Mermaids have long been the subject of fables and fantasies, and we can attest from looking at keyword searches that land people here on MT, that a lot of people still believe, or want to believe, that they exist. Christopher Columbus probably made the most famous mermaid sighting ever as he sailed near the Dominican Republic in 1493, though he wrote wistfully that they were "not half as beautiful as they are painted." People suggest, however, that these were probably manatees, not mermaids.
But of course the thing everyone wants to know, given that they are tail from waist to toe, so to speak, is how mermaids can reproduce without apparent access to the requisite machinery. (And yes, we can attest to this being what everyone wants to know.) In our book, MT, we tried to explain in basic biological and genetic terms, why it was not possible--or at least very unlikely!--that a vertebrate could really be half fish and half human. We discussed the idea that there could be mermaids as an issue of poorly understood embryology and genetics.
However, we may now know the answer to the reproductive question, having walked around Fisherman's Wharf in San Francisco last week. The Ruth Asawa statue of mermaids, called Andrea, on Ghirardelli Square since 1968, shows us two mermaids with tails that extend only half way up their thighs. If the same is true for mermen, mystery solved, though the baby held by one of the mermaids seems not to share that trait. Of course we have not seen any images of mermen, and don't know what sort of reproductive appendage or device or space they might employ.
Somehow this artist found appropriate models. We also might note that every mermaid image that we are aware of is of northern European descent--or, that is, their northern half seems European. This may focus the search for, say, fossils, that could reveal how they evolved. It's an open question, and not one for which there are any scientific sessions at the Human Genetics meeting, alas.