This depressing claim is made by Kathy Phillips, the author of a book due to be published later this month, The Vogue Book of Blondes, which traces the history of fair hair. She has based her theory on the work of Professor Steve Jones of University College, London, one of the world's leading geneticists.
Ms Phillips believes that the male fantasy figure of the nubile Scandinavian blonde will soon exist only in their imagination. The only blonds around will be of the bottled variety.
The culprits are recessive genes. Fair hair is caused by weak genes whereas dark hair is the product of dominant ones. When a dark-haired person and a natural blond have children together, the offspring will almost always be dark-haired.
Until now, natural blond populations have flourished because Scandinavia and northern Europe have remained relatively closed societies. But in recent years the Nordic countries have opened their doors to immigrants, and the ease of global travel has seen northern European blonds liaise with dusky southern Europeans.
This means the peroxide bottle will be the only answer for those who cannot face life with mousey brown hair.
In her book, Ms Phillips argues that blonds have a far more enduring appeal than brunettes because their image is so much more diverse. She said: "There's an extraordinary range of blond icons from Venus rising from the waves, to Gazza and Peter Stringfellow, and everyone else in between."
Ms Phillips breaks down blond hair colour into different categories including contemporary sex kittens, Hitchcock blondes, blonde bombshells and athletic blondes, typified, she says, by the bare-footed James Bond girl Ursula Andress.
The book also features a section on the rise of the male blond, often overlooked despite the fact that platinum pop artist David Hockney coined the phrase, "Blondes have more fun".
"In Hollywood, men were always tall, dark and handsome," Ms Phillips said. "Suddenly in the 1960s, leading men were blond, like Paul Newman, Robert Redford and Peter O'Toole. For the first time they didn't seem to mind exposing a more female and vulnerable side, associated with blond hair."
The book also examines the association between hair colour and power and how one appears to augment the other. Margaret Thatcher became blonder as she became more powerful, as did Eva Peron and Hillary Clinton.
Ms Phillips said that some women steered clear of being blonde for fear it would mean they were taken less seriously than their brunette colleagues. Although this is not a concern for some powerful women. "It may be because when you're secure you can enjoy doing anything you want," Ms Phillips said.