So you can predict what species will win?
Yes, and no. Depending upon the time frame that you're looking at, and the details of the prediction.
For example, a new volcanic island out in the middle of the ocean will probably end up colonized by reptiles and birds, but not by mammals. If it is colonized by mammals, they will probably be aquatic mammals like seals or flying ones like bats, buy not terrestrial ones like squirrels. Birds are rolling a large die, in this regard, than mammals, as is demonstrated by the wide variety of bird life (and the number of island groups with almost no native mammals whatsoever, such as Mauritius. (THe only native mammals known on that island group are bats, which of course fly, and dugongs, which are of course aquatic.) This is one reason that so many islands also have native flightless birds, because they can evolve into niches that would "normally" be taken up by mammals. Similarly, the Galapagos islands have local species of bats and seals/sea-lions, but the only other native species is a kind of rice rat. Easter Island has both birds and reptiles, but no native mammals at all. St Helena had native birds, but no mammals (or reptiles).
So given a choice between a random bird species and a random mammal species, I can predict that the bird will win when playing this "let's colonize a new island" game (and history suggests that my choice is pretty accurate, but not perfect). Which is exactly what would be expected if "winning" were random, but strongly biased. I suspect that a founder population of rice rats -- possibly a single pregnant female -- got caught on a log or something and ended up drifting to the Galapagos, in one of those freak one in a zillion chances that happen every so often, but that cannot be relied upon. The chance of a flighted bird being blown of course is much more likely, and thus happens much more often -- and thus we see many more native island birds than native island mammals.
