Furry good news: Professor John Bradshaw engages in a tug-of-war with Kate Kellaway's dog Lily. Photograph: Karen Robinson

Professor John Bradshaw is leading a revolution in the study of canine behaviour. 'Dogs don't want to control people, they want to control their own lives, ' he says.

Professor John Bradshaw is holding out a clenched fist – you might see this as a novel way of greeting a stranger were it not that it is my dog, Lily, he is approaching. He is giving her a chance to have a good sniff at him. Before we go any further, it needs spelling out that Bradshaw is not a dog trainer. He has not come to my house to turn Lily into a reformed character. He is a scientist – founder and director of the Anthrozoology Institute at the University of Bristol – who has devoted the last 25 years to studying the domestic dog and has just written the most fantastic book, In Defence of the Dog, which is already on US bestseller lists and is about to become required reading for dog lovers everywhere. Bradshaw is not interested in canine hearsay. He does not peddle opinions. His style is tolerant, clear and benign and he is interested only in what science can support. His book is a revelation – a major rethink about the way we understand our dogs, an overturning of what one might call traditional dogma.

The first idea to bite the dust is so huge and entrenched that some owners will struggle to adjust. We have had it drummed into us by trainers such as Cesar Millan that because dogs are descended from wolves (their DNA is almost identical), they behave like wolves and can be understood as "pack" animals. The received thinking has been that dogs seek to "dominate" and that our task is to assert ourselves as pack leaders – alpha males and females – and not allow dogs to get the upper paw. (I remember sitting in the back of a puppy-training class with Lily who was crying while the teacher was talking. I got ticked off. I was told she was demonstrating "dominant" behaviour.) Bradshaw has no quarrel about DNA. His argument is that scientists have been studying the wrong wolves and jumping to the wrong conclusions. He says: "People have been studying American timber wolves because the European wolf is virtually extinct. And the American timber wolf is not related at all closely to the ancestry of the domestic dog."

Bradshaw's hypothesis is that domestic dogs were descended from more sociable wolves but that "whatever the ancestor of the dog was like, we don't have it today". The wolves alive now are unreliable specimens, necessarily rough diamonds, who have been able to "survive the onslaught we have given them". And here is the rub: new research – including work with Indian village dogs – shows that dogs "do not set up wolf-type packs. They don't organise themselves in the way wolves do". Dogs are not striving, in other words, for household domination. Bradshaw believes our relationship with dogs has been sadly distorted. He writes: "The most pervasive and pernicious idea informing modern dog training techniques is that the dog is driven to set up a dominance hierarchy wherever it finds itself." He explains that apparently dominant dogs are usually "anxious" rather than "ambitious". He says: "They don't want to control people, they want to control their own lives. It is what we are all aiming for – to keep control of our own lives. It is a fundamental biological urge."

But Bradshaw is far from suggesting we slacken in our efforts to train our dogs (it is the more brutal training methods he would like to banish). But I wonder how Cesar Millan and his followers will respond to these findings. Millan, America's internationally influential "dog whisperer" has made a television career explaining dog psychology in terms of wolf lore. Bradshaw says: "I am reluctant to demonise Millan, he has come under a lot of pressure." On a recent tour of the UK, Millan was told his methods were close to breaching Defra guidelines (which forbid harsh training). "He is a smart guy and sees which way the wind is blowing. He is now embracing reward-based methods. All that stuff he spouted about wolves was not based on science." Besides, as Bradshaw observes, there are more "hardcore" trainers out there – such as the massively influential Monks of New Skete in the United States who "sound as if they ought to be the gentlest people in the world" but base their bogus, punitive methods on wolf biology: they urge owners to shake their dogs "because this is what wolf mothers do to keep their cubs in line".

Bradshaw favours humane, reward-based training. The latest science shows that dogs learn to "please their owners". It is wonderful to hear this: he makes one feel fantastically upbeat about being a dog owner (and it is a relief to drop all thoughts of a primitive power struggle).

Bradshaw first went to the dogs – in the best sense – because of his interest in "the science of smell. I used to study ants, wasps, moths… then I thought: why not broaden this out?" When he started out, a quarter of a century ago, he was in an unglamorous minority. Now canine science is a "huge industry – with 200-300 people working worldwide". The reasons for this include the sequencing of the canine genome, the rise in animal welfare science, increased interest from vets wanting to specialise in dog behaviour and primatologists who can no longer afford to study chimpanzees. But the most remarkable reason, Bradshaw explains, is that since 9/11 there has been a huge increase in the use of sniffer dogs. Dogs are now used not only for narcotics but to help epileptics (able to alert them when they are on the edge of a seizure) and to sniff out everything from bedbugs to shark's fins and even certain kinds of cancer. Bradshaw, in his book, follows the dog's nose brilliantly (it was intriguing to learn that while dogs love to sniff other dogs they "do not much like being sniffed themselves"). He urges us to show "manners" and be aware of our dog's sense of smell. And his championing of a dog's right to be a dog is attractive. But I had been hoping he might have a solution to what happens when the sense of smell gets out of hand: Lily, whenever there is a roast in the oven, is overcome with greed and longing – and barks. On this matter, he says only: "Ignore her." (I suspect him of being on her side.)

For anyone interested in dog emotion, In Defence of Dogs is also a sentimental – and surprising – education. The first shocker is this: dogs do not experience guilt. So the look Lily gives us when discovered illegally on the sofa (creeping off, flashing the whites of her eyes) is not guilt? Bradshaw explains she may know to associate that basking on the sofa leads to owner disapproval but that is not the same as feeling guilt, or as having the mental equipment to differentiate between right and wrong. Less surprising is Bradshaw's sense that dogs may be capable of jealousy (when I give my husband a hug, Lily wants to be part of the action). But dog jealousy is not of the all-consuming, Othello sort: "They may be able to feel jealousy in the moment but don't obsess about it or trawl Facebook for evidence."

Bradshaw's most incredible – and gratifying – assertion is that dogs are more interested in people than in other dogs. This is not soppy wishful thinking but the result of studying "co-evolution, the two species evolving towards each other". We forget that the play between species, enjoyed by dogs and humans, is very rare. The family feeling that wolves display has been replaced in dogs by "an intense need to bond with people". Bradshaw says that from the moment puppies open their eyes, they start to bond with people "completely, spontaneously and as hard as they can".