Not sure of the exact relationship, but I can give a data point or two: First CPA of the game at 11 AIP was ~4,000 ships, a later CPA at 160AIP was ~21,000 ships. (This was diff 10)
That was a while back, though, so that first one should be taken with a pinch of salt, as it's from memory- the second one is definite, I had a save with a CPA guard post alive.