‘See what I mean?” says Falcon Frost, blue eyes smiling beneath his deerstalker. “Such a magical sound.”

We are on the Glenfalloch estate in Loch Lomond and the Trossachs national park. Silver cloud drifting across the glen, golden sunlight on the peaks, it certainly is a magical spot. That “magical sound”, meanwhile, is the roaring of stags, the signature of the red deer rut. As the cuckoo is to spring, so the bellowing stag is to autumn in Scotland’s wild places. “It is,” says the stalker and gamekeeper, “one of nature’s great events.”

Small and stocky, in his early 40s, Frost has two qualities which suit him to his trade: a low centre of gravity and a low voice. He is also a fine example of nominative determinism, having an intense love of winter (which round here can get down to -15C or so) and the sort of eyesight one might expect from a bird of prey. He seems able to spot deer at vast distances; the telescope slung across his body in a leather case is merely there to confirm the sighting. He also carries a rifle – deer are culled on Glenfalloch, and elsewhere in Scotland, in order to protect the environment from being overgrazed.

Stalker Falcon Frost with his telescope. Photograph: Murdo Macleod/The Guardian

The red deer is Britain’s largest land mammal. It is estimated there are 400,000 in Scotland, and approximately 50,000 in the rest of the UK, the vast majority of those in Exmoor, East Anglia and Cumbria. There are around 700 on Glenfalloch. This is hill country. Glenfalloch contains six Munros – peaks over 3,000 feet high – including Ben Lui, known as the queen of the Scottish mountains. Most of the folk walking on this land will be Munro-baggers, but, keeping off the paths, we don’t see a single soul all day. What we do see is deer, and plenty of them.

From mid-September to early November, red deer display rutting behaviour; stags battling for the right to mate with as many hinds as possible. The biggest stags, when I see them roar, tilt their heads back and gape wildly, drawing attention to their powerful neck muscles and shaggy manes. This is usually enough to make challengers walk away, but sometimes it comes to a fight: the butt and clash of antlers.

We are here just a bit too early in the season for me to witness these battles, but Frost explains that these great warriors, testosteroned and reckless, do sometimes get hurt or even killed, especially if one of them is a “switch”, also known as a “murder stag”, meaning that his antlers end in sharp points rather than cups. One stag can impregnate up to 30 to 40 hinds during the rut; they are known as his “harem”, a usage which gives him a despotic, sultry air.

“You do feel as if you are spying on something you shouldn’t be seeing,” says Bella Lowes, a member of the family that owns the estate, as she passes me her binoculars. “It’s very primal.”

Pure sex and death? She nods. “It is.”

Experiencing the rut in the wild like this is utterly different from seeing it in the likes of Richmond Park. We walk for hours and miles for glimpses of deer, but what glimpses. Sixty or more gathered on a hillside, the biggest stag charging around, keeping his hinds together, warning off rivals. Smaller, younger stags loiter on the edges of the herd, newcomers at a dance, waiting for a chance to cut in and make a conquest.

A roaring rutting stag. Photograph: Murdo Macleod/The Guardian

Stalking deer – getting close enough to hear the roar – is hard going. You walk into the wind so the animals don’t smell or hear you coming. You walk up the course of burns, keeping below the level of the bank, sometimes wading against the icy current. You crawl over cold bog, wrist deep in peaty water. There is a lot of sitting in silence, face lowered close to the ground; in these meditative moments one’s perspective distorts and the miniature world looms up. This is a landscape of browns and greens, but up close the colours pop. Pink lousewort, blue milkwort, yellow potentilla. The heather is full of a lichen known as stag moss; pale and branching, antler-like.

Frost, stalking, is alive to wind and weather. He stoops now and then for a fist of grass, tossing it into the air to check the direction of the breeze, and shaking his head at the results, a diviner dissatisfied with the prophecy of the I Ching.

He shot his first hind when he was nine, but he loves these animals, and – through close study of their behaviour – believes he has come to think like a deer. He adores the strategy of stalking, pitting his wits against these masters of evasion. Everything up until the pull of the trigger is a pleasure; the rest is duty.

How, I ask him, does he feel when a deer is culled? “Remorse isn’t the word. But you’ve got to feel it. The day I lose that feeling, I shouldn’t be in the job.” What would he call the feeling? “Sadness,” he says.

At a little before 5pm, Frost leads us on to the east face of the smaller Munro Beinn a’ Chleibh. The cloud has come down, grey and blinding. But we can hear the roar. Five or six stags, lost in the mist, bellowing at each other. It is a deep and defiant grunt, zealous and jealous. Keats had it wrong: there is nothing mellow about this fruitfulness. Anger, aggression, braggadocio and extreme sexual promiscuity are not characteristics and behaviours one would admire in a man, but in a stag they are undeniably impressive. When one of these beasts appears in silhouette, black-antlered and roaring on a nearby ridge, it has a heraldic quality: a rampant beast from a barbarian’s shield; or perhaps a cave painting glimpsed by torchlight.

That roar ... it’s a rage against the dying of the year. It has been a privilege to experience it, especially in such a raw environment, feeling something of the wet and cold that these animals must endure as they struggle to survive as both individuals and a species. The rut has been going on for ever, and for ever may it continue echoing through these glens.