Contrary to the old adage, you don’t have a reptilian brain. At least, not any more than you have an amphibian brain or a fish brain. The idea that the baser functions of our brain evolved in and were inherited from our reptilian ancestors is decidedly false. In fact, all the basic components of our brain have existed for over 500 million years, which was long before fish crawled up onto land, let alone evolved into amphibians and eventually reptiles.
The idea of the reptilian brain was developed by American physician and neuroscientist, Paul MacLean, in the 1960s and later popularized in his book, The Triune Brain in Evolution (1990). In his view, the reptilian brain was composed of a structure known as the basal ganglia as well as other parts of the hindbrain such as the cerebellum and brainstem. According to his theory, the reptilian brain evolved first in reptiles and was involved in base instinctual behaviors. Later, the limbic system (paleomammalian brain) evolved in early mammals, which regulated emotion, and, finally, the neocortex (neomammalian brain) in more recent mammals, which was involved in things like planning, perception, and language.
Even though MacLean’s theory is now generally discredited by comparative anatomists, the idea of a three-part (or “tripartite”) brain is actually spot on– even though it has nothing to do with reptiles. In fact, the earliest brains all had three parts to them: the forebrain, midbrain, and hindbrain. According to paleontologists who study very early brain evolution, these three components are part of what defines all brains in vertebrates.
Interestingly, brains are as old as as some of the earliest vertebrates, evolving most probably during the Cambrian Explosion, over 500 million years ago. But you may ask: How did brains evolve in the first place? Good question!
It all begins with a creature like the sea anemone. The sea anemone doesn’t have a brain; instead, it has a structured nervous system known as a “nerve net” or “plexus.” These are collections of neurons that form, you guessed it, a net throughout the organism! In particular, these nerve nets underlie the epidermis (skin) of the sea anemone, which helps it move its tentacles about in order to catch food floating by. A separate nerve net underlies its gut, helping it to move the food through for digestion. It’s for this very reason that even today, we have two separate nervous systems: the central nervous system that, embryonically, develops from the same layer as the skin (a region called the “neuroectoderm”), and the enteric nervous system that controls our gut. In essence, we’re just complicated sea anemones!
Eventually, these nerve nets started to get a little more complicated in some organisms (sorry, sea anemones!), and they started forming what are known as “ganglia” or clusters of nerve cells around important areas, such as locations where sensory information is coming in. For example, you can see in the diagram of the flatworm below, this little guy has “cerebral ganglia” right around the region where his eyes are. So, it seems that the development of the sensory system in the “head” region was a major stimulus for the development of centralized ganglia.
After awhile, a branch of our early ancestors developed three centralized ganglia, as you can see in the diagram of an amphioxus below (a modern animal that is a throwback to these early organisms). These ganglia roughly correspond to the forebrain (diencephalon), midbrain, and hindbrain in animals with a true tripartite brain and share some of their important functions, like processing visual information and controlling movement.
It’s not long after this that we see the evolution of the true tripartite brain in early jawless fish. Modern day jawless fish like the lamprey and hagfish give us a good idea as to how far brain evolution came in such a short span of time. We go from nerve nets and simple ganglia in the Ediacaran period to a veritable Cambrian explosion of the vertebrate nervous system.
Thanks to popular works like Stephan Jay Gould’s book, Wonderful Life, the ancestors of insects and worms have drawn the lion’s share of attention for all their wacky and weird forms that radiated during the Cambrian period. But even though our ancestors were more streamlined and lacked as many outward frills, our guys sure were packing a lot of heat under the proverbial hood. And for that reason, even though creatures like Opabinia and Hallucigenia may boggle the mind with their wondrous and bizarre forms, at least we have giant brains with which to be boggled! 
