Berlin Zoo
Even if Berlin Zoo still has the world's largest collection, I am sure that it was just as large as before WWII until 1977 or thereabout, when they started combining enclosures, which meant more space for each species but a fewer species in turn. Berlin Zoo has (or used to) traditionally printed its species and specimen inventory in the guidebook, I seem to recall comparing those figures from my old guidebooks at home, and noticed an increase up to 1977 but then a slow decrease. But I am abroad at present, in Switzerland, so I cannot check.