I just finished a challenging but deeply edifying book called Consciousness: Confessions of a Romantic Reductionist, by Cal Tech biologist Kristof Koch. The book is the finest example of making hard science accessible without dumbing it down that I've encountered in some of the modest reading I'm doing on the physical basis of consciousness. My underlying goal is to get a sense of what the most knowledgeable experts on the brain have to say about the connection between neurological sophistication and consciousness.
Koch, for one, certainly posits a correlation. He writes, "Consider simpler animals-simplicity measured by the number of neurons and their interconnections-such as mice, herrings, or flies. Their behavior is less differentiated and more stereotyped than that of dogs. It is thus not unreasonable to assume that conscious states of these animals are less rich, filled with far fewer associations and meanings, than canine consciousness."
I know this line of thought makes some animal rights advocates, many of whom prefer to view all animal life as deserving the same moral consideration, nervous. But I like the proposition in part because neurological complexity is the same physical basis that biologists use to distinguish a category of life that we do not grant equal moral consideration: plants. This distinction is one that animal rights advocates very much need to preserve at all costs. Consider this excellent overview of the plant/animal distinction on the basis of evolutionary cellular development by Oliver Sacks: