To test this idea, Dr. Brennan traveled to Alaska. Many species of waterfowl breed there, with a wide range of mating systems. Working with Kevin McCracken of the University of Alaska and his colleagues, she caught and dissected 16 species of ducks and geese, comparing the male and female anatomy.

If a male bird had a long phallus, the female tended to have a more elaborate lower oviduct. And if the male had a small phallus, the female tended to have a simple oviduct. “The correlation was incredibly tight,” Dr. Brennan said. “When you dissected one of the birds, it was really easy to predict what the other sex was going to look like.”

Dr. Brennan and her colleagues are publishing their study Tuesday in the journal PLOS One.

Dr. McCracken, who discovered the longest known bird phallus on an Argentine duck in 2001, is struck by the fact that it was a woman who discovered the complexity of female birds. “Maybe it’s the male bias we all have,” he said. “It’s just been out there, waiting to be discovered.”

Dr. Brennan argues that elaborate female duck anatomy evolves as a countermeasure against aggressive males. “Once they choose a male, they’re making the best possible choice, and that’s the male they want siring their offspring,” she said. “They don’t want the guy flying in from who knows where. It makes sense that they would develop a defense.”

Female ducks seem to be equipped to block the sperm of unwanted males. Their lower oviduct is spiraled like the male phallus, for example, but it turns in the opposite direction. Dr. Brennan suspects that the female ducks can force sperm into one of the pockets and then expel it. “It only makes sense as a barrier,” she said.

To support her argument, Dr. Brennan notes studies on some species that have found that forced matings make up about a third of all matings. Yet only 3 percent of the offspring are the result of forced matings. “To me, it means these females are successful with this strategy,” she said.

Dr. Brennan suspects that when the females of a species evolved better defenses, they drove the evolution of male phalluses. “The males have to step up to produce a longer or more flexible phallus,” she said.