A few months ago, I sat down at my desk to open a letter that could tell me whether my father was really my father. In fact, that letter could tell me whether the men going back 10 generations on my paternal side were the biological fathers of their children.

I wasn’t caught up in some bizarre multigenerational paternity suit. A scientific officer at a genetic testing company knew that I was interested in genealogy, and he had offered to run my DNA through a sequencer. A few weeks earlier, I’d swished mouthwash inside my cheeks, sealed the mouthwash in a tube, and mailed the tube to the company.

My doughty Scandinavian ancestors passed the test. My DNA revealed no obvious instances where the man named on a birth certificate differed from the man who was my biological ancestor. But I was lucky. Many efforts to trace male ancestry using DNA terminate at what geneticists delicately call a “non-paternity event.” According to Bennett Greenspan, whose company, Family Tree DNA, sponsors proj­ects that attempt to link different families to common ancestors, “Any project that has more than 20 or 30 people in it is likely to have an oops in it.”

The law of unintended consequences is about to catch up with the genetic-testing industry. Geneticists and physicians would like us all to have our DNA sequenced. That way we’ll know about our genetic flaws, and this knowledge could let us take steps to prevent future health problems. But genetic tests can also identify the individuals from whom we got our DNA. Widespread genetic testing could reveal many uncomfortable details about what went on in our parents’ and grandparents’ bedrooms.

The problem would not loom so large if non-paternity were rare. But it isn’t. When geneticists do large-scale studies of populations, they sometimes can’t help but learn about the paternity of the research subjects. They rarely publish their findings, but the numbers are common knowledge within the genetics community. In graduate school, genetics students typically are taught that 5 to 15 percent of the men on birth certificates are not the biological fathers of their children. In other words, as many as one of every seven men who proudly carry their newborn children out of a hospital could be a cuckold.

Non-paternity rates appear to be substantially lower in some populations. The Sorenson Molecular Genealogy Foundation, which is based in Salt Lake City, now has a genetic and genealogical database covering almost 100,000 volunteers, with an overrepresentation of people interested in genealogy. The non-paternity rate for a representative sample of its father-son pairs is less than 2 percent. But other reputed non-paternity rates are higher than the canonical numbers. One unpublished study of blood groups in a town in southeastern England indicated that 30 percent of the town’s husbands could not have been the biological fathers of their children.

Even with a low non-paternity rate, the odds increase with each successive generation. Given an average non-paternity rate of 5 percent, the chance of such an event occurring over 10 generations exceeds 40 percent.

Most people can’t look that far back on their family trees, but I can. Someone on the Olson side of my family once spent an inordinate amount of time tracing the family’s male lineage. My relative’s genealogical research indicated that my father’s father’s father’s father’s father’s father’s father’s father’s father’s father migrated from Finland to Norway in the middle of the 17th century. If that is the case, I have a particular connection to that man.

Men pass most of their Y chromosomes down to their sons intact and unadulterated. I therefore have the same Y chromosome as my father, and his father, and so on. (In fact, all men living today have inherited the Y chromosome of a single man who lived about 50,000 years ago, probably in eastern Africa. But mutations have slowly changed the Y chromosome over many generations, which is why the Y chromosomes of Finns generally differ from those of Greeks. Nevertheless, over the course of 10 or even 100 generations, the changes typically are small and the heritage is clear.) The continuity of the Y chromosome is how we know that Thomas Jefferson almost certainly had children with his slave Sally Hemings: Her direct male descendants have the same Y chromosome as Jefferson’s paternal uncle, who presumably had the same Y chromosome as Jefferson. (Similar tests can reveal whether sons and daughters are really descended from their mothers and grandmothers, though non-maternity is much rarer than non-paternity.)

My Y chromosome turned out to be as Finnish as sautéed reindeer—I al‑ most certainly inherited it from that 17th-century Finnish émigré. But even if my Y chromosome had turned out to be suspiciously un-Finnish, I probably could have come up with a story to protect my legitimacy. I could have said that my Finnish ancestor was the descendant of a Mongolian invader, or the son of a trader from Istanbul, or even a Spanish diplomat fallen on hard times (though in fact I know that he was a peasant farmer). I could have said that one of the men in my paternal lineage was adopted after his mother and father died. The imagination is a wonderful balm for bruised expectations.

But genetic tests don’t lie, which means that our imaginations may be in for a workout. For example, groups of people in many parts of the world trace their lineage to particularly prominent male ancestors. In some cases, genetic tests reveal a kernel of truth behind these stories. Genghis Khan’s Y chromosome really is widely distributed in Asia, for instance. Still, many of these stories have social rather than genealogical roots. “Many times we romanticize about the different groups that we have ancestry with,” says Rick Kittles, a geneticist at the University of Chicago who founded the company African Ancestry. When Kittles has told clients that their genetic tests don’t coincide with what they believe, a few, he says, have been shattered.

Frankly, I hadn’t thought much about these issues before sitting down to open that letter from the genetic testing company. If I had, I doubt I would have agreed to the test. If my Y chromosome was not what I expected, would I tell other family members about it—including my teenaged son? Would I have been tempted to encourage my brother, then my male cousins through my father’s brothers, then my male second cousins through my grandfather’s brothers, and so on to be tested so that I could determine where the non-paternity occurred? I think we’d all have been better off assuming the best and shunning the test.

But the pressure to undergo genetic testing is about to increase. New technologies are reducing the cost of sequencing DNA. Researchers are now establishing extensive databases of DNA sequences combined with health information so they can link specific genes to diseases. And once the contributions of our genes to common diseases are discovered, everyone could benefit from DNA testing. Already, the Personal Genome Project at Harvard University is seeking volunteers who are willing to have their DNA sequences and medical information posted on the Web for biomedical purposes, even though the project warns that a person’s DNA could be used to “infer paternity or other features of the volunteer’s genealogy.”

Two of the men most responsible for the sequencing of the human genome—James Watson and Craig Venter—are making most of their genomes available on the Web. But if their sons ever decide to have their DNA tested, they could face the same situation I did in opening that letter. Watson has kept part of his genome private because he doesn’t want his sons and the public to know whether he has a genetic variant predisposing him to Alzheimer’s disease; he seems unconcerned about what the rest might reveal.

Genetic counselors have been struggling with the issue of non-paternity for years. When a child is born with a genetic disorder, the parents may go to a counselor to learn whether they should try to have more children. If tests reveal that the presumed father of the child is not the biological father, most counselors will tell only the mother. But a vocal minority insists that paternity should be known to all.

So far, the expense of these tests has limited their use to cases like the one above, where a serious genetic disorder is already apparent. But what will happen when people begin sequencing large parts of their DNA routinely, to see whether they are vulnerable to specific diseases? If you discovered a predisposition to heart attacks or prostate cancer, and medications could reduce your vulnerability, wouldn’t you want to tell your siblings and cousins? And shouldn’t they be tested, too? Yet in the absence of stringent and possibly unattainable privacy protections, widespread testing will lead to many unpleasant surprises.

Geneticists have only begun to think about how to protect people from knowing themselves too well. But they probably should have seen this problem coming a long time ago. An oft-quoted definition of their field is: “Genetics explains why you look like your father—and if you don’t, why you should.”