Some dogs can't resist a good belly rub, and the reasons are both behavioral and neurological. While showing off his tummy is a conscious act that speaks to his relationship with you, your dog also undergoes a neurological reaction when you start stroking his fur. The combination of the two can make tummy rubbing a wholly satisfying experience for your pet -- if he lets you do it in the first place.
When your dog displays his tummy for a rubdown, he is performing an act that is, at its core, submissive. Rolling over to show you his belly leaves him physically vulnerable, and represents a strong degree of both trust in and submission to you. Rubbing his belly just plain feels good, much like other types of petting, but it also shows him that his trust and submission were well-placed, and that you won't take advantage of his vulnerability.
Science also plays a role in why your dog likes tummy rubbing, and his appreciation for the rub is linked to the reasons he enjoys all types of petting. Dogs have a particular brain neuron that responds exclusively to the stimulation of hair follicles, which means that when you rub his tummy, the stroking of his tiny belly hairs is actually providing a specific type of stimulation in your dog's brain. This neurological stimulation is only possible through stroking, which makes petting like belly rubs uniquely satisfying.
While your dog may love tummy rubs, don't confuse his uncontrollable leg-kicking with the throes of ecstasy. The leg-kicking associated with tummy rubs is often considered a sign of your dog's enjoyment, but in reality, this is an involuntary reaction, much like kicking your own leg when a doctor tests your reflexes with a mallet to the knee. If your dog always kicks his leg and doesn't appear to enjoy tummy rubbing, try stroking an area of the belly that doesn't induce kicking, and he may like it more.
Not all dogs enjoy tummy rubbing, and while this may be related to the potentially-irritating involuntary kicking reaction, it may also be behavioral. Rolling over to display the tummy and engage in rubbing requires submission and trust on your dog's part, and if he is unwilling to concede dominance -- or unable to trust humans -- he is unlikely to do so. Don't force a dog to engage in tummy rubbing -- if you roll your dog over and rub his belly, it can be an upsetting experience that further shakes his trust.
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