As we strode across the Mansion Lawn towards the lake, bathed in the golden marmalade light of the setting sun, it felt as though we had stepped into Turner’s painting, Sunset, Fighting Bucks. Surprisingly, the view differs little from the idealised landscape depicted by the artist in the early 19th century. Some 800 fallow deer still roam freely in the park, and we could see that the bucks and does had begun to congregate, having spent most of the year in single-sex herds.

During the red deer rut, dominant stags manage large harems and vigorously defend them from rival males. But it was immediately obvious that the fallow deer had a different mating strategy, displaying lekking behaviour.

Dominant bucks had established rutting stands in close proximity to one another, each stationed beneath one of the park’s ancient, low-boughed, oak, sycamore or chestnut trees. The does sniffed the pheromone charged air, their tails flicking left and right like inverted metronome pendulums as they clustered round their chosen suitors.

At the centre of the lek, the master buck, a magnificent barrel-chested beast, gave a throaty, belching roar, his Adam’s apple bulging in his thickened neck. He had already attracted twice as many females as the bucks that held the surrounding ring of satellite stands.

Testosterone-enhanced muscles rippled beneath his glossy, white-spotted chestnut pelage. He strutted up behind each doe in turn, rolling back his lips to scent their rumps in order to ascertain whether they had come into oestrus and were ready to mate.

The master buck tolerated the presence of the skittish male yearlings and prickets that milled about on the periphery of his stand, but as soon as he spotted a challenger stalking into his territory in pursuit of a dusky-coated doe, he charged up to confront him.

The two males were so closely matched in stature and antler size that when they started parallel parading it was like looking at a mirror image. Suddenly there was a thunderous crash as they spun round to face each other, their spatulate antlers interlocking like splay-fingered hands.