Between 2008 and 2012, the percentage of women who said they wanted an egg donor from a “similar gene pool” declined from 40 percent to 25 percent. At the same time, looking for a baby with a “similar appearance” was relatively rare and held roughly steady, with 15 percent of women in 2008 saying it was important to them, and 22 percent saying so in 2012.

The most important thing that recipients cared about was the same thing mothers have cared about since time immemorial — the baby’s health. Nearly three-quarters of the women in the Mt. Sinai study said the health of the egg donor was a crucial factor in making their decision.

But other factors were also important, and became more so during the five years of the study.

From 2008 to 2012, the percent of women who cared about a donor’s “intelligence” increased from 18 percent to 55 percent, and the percent who cared about “athletic ability” increased from 1 percent to 17 percent.