Parrots are PANTROPICAL (they are found all across the tropics): how did they achieve this? Did they evolve before breakup of Pangea? But Pangea broke up way before main radiation of birds! North America was connected only to Asia at time of Archaeopteryx. Most major splitting occurred 65 million years ago (beginning of Cenozoic). 1) So only birds affected are the most primitive ones (or) 2) birds are far older than we think and we haven't found fossils. As far as we know, the major radiation of bird families occurred in the EOCENE, at the same time of the major splitting of the continents. SO WE HAVE THE PANTROPICAL DILEMMA. How do you explain the world wide distributions of parrots, trogons, barbets or sungrebes? Is this an example perfect convergence? Most landbridges are temperate, so did these taxa move across temperate zones? This seems UNLIKELY, since they are strictly tropical groups and the temperate zone would be a severe barrier. I have seen Mangrove Swallows in temperatures in the 40's.
Prehistoric climates and fossil floras suggest tropical floras did exist on these landbridges during EOCENE! (a shifting of poles towards Siberia). It's also possible that there once existed temperate members of the taxa that are now extinct: we need more fossil evidence.