Many would have been taken by ship, as that's how human's would get there. Birds can transfer things, either young animals, eggs or seeds of plants etc. Some things could have got there via sea, in a storm for instance. Also, perhaps they used to be closer to Ecuador than they are now? The earth's plates move (albeit slowly)
http://en.wikipedia.org/wiki/Continental_drift.
Sea levelsmay be different now, so perhaps the amount of water to cross was much less than it is now..
Land animals could have evolved from sea creatures and become land-dwelling over many (many) years.
I would say at least some of the above is the case