Fresh pugmarks. We can just about make out the inverted ‘W' shape in the dust. ‘W' is for big cat. This is how you distinguish your cats from your dogs. Wild dog and hyena prints have a distinct ‘U' shape opposite the business end. But there are no wild dogs here and with plate-sized paw-prints like these you don't need a B+ in bushcraft to realise they belong to a large male lion. We swap glances. If we're right this is the purposeful stride of the black-maned bruiser who heads up the local pride like an old Mafia don - we call him The Big Guy. This is what we scrambled out of our sleeping bags in the cold and the dark for. It's why we left camp ahead of the others - to find his pride before it's too late.

During the night soft desert winds have blown a fresh layer of dust onto the sandy track, covering yesterday's tyre marks. Etched on this blank canvas is a varied tracery of animal spoor, now becoming discernible in the early light. For a brief moment the secret stories of the Kgalagadi night are laid bare. This is the best chance we have to pinpoint our quarry. Soon to be overwritten by the tyre tracks of today's tourist vehicles, including our own, are the spidery, seemingly pointless circles made by a toktokkie beetle and the meandering trail of a jaywalking black-backed jackal. The jackal's tracks stop by a thorn bush, marking the point, perhaps, where it tried to dig a striped mouse from its burrow. A posse of broken hoofprints indicates the spot where a herd of wildebeest trampled the sand in a hurry. What disturbed their nocturnal grazing? Had they, too, sensed the presence of our lion?

A cocktail of adrenaline and panic is helping fuel our search. Tomorrow we leave this remote camp for another, some 160km away in this vast 3.6 million hectare reserve, known as Kgalagadi. Our hopes are raised when we pick up distinct tracks again, heading north. For almost two weeks we have attempted to track our big male through this forbidding yet compellingly beautiful wilderness, in the hope he'll lead us to his four one-week-old offspring. If we are to see, let alone photograph, the cubs before they are cached away for the day, we need to find them fast. It's now five days since they were last sighted and a week since we caught a glimpse of them. That their father is on home turf today is encouraging. For the last 36 hours there's been no sign of him. We reckon he's been up in the dunes on a kill. The tracks continue confidently ahead. A lion, lazy and somnolent by day, will walk tens of kilometres by night, further in a dry and seemingly barren landscape like this, where prey species are often few and far between. Our own progress is less sure.
"He could be anywhere by now. If the tracks leave the road we've had it."
"The terrain's quite open, we might still pick him up out there in the valley floor."
"Not if he's already resting under a camel thorn or has..."

Before we can finish this interchange our attention is distracted by what looks like a swirling, gold curtain heading towards us. Silhouetted against it is a bachelor party of springbok, their athletic outlines picked out against the backlit veil of fine sand kicked up by their exuberant pronking and prancing. The dawn ballet of light and dust is a daily ritual. Some days the principal parts change: fighting gemsbok lock metre-long horns in combat, gyrating hartebeest chase their tails, jackals spit and bicker over a newly-abandoned cheetah kill or dust-bathing female ostrich resemble fading starlets applying too much powder.

No other reserve is quite like Kgalagadi. Here conservation management has a light touch and the fragile, semi-desert ecosystem is left to find a natural rhythm. You may not see a huge density and diversity of game but you will find some of Africa's most magnificent lions, its majestic raptors and some of the best opportunities to observe cheetah hunting at full tilt.

On paper South Africa's Kalahari Gemsbok National Park, in the remote north of the country, looks oddly like a narrow door wedge jammed between the borders of Botswana and Namibia. There are no fences between this and the adjoining Botswana side, an arrangement which has facilitated the recent establishment of Africa's first cross-border conservation area or ‘peace park', uniting the South African park and Botswana's Gemsbok National Park under the new banner of Kgalagadi Transfrontier Park. But all this hardly seems to matter. It only takes one night here, teased from sleep by your rest camp's resident teas-maid (the pocket-sized pearl-spotted owl with a voice like a whistling kettle), to realise that, in this unremitting landscape of blood-red sand dunes and desiccated river systems dotted with skeletons of dead acacia, only one thing matters - the daily struggle for survival.

