Today there are 150 children, all conceived with sperm from one donor, in this group of half siblings, and more are on the way. “It’s wild when we see them all together — they all look alike,” said Ms. Daily, 48, a social worker in the Washington area who sometimes vacations with other families in her son’s group.

As more women choose to have babies on their own, and the number of children born through artificial insemination increases, outsize groups of donor siblings are starting to appear. While Ms. Daily’s group is among the largest, many others comprising 50 or more half siblings are cropping up on Web sites and in chat groups, where sperm donors are tagged with unique identifying numbers.

Now, there is growing concern among parents, donors and medical experts about potential negative consequences of having so many children fathered by the same donors, including the possibility that genes for rare diseases could be spread more widely through the population. Some experts are even calling attention to the increased odds of accidental incest between half sisters and half brothers, who often live close to one another.