What would it be like if women could have babies on their own? As a single mother, I thought it would be fabulous to have the option of another child without first having to find the right man. You can hear my investigation of the science of virgin birth on New Year's Day on BBC Radio 4.

I went to Catholic schools as a child, and so spent many years with the nuns contemplating the miracle of Mary's virgin pregnancy [corrected]. Hers is the best known story of a virgin birth in the world, but it is by no means the only one. From the mothers of Buddha to Genghis Khan, most cultures tell the tale of a maiden untouched by man who gives birth.

In the 3rd century AD, the influential Greek church father Origen dismissed the legend of the immaculate conception of Plato, but worked hard to promote Mary's virginity:

There is a certain female animal which has no intercourse with the male (as writers on animals say is the case with vultures), and that this animal, without sexual intercourse, preserves the succession of the race. What incredibility, therefore, is there in supposing that, if God wished to send a divine teacher to the human race, He caused Him to be born in some manner different from the common!"

As far as we know, vultures don't have virgin births – that observation may have had something to do with the fact that in some species of vulture, males and females are tricky to tell apart. However, what science told us back in 1984 was that human females certainly could never have a natural virgin birth, because of a genetic barrier in mammals called imprinting.

So Origen was right – if Jesus was going to have a human mother but no human father, there had to be something rather interesting going on. But what?

Sam Berry, emeritus professor of genetics at University College London, explained to me what he calls the biological "implausible possibilities" for how Mary could have given birth to a son while remaining a virgin.

The keen reader will have spotted two biological roadblocks: the lack of a father, and the fact that Jesus was male. While Mary should not have been able to sire a son through a virgin birth, your Christmas turkey could – at least in theory.

In humans, a virgin birth would mean that a woman's eggs develop successfully without sperm. This presents a sex chromosome problem. In mammals, females are XX while males are XY so a woman should never be able to provide the necessary Y chromosome genes to produce a son. They can only come from a father.

In turkeys, sex determination is different. Females have Z and W chromosomes, while males are ZZ. So mother turkeys do have the genetic stuff for making males, although there may be other barriers to a "virgin birth".

That's fine for turkeys, but is there any earthly way Mary could have done it? One possibility, according to Prof Berry, is that Mary may have had a condition called testicular feminisation. Women with this condition have an X and a Y chromosome like a man, but their X chromosome carries a mutation that makes their bodies insensitive to testosterone. This leads to their developing as a female.

Genetically male, and probably sporting ambiguous genitals, Mary would have been sterile. But had she become pregnant spontaneously, her child could have inherited an intact Y chromosome.

To stop him developing as a female, like his mother, Jesus would have needed what geneticists call a "back mutation" – a highly unlikely reverse of the X chromosome glitch that caused the testicular feminisation in the first place. Other possibilities to explain the virgin birth include Mary being a genetic mosaic, formed from twins that fused into one body while maintaining chromosomes from both, Y and all.

You could be forgiven for thinking that the scientific possibilities are no more plausible than a miracle. If there needs to be a rational explanation for the stories generated around Jesus' birth, we are perhaps more likely to find it in a Biblical mistranslation or through a liaison between Mary and man who was not Joseph.

Still, when it comes to having babies without males, the hand of God now seems redundant. Zoologists have long known that there are many species that can reproduce without sex, and have now started to discover that it can also happen in the most unexpected places. In the last five years the list of virgin mothers has expanded to include a python, hammerhead sharks, blacktip sharks, and Komodo dragons. As the British zookeeper who discovered virgin births in Komodos put it, rather like buses, you wait ages and then loads of them come along all at once.

Similar things are now happening in the laboratory, with scientists creating healthy, fertile mice with no fathers. The fact that they were able to make such animals means that we can now get over the genetic barriers to a mammalian virgin birth – in mice at least. Who knows, one day a virgin birth in humans may not be so implausible after all.

Dr Aarathi Prasad began her career researching cancer genetics at Imperial College London. She now works in science policy and communication and is writing a book about reproduction without men. The Quest for Virgin Birth is on BBC Radio 4 at 8pm on New Year's Day.