The kill was before first light. The funeral took place that afternoon.

A lioness, returning empty-bellied from a nocturnal prowl in Botswana’s Chobe National Park, spotted a baby elephant separated from its herd in the night and walking uncertainly along a shallow valley.

Her muzzle and pale stomach only inches from the ground, her tawny coat almost invisible in the grey gloom, the lioness made its feline stalk to within 15 metres downwind of its prey, then exploded into a rush and pounce. Claws sank into the elephant’s neck, pulling it to the ground, jaws tearing open the exposed throat. The baby elephant would have died without a whimper.

Over the next two hours, the lioness enjoyed a leisurely breakfast, watched by her three cubs hidden in a grove of the woolly caper bush overlooking the valley. Only when she exchanged places with them – allowing three smaller mouths to explore the crimson tunnel she had made into the carcass – was there activity from the surrounding trees.

All morning, a growing assembly of vultures had flown into view, lining every bough, necks sunken, eyes fixed on the small mountain of flesh. Now they took to the air and paraglided into a semicircle around the dead elephant, landing gaitered feet first, wings unfurled to the span of a boastful fisherman, then promptly folded tight as an umbrella. Undeterred, the cubs continued tearing out flesh from within the armoured hide. They chewed on even when the more daring of the vultures, pink-faced and white-legged, began to edge forward to join in the feast.

This was the signal for the lioness to erupt from the bushes and drive them 20 to 30 metres back in a flurry of wings. But no sooner had she returned to the shade and the cubs resumed their meal than the vultures advanced once more – prompting the lioness to give them another warning dash. This weary process was repeated several times during the morning, but when the noonday sun was blazing into its fiercest heat, the cubs suddenly retreated to their mother and the vultures returned to the trees, leaving the tempting dish unattended.

A dark mound had appeared above the horizon, followed by another, then another and another, all heading in this direction.

As they grew closer, we could see a column of elephants, headed by their matriarch, the grandmother (or even great-grandmother) of the herd, her tattered ears indicating great age.

On they came, until they began to assemble around the bloody remains of the baby elephant, some stamping their feet and snorting in the direction of the lion family they knew still to be near. But most would lightly touch and sniff the body with their trunks and then move to a respectable distance, standing in silent groups.

Still more elephants arrived until there were at least 100 in all, the latecomers filtering their way to the body, seemingly paying their respects, then moving to the rear of the congregation.

All the time, the lions watched from the shade of the bushes, great oval eyes unblinking – perhaps like terrorists relishing the extent of the grief they had caused without ever being able to comprehend the depth of that grief.

Then the matriarch abruptly turned away and began to head back along the valley. Others followed until only one female was left. Our Botswanan guide was certain it would be the mother.

She took a last look at the body, then moved down the slope to where she scented the actual kill had taken place. There she straddled the spot, urinated and defecated, then brushed dust over the small mound she had created.

Finally, she half-raised her trunk in the direction of the lions – more in dismissal than protest, leaving the carcass for them to gorge and the vulture to pick clean. With that, she joined on the doleful procession, now stretching as far as the eye could see, heads lowered, moving trunk to tail in a stately slow march.

So had we experienced the rare spectacle of an elephant funeral? Or had we? Weren’t we investing a primeval animal with human feelings? Were we mistaking their natural solemnity for a formal display of grief? Do elephants really have the capacity for sorrow?

In a paper for the journal of Applied Animal Behaviour Science, Iain Douglas-Hamilton, the founder of Save the Elephants, wrote: “The question of whether there might be emotional or mental suffering among surviving elephants who encounter and interact with ailing or dead elephants is open, but behavioural data suggests this is the case.”

“There’s no doubt that elephants do have feelings,” insists Bob Flaxman, a sturdy, white-bearded veteran of the African bush, now the manager of the Xakanaxa Camp in the Moremi Game Reserve. “They certainly grieve over their dead and look after their sick. I once saw a man winch a baby elephant from the depths of a quagmire, and the grateful mother rushed up to him and wiped the mud from his clothes with her trunk.”

What’s hard to reconcile with this image of caring creatures is the way an army of elephants marches through the African bush with the ponderous progression of first-world-war tanks. Unfortunately, their frequent advances leave behind a swathe of first-world-war destruction: tottered trees left leafless, limbless and splintered, the stricken landscape littered with piles of their half-brick-sized dung like battlefield debris.

Eating for 14 hours at a stretch, an elephant consumes 325 kilograms of food a day. When leaves and fruit fail to fill that giant stomach, it tears off whole branches and eats the wood. Its tusks gouge so much bark from around the stems of full-grown trees that they turn into whitened skeletons and eventually fall at dizzy angles. Trees that survive are pushed sideways to the ground so that their roots can be munched.

Now numbering one for every 14 human inhabitants, the relentless roaming of Botswana’s 120,000 elephants is driving villagers from the land by indiscriminately destroying their crops. Even the staunchest conservationists now concede that some significant culling is necessary.One proposal is to deplete their numbers by taking out the juvenile members of a herd. Having witnessed the display of grief over the death of one baby, it is disturbing to imagine the degree of communal trauma at any systematic slaughter of the young.

An alternative is to cull a percentage of the elders. But this would shatter the social hierarchy of the herd, in which age is revered and the adults are responsible for the upbringing and disciplining of the young, especially teenage bulls. “The only realistic way to make any sizable reduction in numbers,” says the game-camp manager Bob Flaxman, “is to take out a whole herd at one go. That would be the cleanest, kindest method, with no survivors left to grieve or go wild. But are we ready to go that far?”

If UK animal-rights activists were driven to mount overnight commando raids on a tiny Scottish island to rescue hedgehogs under threat of culling, it’s not difficult to calculate the degree of worldwide fury at what would be seen to be wholesale massacre of these gentle giants.

For, regardless of the urgent need to limit the massive damage they are clearly inflicting on their environment, elephants are universally regarded as the most majestic of our fellow mammals, seen as sharing many of our emotions. And that makes us pretty sentimental too.

HOW TO GET THERE

Peter Jackson travelled to Botswana with Okavango Tours & Safaris. Seven nights, including flights, from £2,785 per person. Tel: 020 8343 3283. Visit www.okavango.com