Question

in what way did an increased skull and brain size affect hominid evolution from early ancestors to modern humans

Answer 1

The more the brain size have increased, the more the human ancestors have been able to adapt their behavior to their environment. As Darwin said, the main rule in the nature is "the survivor is the most adapted." The cerebral cortex is the main zone of the brain whose size is important, and with the increase of the skull size, the cortex got bigger.
With the evolution of our behavior, we have been able to use fire for exemple. The meat have been easier to eat and when lived easier. Thanks to a lot of time, evolution gave us weaker skull muscles. The skull have been under a weaker pressure, which allows the skull size to increase. That is another cause of the growth of the brain size, and that is a direct cause to the evolution of our behavior.
Finally, we can say that brain size and human behavior affects each other and brought us to the modern hominid.

I don't know if I am understanable as I'm French and my English is approximative.