Why is my dog food aggressive?

We've had our puppy, Gibson, for about 8 months now. He's perfectly fine with us humans. We have trained him against being vicious to other people, and even around strangers he's perfectly fine. With animals, it's a different story. Each time our other dog or one of our two cats comes around Gibson while he's eating, he becomes terribly protective of his food. He snarls at them, bares his teeth, and occasionally snaps at them. I'm afraid they're going to get hurt. I don't want to isolate Gibson (i.e., putting his food in different room) or punish him, but it's getting a bit out of hand. Is there any way that I can wean him off of this behavior?