This clip from the Smithsonian Channel's Truly Strange: From Here to Paternity is this clip of researchers doing DNA testing on swans and their offspring. Ugly Duckling, you are not the father.
Mostly, this is further proof that human beings have decided that swans embody certain virtues value because we think they're pretty. But that ignores the fundamental truth (determined by me through the experience of feeding swans as a child and then being attacked when I stopped) that swans? Are dicks.