We've stopped our hunt for The Big Guy to photograph the springbok circus. The antelope seem more alert this morning and a couple are making the restrained alarm call that sounds like a suppressed sneeze. What has spooked them? We don't say a word to each other, but we're thinking the same thing. Within moments we're moving forward again.

This time we keep our eyes glued to the lion tracks. One…two…three…four…until…cool as you like, with chocolate tail pom-pom swinging like a pendulum, around 250 kilos of Africa's largest carnivore is planting one huge paw firmly in front of the other, creating the very trail we're following. The noise of our vehicle approaching doesn't divert him. Only when we draw up level does he deign to turn that massive head and we can see his lion breath condensing in the cold morning air. It's impossible to describe the feeling when your eyes meet the unwavering stare of a male lion. Vulnerable is one word that springs to mind. He has scars on his muzzle, like most experienced pride males. It's likely many were made by females in amorous exchanges during mating - the lion's equivalent of notches on the bedpost. From the look of his full stomach he has been on a kill. But will he lead us to his cubs?

Just a week ago we saw his pride regroup in a clearing one morning, only ten kilometres from camp. We watched the two lionesses bring the cubs to greet him, but couldn't see more than the tops of their ears and tails above the short grass. The Big Guy, not normally prone to spontaneous outbursts, revealed an apparently sensitive side when he rushed enthusiastically to join them from his resting place more than 100m away. We smiled as the two cubs practised rudimentary ambushes on their father's tail until he turned and cuffed the nearest on the nose. This was the last we'd seen of the cubs. We knew the mortality rate of young lions was surprisingly high. In this place of boom or bust the odds were stacked against them. Starvation and abandonment are common. At this age they'd make a welcome meal for any smart jackal lurking in the grasses.

The Big Guy has stopped now and is lifting his tail to scent-mark a clump of bushes and deposit his calling card. Either he's getting tired of us hot on his heels or he simply wants a break from all this walking. He yawns, revealing a blunt, broken canine, and settles down on the raised sandy bank to sleep. There is still no sign of the other pride members and, apart from a flick of his tail to bat away some annoying insect, The Big Guy is motionless. It looks like our quest is over. If he moves at all again today it will only be to search out more shade. Another strike out.

Still, we decide to wait with him. I don't know what we think he's going to do. Perhaps he'll let out a series of characteristic rumbling roars to call the other pride members to him. They'd hear him miles away on a still morning like this. We open our bag of ystervarkies, the little coconut cakes that are made and sold for pocket money by some of the staff back at camp. Washed down with a flask of strong coffee these have become our bush breakfast of choice. It seems an oddly surreal luxury to be eating them here just a metre or two from a snoozing lion.

Suddenly Steve starts spitting crumbs of desiccated coconut and waving the remains of his sponge in the direction of the river bed. The Big Guy too is looking up and staring intently beyond our vehicle. There in the distance the distinct tawny shape of another lion is walking purposefully towards us. It's got to be one of the other two lionesses and she's carrying something in her mouth. It's one of the cubs. Hanging loosely in the grip of her jaws the little body swings. We look through our binoculars to check that this is really happening and spot the second cub trotting along under her feet, struggling to keep up. The lioness has already seen the male and is picking up speed. We scramble for our cameras. She's bringing her cubs right to us. We could almost reach out and touch them…

Less than four weeks old, they seem as fragile as kittens. Their paws look at least three sizes too big. We can make out the tawny coloured spots in their fur as we watch them playing in the dust just next to us. Their mother, sensing no real threat, is not in any hurry to leave. For now she's more interested in the male than us, but the cubs are watching us intently, fascinated by the continual clicking of our cameras. These helpless ‘little guys' represent the future for The Big Guy's pride and we're reassured that for today, at least, their future seems secure. Tomorrow, however, is a new dawn in the Kalahari, and the struggle for survival will start all over again.