

Not sure about the genes affecting connectivity, but I can tell you that neurons in both chimpanzees and humans connect to wayyy more than 7 neurons. Like orders of magnitude more. In the Prefrontal Cortex, pyramidal neurons can have upwards of 30,000 excitatory inputs alone

Dendrites are the inputs; axons are the outputs. Both tend to branch and each dendrite has many “spines” which form the input synapses.
But yes, that sounds more likely since it is theorized that the basal dendrites in the prefrontal cortex being larger and more complex than others is what allows them to integrate larger amounts of information and could correlate with intelligence.