Read more: Blog - why are beards sexy?
"When beards were rare, hirsute faces were more attractive than when beards were common ..." the authors said.
"Conversely, when clean-shaven faces were rare, clean-shaven faces and light stubble enjoyed their greatest attractiveness, and beards became less attractive."
The authors however said there was not an "inversion of preferences", such as clean-shaven faces becoming more attractive than beards when rare, with clean-shaven faces rating lowest in all tests.
"However, the mean attractiveness of a suite of faces is altered by the frequency of beards, suggesting negative frequency dependence could alter the cultural dynamics by which facial hair fashions vary."
Novelty effects - possibly spurred by imitation of "influential early adopters" - could affect the rise in frequency of new fashions, they said.
The study was published today in Biology Letters.
The beard has enjoyed a resurgence in popularity over recent years, with bearded celebrities including George Clooney, Hugh Jackman and Bradley Cooper raising the appeal.
As a Victoria University PhD student in 2009, Dr Dixson made headlines with a study that showed men noticed women's breasts first - and could zoom in on a woman's most attractive features within 200 milliseconds.