The question of whether nature or nurture has more to do with determining behavior in humans and animals is, and has been for a long time, a matter of some controversy. I personally believe that nature and nurture play equal roles in determining animal behavior, but I also believe that an over-abundance of one cannot be used to compensate for a lack of the other to produce a psychologically healthy human or animal.
The behavioral instincts and the physical bodies of all animals are predetermined, inborne categories of characteristics. It is therefore self evident that a puppy will not grow up to become a giraffe with a long neck and an instinct to eat leaves, no matter what occurs in its environment. A puppy has a surprisingly wide, but still very limited range of the types of behaviors it can develop and utilize in order to be as successful as possible in the environment it is faced with, but no matter what a puppy's environment is like there are certain biological restrictions that will prevent it from growing up on a diet primarily based on foliage. Meat is a biological requirement for dogs, they must consume it in order to survive. Those puppies growing up in environments which force them to eat leaves as their primary food source do not grow up. That's nature.
Nature aside for a moment though, nurture has a heck of a lot to do with animal behavior as well; most notably in social animals like dogs and humans. The social environment an animal is in will determine its social behaviors. Imagine yourself in different social situations; the situation has a bearing on how you behave, doesn't it? You would be having a different conversation with totally different mannerisms if you were speaking to a police officer casually at the counter of a coffee shop than you would if you were talking to the same guy from behind a row of steel bars. The whole point of government, prison, military interventions and all religions is to influence people through environmental factors, and it works on a massive scale.
Children who grow up in foster homes are far more predisposed to become criminals than children growing up in "normal" middle class families. A child's self identity will be determined by his or her environment; how he or she is treated by the rest of the family will determine how he or she treats others and how the rest of the family relates to society will determine how the child will relate to society as well. That's why over 50% of children who grow up while a parent is in jail end up in jail themselves. That's nurture.
So I think, obviously, both nature and nurture play an important and equal role in the creation of physically and mentally healthy human and nonhuman animals.