I found this great article from Mud Bay about the relationship between diet and behavior. I'd like to share it with you:
Unlike humans, dogs' digestive systems are built to obtain energy from diets that are high in protein and fat, with few if any carbohydrates. Diet that are too low in protein and fat, too high in carbs or difficult to digest, can lead to a variety of challenging behaviors:
Diets that are to low in a particular nutrient can lead dogs to look for it someplace else - in garbage, plants, furniture, clothes, etc. We experience this as a behavior problem, but it's often actually a nuturitional problem.
Frequently, challenging behaviors in cats are directly connected to a diet that's deficient in one or more nutrients. Here are two examples:
In some cases of feline aggression, cats seem to respond to a dietary deficiency by aggressively guarding their food supply. In other cases of aggression, deficiencies may make cats feel irritable or grumpy, leading them to act aggressively with other annimals or with people.
Pooping in inappropriate places is often a result of constipation. Transitioning to a diet that includes a higher level of moisture, more fiber and pre-biotics can improve the health and function of a cat's digestive system and reduce or eliminate pooping outside the box.
Behavioral challenges like these frequently vanish when the nutritional cause is identified and addressed.
--From Mud Bay