Female twins are up to four times more likely to reach the menopause early than other women, say researchers.
Melanie donated healthy ovary tissue to her twin Stephanie
The findings come from a study of 1,700 female twins presented at a fertility conference in Montreal, Canada.
In some of the cases only one twin was affected, like the Yarber sisters who made the news when one donated healthy ovary tissue to her infertile twin.
Since the transplant Stephanie Yarber, who went through the menopause at the age of 14, has had a baby.
Professor Roger Gosden, of Cornell University in New York, who presented the study findings at to the American Society for Reproductive Medicine, said experts hope to find a molecular basis for the differences between such twins.
"That would, for the first time, help us predict the size of the egg pool and give us a good predictor of when the menopause might happen," he said.
He believes premature menopause in identical twins might be to do with the embryo splitting process.
He and colleagues from Brisbane, Australia, and St Thomas' hospital in London, the UK, looked at data from studies of 418 pairs of identical twins and 432 pairs of non-identical twins who had reached the menopause due to ovarian failure.
About 1% of women in general have gone through the menopause by the age of 40, but among the twins the figure was about 5%.
By 45, more than 15% of the twins had gone through the menopause, in contrast to about 5% of the general female population.
Given that the rate of premature menopause was similar among the identical and non-identical twins, the researchers do not believe it is simply down to genes.
Dr Margaret Rees, consultant gynaecologist and editor in chief of the journal of the British Menopause Society, said: "It's interesting, but it's not the whole story.
"There are other things that can affect the age of menopause, such as smoking.
"It's important that women should be aware of declining fertility with age."