Reputation: Elephants are frightened of mice. They have elephantine memories. When it's time to die, they travel with purpose to elephant graveyards. They grieve. They are related to hyraxes.

Reality: Elephants are frightened of bees. They have good memories. Graveyards are a myth but elephants clearly show interest in the remains of the dead. All living organisms are related to hyraxes.

Did you know that elephants are related to hyraxes, those vaguely rodent-like animals that live in Africa? This is one of those little factoids that people like to float.

Elephants are more closely related to dugongs and manatees than they are to hyraxes

It's also an entirely banal observation. At some level, after all, everything is related to hyraxes.

Even the more precise claim – that elephants' closest living relatives are hyraxes – is misleading.

First, it implies a recent common ancestor. Yet these two lineages have been going their separate ways for around 65 million years.

Second, it is probably wrong. Several lines of molecular evidence indicate that elephants are more closely related to dugongs and manatees than they are to hyraxes.

Our obsession with juxtaposing the big and the small is also evident in the belief that elephants are afraid of rodents.

There's all of these myths about mice running up elephants' trunks

This notion may date back to Pliny the Elder: "Of all living Creatures, they most detest a Mouse," he wrote in The Natural History.

Walt Disney ran with the idea in Dumbo, in which Timothy Q. Mouse terrifies the circus elephants before befriending the eponymous hero. But is there anything behind this stereotype?

"There's all of these myths about mice running up elephants' trunks," says Craig Bruce of the Zoological Society of London. But there's no serious evidence for elephantine murophobia, he says.

What is clear is that elephants do not like bees.

When recordings of disturbed African honey bees are played to elephant families resting under trees in Kenya, the elephants either walk away or, more commonly, run.

This and other findings are behind the Elephants and Bees Project, an initiative to explore the possibility of using bees to deter crop-raiding elephants in Africa.

How about memory? Not only can elephants remember landmarks and migration routes, they have an incredible social memory too.

Working in the Amboseli National Park in Kenya during the 1990s, researchers used playback experiments to explore the way in which elephants communicate.

In one case, they played the call of an individual that died almost two years earlier to her family. The elephants crowded round the loudspeaker and called back, a response characteristic of a strong social bond.

It's true that there are large aggregations of elephant bones

In another setting, where a female had switched to another group, her original family still responded to her call 12 years after she'd left.

However, there is no reason to think that elephants have graveyards, where old animals go to die. It's true that there are large aggregations of elephant bones, but drought and hunting are much more likely explanations for them.

There is better evidence, both from anecdotes and from experiments, for another remarkable idea: that elephants mourn their dead.

In her book Elephant Memories, conservation pioneer Cynthia Moss recalls how she brought the jawbone of a recently deceased matriarch back to her camp.

Elephants may recognize tusks from individuals that they have been familiar with in life

Several days later, the dead elephant's family happened to pass nearby and came to inspect the jaw. The animal that showed the most interest, lingering long after the others had moved on, was the matriarch's seven-year-old son.

Moss and her colleagues have followed up on such anecdotes with controlled experiments designed to explore this behaviour more systematically.

When presented with three objects – a piece of wood, an elephant skull and a bit of ivory – elephants showed a marked interest in exploring the ivory and a clear preference in the skull over the wood.

Although the researchers were unable to demonstrate that elephants are more interested in the remains of relatives than those of non-relatives, they concluded that "elephants may, through tactile or olfactory cues, recognize tusks from individuals that they have been familiar with in life."

All of this confirms that elephants really are extraordinary, intelligent creatures with a profound emotional range.

A bull elephant never enters the female's vagina

But there is a morphological truth about elephants that might be even more striking still.

It pertains to the female's reproductive anatomy, which at around 3m from start to finish is the longest of any land mammal. Even with his legendary penis length, a bull elephant never enters the female's vagina, as its opening is located 1.3m into her body.

This strange design is also found in marine mammals. It may be a hangover from the elephant's aquatic ancestry, as it would have prevented water entering the reproductive tract during mating.