There he is, at the bottom of the hill, his mane all puffed up, like his attitude. Behind him are the 30 females he has spent the last two weeks claiming as his own; up above him are two of his male rivals who still hope they might be in with a chance of mating this year. Rhum thinks not. He wants the right to pass on his genes, and his genes only, and is willing to fight anyone to defend that right.
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Within a few minutes of our arrival at the deer park, one of Rhum's rivals, a young male called Spike, decides to have a bit of a go. He wanders up to the pen where the females are gathered, but Rhum runs up to meet him and thrusts his antlers forward. It is followed by a roar that sounds something like a fog horn with a bad temper. It is nature's way of saying: beat it. Spike turns and runs.
This is the deer rut, the strange, enthralling, violent ritual in which males fight for the right to mate with the females. It happens every year around the end of September and the beginning of October and this deer park in the middle of Galloway Forest Park is one of the best places to see it. The colony is small and lives close to a hide where you can sit all day and watch.
As we stand and observe the ritual play out - the ritual of friends becoming enemies then friends again - it is hard not to anthropomorphise, to turn these stags into humans in an attempt to understand them. Rhum could be a bouncer on a nightclub door, or a drunken alpha male high on beer and women, or even, with his mane smeared with mud, a warrior covered in woad. But he is none of these things; he does not need to be reduced by comparison with man.
Hugh Gunning, the wildlife ranger who looks after the colony, tells me a little of Rhum's history. The seven-year-old has been the dominant male here for two seasons now and for the last two weeks or so has been seeing off all-comers. As is traditional during the rutting season, he has gathered the females into a group and kept them there for mating. We catch him sniffing the air to work out which of them has come into season.
When he is not mating, he has to put up with challenges from the other males that take the form of constant eyeballing and frequent posturing, punctuated by violent episodes in which two males lock antlers and fight until one of them backs down or, in some cases, dies. It is very tough physically on all the males but particularly the dominant stag who gets no sleep or food for weeks. Rhum could do with a rest.
He will get it in a matter of days when the rut calms down and the colony returns to normal. Then the group will start to wander across the whole range again, which is about 200 hectares. This is a managed group of animals but they still live pretty much as they would in the wild, although they are much tamer. There is also no culling here; instead, when the group gets too big, animals will be moved to other herds or parks (where there may be culling).
Along with the wild goat park further down the road, this is one of the best reasons to visit Galloway Forest Park. The park has also become famous as one of the best places in Scotland to star gaze because of the low levels of light pollution. On the way home after dark, I pull in to a layby and switch off all the lights and my city-boy heart jumps.
The park is also perfect for other more traditional outdoor activities, such as mountain biking and walking (there are several good way-marked routes that start at the Clatteringshaws visitor centre) but it is the park's combination of the outdoors and the indoors, the feet and the brain, the mind and the body that makes it unique in Scotland. This is the only country park in Scotland that has a book town, Wigtown, at its heart. There are dozens of book shops there but particularly good if you are a fan of science fiction or crime fiction is At The Sign Of The Dragon, which is run by the informed and passionate Richard van der Voort.
More patchy - and this is something perhaps they will get to grips with as visitor numbers grow - is finding a good place to eat in the area. I drop into The Ken Bridge Hotel in New Galloway but I have the gall to do so a couple of minutes after two o'clock. Reluctantly and grumpily, they agree to serve me but I then have the audacity to ask for an omelette.
The Ken Bridge Hotel cannot accommodate my request, I'm told. It's disappointing, especially when we hear so much about improving levels of service in Scotland.
Much better, friendlier and cheaper is the cafe at Clatteringshaws visitor centre, which has just had a makeover. It sits on the edge of a loch and a range of hills that seem to be constantly posing for iPhones and on the day I visit, there is some late autumn warmth, which means I can sit outside. The food is excellent too: Scottish but modern, healthy but reasonably priced. It is a little bit of subtlety in the middle of all this beautiful wildness.