thousand progenitors in the generation born at the time America was discovered, and ninety-five per cent of the slots on that tier of his pedigree would still be filled by different people. At the twentieth generation-around the time of John Wycliffe and the Peasants' Revolthe would have roughly six hundred thousand progenitors, with a third of the slots filled by duplicates. Just before the Black Death, thirty per cent of England's estimated population of three million six hundred and fifty thousand would be his progenitors. Around the time of King John, the widest point of his pedigree, with about two million different progenitors along a horizontal line, would be reached. Then the pedigree would start to narrow. At that point, each progenitor would be filling an average of sixteen slots, and the child would be descended from eighty per cent of the people in England.
      The mathematics of descent has fascinated many people. "If we could go back and live again in all of our two hundred and fifty million arithmetical ancestors of the eleventh century," Henry Adams wrote in 1904 of those with Norman-English blood, "we should find ourselves doing many surprising things, but among the rest we should certainly be ploughing most of the fields of the Contentin and Calvados; going to mass in every parish church in Normand y; rendering military service to every lord, spiritual or temporal, in all this region; and helping to build the Abbey Church at MontSaint- Michel." And, more recently, the sociobiologist Edward O. Wilson has written, "The gene pool from which one modern Briton has emerged spreads over Europe, to North Africa, the Middle East, and beyond. The individual is an evanescent combination of genes drawn from this pool, one whose hereditary material will soon be dissolved back into it."
      The genetic consequences of distant-cousin marriage are negligible. Only "relatively recent consanguinity . . . is pertinent," Cavalli-Sforza and Bodmer explain in "The Genetics of Human Populations." "In some human societies more distant consanguinities may have social significance, but from a genetic point of view the connection between two individuals who have one great great great grandparent in common (fourth half cousins) is . . . very tenuous indeed." The children of couples more closely related than fourth half cousins, however, are at higher risk of inheriting a recessive genetic disorder. The more common genetic consequences of inbreeding include defects of the ear and eye, structural malformations, and various forms of mental deficiency. There is also a greater chance of miscarriage; inbreeding can reduce reproductive fitness, in other words.
     Inbreeding greatly increases the possibility that a deleterious recessive will meet up with itself-that two genes that have passed down through different lines from a common ancestor will double up and produce the trait. The more recent the couple's consanguinity is, the greater are the odds of their offspring's being affected. The risk is determined by computing the average proportion of genes the consanguineous couple share from the common ancestor or ancestors; this proportion is the same as the probability that both will have anyone of these genes in common-a value that is known as the coefficient of kinship. A child shares half his genes with one of his parents, and thus their coefficient of kinship is one-half; full siblings share a quarter of their genes through each parent, and thus their coefficient is also one-half. For uncles and nieces, the value is one-eighth; for first cousins, one-sixteenth; for first cousins once removed, one-thirty-second; for second cousins, one-sixty-fourth; and so on. (It often happens that couples who are related in one way have other connections to each other as well. As Cavalli-Sforza and Bodmer explain, "the effect of multiple consanguinity is additive;" that is, such a couple may have a higher coefficient of kinship than the one they know about.) If both consanguineous parents are carriers of the recessive gene, the odds that their child will inherit it from both of them proceed according to the laws of Mendelian inheritance: the child has a onein-two chance of inheriting one copy, and thus being only a carrier; a one-infour chance of inheriting both copies, and thus expressing the trait; and a one in-four chance of inheriting neither.
     Arthur Bloom, the director of the genetics division at Columbia-Presbyterian Medical Center, in New York City, has studied the genetic consequences of inbreeding on Grand Cayman, a Caribbean island, northwest of Jamaica, that was colonized by the English in the eighteenth century and has about fifteen thousand inhabitants of mixed slave-and-English ancestry, who lived for many generations in five isolated population centers. Bloom told me not long ago that genetic problems have emerged in the last several generations. "It takes a number of generations before the gene frequency goes up enough for disorders to occur in significant numbers," he explained. "Each population center has its own spectrum. A lot of children in West Bay have San Fillipo 'A' syndrome, a mucopolysaccharide-storage disease, usually lethal by adolescence, which is not seen on the East End. One per cent of the West Bay population is afflicted with a recessively inherited syndrome that we call Cayman disease-it includes retardation, ataxia, and disturbance of gait-and eighteen per cent are carriers, so it is a risky situation in terms of mating. Six in every thousand people in the East End are born deaf, which is the highest incidence known in humans-the normal incidence is one per thousand," On Grand Cayman, as elsewhere, the deaf tend to marry each other, so that all their children are born deaf. Bloom collected several eight-generation pedigrees there that show a steady rise in the frequency of congenital deafness.
    The Old Order Amish are the beststudied religious isolate. More than eighty thousand Amish live in the United States and Canada, seventy-five per cent of them in Pennsylvania, Ohio, and Indiana. Most are descended from the followers of a Mennonite bishop named Jacob Amman, who in the sixteen-nineties broke with the mother church and started his own sect. The main immigration-to Pennsylvania from Bern and AlsaceLorraine-began no later than 1727 and lasted until about 1790. The genealogical records of the Amish are extraordinarily good; most members of the sect can trace their complete ancestry, on every line, to the first immigrants. Eighty per cent of the Amish in Lancaster County, Pennsylvania, have only eight surnames among them. The Amish do not proselytize, and they forbid marriage with outsiders. Some leave the fold, but very few enter it. "A strong system of sanctions, including. excommunication and shunning (M eidung), helps maintain the group," the geneticist Victor McKusick and the sociologists John Hostetler and Janice Egeland write at the beginning of a book entitled "Medical Genetic Studies of the Amish." The average consanguinity among the Amish may be at the level of third or fourth cousins; of a total of six hundred and twenty-seven marriages involving descendants of Johannes Schwartz and his wife, Anna Ramseyer, who were from Berne, Indiana, for instance, twenty-one and a half per cent were between second cousins or closer consanguines. The price of the Amish people's endogamy has been a greater than normal occurrence of such afflictions as albinism, two recessive types of dwarfism, agoitrous cretinism, limb-girdle muscular dystrophy, lateral sclerosis, and neurofibromatosis. Not surprisingly, they take a great interest in hereditary illness. The Budget, an Amish weekly, runs long, detailed accounts of genetic ailments, which are sent in by members of Amish families from all over the country.
 
 

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