Good day Jeff:
One of the sources is Carlo D'Este's "Bitter Victory" which covers a lot. There was at the start enough to transport all the first wave of Operation Husky with little to spare. No sooner had the invasion begun the demands of Overlord would be felt. The British were willing to hold off sending the various landing ship assets, yet it was the American demands that they be sent to England as soon as possible that actually took place. The Americans were not willing to give up any of their Pacific assets, so it fell on the British to give up theirs.
I could not find any definite day to day figures as far as what the capacity was. There is a difference between ship transports, which the Allies continued to always have a large number rotating in the Mediterranean, and the various landing craft types.
Initially after the landing they were used to bring in supplies. But as ports were captured they began their withdrawal. By the last two weeks we hear that there is enough stationed in Palermo for Patton to land a reinforced battalion behind the San Fratello Line at Sant' Agata. Also what must be taken into consideration is that the Allies were already planning to invade Italy which would also place a restriction of the use of the valuable landing assets. So there was probably many still left in North Africa in reserve.
So it went from an initial capacity to land seven divisions on Sicily to about three and a half for Italy.
In my scenario "Bitter Victory Sicily 1943" I tried to be as close as posible for the time scale I used at half days. Much of the sea transport capacity in the later turns is not specifically for amphibious use, but what was used to transport the reinforcements ashore.
Hope this helps in some way.
