Surely range is the most important factor? Even a huge population can be contaminated by hybridisation eventually if range is limited?
A
Well, restricted species are more sensitive to ecosystem modifications than widespread ones, obviously.
However, I'm not sure I explained properly my point. We are talking about genetic pollution; this can happen only with very closely related species, right?
Let's take a example with a restricted range species. Berthelot's Pipit is fairly restricted species, in the Macaronesia. It invaded those islands from Europe, from Tawny Pipit ancestor if I remember well. It adapted to many different habitats of the Canaries.
Now, migrant pipits visit the Canaries, such Tawny, Tree and sometimes others, but they cannot threat Berthelot, whatever the islands where it lives are small or not. Berthelot is familiar with Canarian habitats, while other are not that much. They cannot compete and threat Berthelot! In case Tawny hybridized with Berthelot, as they would mostly produce sterile youngsters (as our both Oxyura ducks - different species!), this is not a threat; the population is healthy enough not to be affected by a few hundreds individuals that would produce nothing. Couples of Tawny Pipits would either compete with Berthelot's and lose, as they are not as well as adapted (they don't have experience Berthelot's have), or they would manage to use a different ecological niche and create a new population, but then threatening no one.
This is true because Berthelot's has a healthy population.
Now, bring hundreds of European Bullfinches in Sao Miguel, and Azores Bullfinch would suffer! That bird was abundant all over the island, even considered as a pest for agriculture. It has been destroyed for that reason, while natural forest has been cleared, replaced by exotic trees. Population of Azores Bullfinch was a low a 2-300 hundreds not long ago. At that point, introducing European Bullfinch can destroy the local species, but I hope you see now that this is not the problem. Destroying the bird and its habitat was the problem!