I suspect even the primates will surrender to the cockroaches, Walter.
Have we not forgotten the all-conquering ants? They eat roaches for breakfast.
Apparently, in some Far-Eastern lands, cockroaches and associates are considered fried delicacies; when food gets tighter, I fear for the roaches even before they fail to outrun the ants.
This is a cold winter, but I currently have ants running over the desk despite one of those all-singing all-dancing things that you plug into a socket to drive them away. I suspect they (the plugs - but I don't really know...) are a product of the power companies.
Rob C