Dogs and cats have biology-driven nutritional requirements that may or may not be satisfied by some pet foods marketed as 'natural.'
According to Susan Nelson, DVM and assistant professor of clinical services at Kansas State University:
"Natural and veggie-based pet foods are based more on market demand from owners, not because they are necessarily better for the pet."
Pet owners should check labels and look for a nutritional adequacy statement from AAFCO -- the Association of American Feed Control Officials. This will insure the formula at least meets minimal nutritional requirements.
Definitions for 'holistic,' 'organic,' and 'natural' pet foods have not been established by AAFCO, so interpretation of what those words mean in terms of formula ingredients is left up to the manufacturer of the product.