This is the story of a dog called Darcy. I met him in the Australian bush, where he was on holiday barking at a piece of barbed wire. Later I found out why. Well, no, not why but how it came about.

Darcy, who is 12, belongs to a breed that the Australians call kelpies. Black and tan, but predominantly black, about the size of a Border collie and lean like a collie, Darcy had in other respects something of the labrador about him, but smaller and packed with vim. Kelpies are a kind of Australian sheepdog, highly intelligent, faithful and trainable, but essentially working dogs that need lots of exercise and should never be cooped up.

Darcy's owners know this, so since he was a pup he has been taken for regular runs in the park when they are in town, and when in the country he has grassland and forest to tear around in - which he enjoys. But he is obedient - good on long car journeys, well behaved indoors, you need only say “turn” to him and (however reluctantly) he'll immediately turn back from wherever he was headed. He sits when instructed.

You can tell he loves the family that own him and they love him. Darcy seems comfortable in his own skin. But when he was about 11 weeks old, something happened. Making his first visit to his owners' property in the bush, he leapt from the pick-up truck to find a dead sheep just inside their boundary fence. Some hardwired dog-knowledge stirred deep within him and he was riveted. Fearing that he would roll in it or worry the carcass or try to eat it, his owners heaved the sheep over the fence.

I'd better describe the fence, because it's going to figure prominently in Darcy's life: a fence strung between steel posts, about 4ft high. The bottom half is deer-netted; above are a couple of strands of plain wire, with a strand of barbed wire on top. This will keep in a puppy or a sheep, but a dog or a human can jump over.

Seeing the carcass on the other side of (for him) an uncrossable fence did not lessen Darcy's interest. He stood, stared, barked, ran at the fence and started jumping at the wire until his owners brought him in. Whenever released he was back at the fence, lunging, barking. And when another day the family returned and the sheep was gone, Darcy went straight back to the fence, stared at the very spot where the dead sheep had lain and began again to bark and jump until they took him inside.

That was 12 years ago. And since that day he has never stopped. I made quite a study of him last week.

I had arrived in the pick-up truck with Darcy's owner. The moment the door opened he made a beeline for the fence. For an hour he ran backwards and forwards behind it - his run has become a channel (“we're down to rock,” the family said) - eyes fixed on a single point on the other side, leaping at the fence, pawing the wires, barking and - and this was weird - snapping his jaws shut with a clack-clack sound, as if snapping at flies. He could easily jump the fence now but he never does.

“Darcy, Darcy, it's OK,” the family would shout, sorry for him. “Come back.” But unless commanded - whereupon he obeys, slinking back to the house with many a backward glance, then running back to resume the barking as soon as he is out from under his master's eye - it is there that he wants to be.

Yet the family say there's relief on his face when they tie him up on the veranda - like the grateful obsessive-compulsive shoplifter as the handcuffs click shut or the child-molester begging for castration. After breakfast, when the front door is opened and he can slip out, he leaves the house with a dutiful expression - almost as if to say: “Mustn't tarry. Work to do at the fence. See you later.” Left to himself he will do it all day until his front paws bleed from continual jumping at the wire. Nor is it simply an excess of energy: Darcy can be taken on a long walk, come home tired and hot - and pad wearily back to his Sisyphean labour at the fence.

The obvious questions. Why not put him on the other side of the fence, where the carcass once lay? We did. The family often have. He runs around looking confused and then makes his way back inside the fence to bark some more. Or why not try aversion therapy - a smack or even electric shocks - whenever the behaviour starts? His owner worries lest this might deepen the inner turmoil. Or why not get another dead sheep and let Darcy have his way for a weekend? Here the worry is that this could reinforce his behaviour rather than bring him closure.

Doubtless there are dog psychiatrists who would venture suggestions for a “cure” for Darcy, but can any be ventured with confidence. Or we'd know what to do about trainspotters, wouldn't we? Or stamp collectors, joggers, horse riders or Sudoku addicts? Or (perish the thought) Brown-bashing columnists? Come to think of it, what does “compulsive” really mean? Bred to herd sheep, isn't a sheepdog meant to be compulsive?

Here I sit, under a jacaranda tree in Sydney, its mauve blossom hot against a cool blue sky, with flowers literally raining down on to a mauve carpet of blossom around me, and Australian householders are out with industrial-strength leaf-blowers, blowing the debris...where? Next door or on to the road. Why?

As I crawl around in the shower on my hands and knees, trying to retrieve a tiny shard of dropped soap that Iwant to use up before opening a new bar, or break my teeth biting the last smear of toothpaste out of an empty tube, who am I to indict Darcy of compulsive behaviour? Maybe it's healthy - and the higher animals need an all-consuming impulse to throw themselves at some internally programmed task - a Moscow to which we will never return, a cherry orchard that will never be planted - and not to reason why. Tireless campaigners against slavery, the third runway at Heathrow or the decimalisation of our currency, are distinguished more by the relative usefulness of their causes than by any differences in the pathology of their behaviour. And a dog leads an unexamined life: he is unlikely to pause during a volley of barking and think: “Where's the sense in this?”

So maybe Darcy's happy, happier than many human beings. His is a blameless life and, when it's over, a merciful providence may reincarnate him as a Eurosceptic MP. Then for decades he can leap up and down on the green leather benches snapping his jaws and barking at Brussels.

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