So it could be possible that it always had the ability to thrive and grow in other environments but had just never been introduced into that environment until.. well.. until it was! It's just some off the cuff thinking here.
Yep, species move on their own all the time. Just remember that nature is slow. We are STILL seeing results of the last ice age as species SLOWLY move north as the warming continues. North/South movement is easier since water is the key and a large percentage of rivers run north/south.