The development of the brain is a case of "higher function areas enveloping lower function areas."
Or rather, the evolution of the central nervous system mostly involves evolving a higher-level structure around the "primitive structure." The "higher-level structures" generally envelop the "lower-level structures."
The most primitive, regulating cardiovascular movement, breathing, swallowing, vomiting, and other important physiological activities, is the reflex center.
Above this, there is the movement center which adjusts fibers, corrects the movement of related muscles, adjusts joints, and maintains coordinated voluntary movements.
Above that again, there is the nerve center that regulates endocrines and influences advanced thinking activities and emotions.
And above that is the striatum.
This involves the differentiation in species evolution.