Blackberries here are far from amusing as they can take over in a matter of months, we simply don't get the frost to knock them back, one corner of our place is overrun with them as the adjoining property won't spray his, I spray them four times a year but they just bounce back, they are controlled on my side but the other side are spreading like wildfire, the coldest we get is about -2°C but only about half a dozen times a year, we curse the English botanist Von Mueller who introduced them here as a food source a few hundred years ago.
The birds are our problem, eat the ripe berries then spread seed filled superphosphate (that was being polite).
We have many plants here which were brought over as ornamentals for the housing boom after WWII which are causing problems now. Several of them have big berries, which the birds eat as you say, then spread through out the landscape; Autumn Olive and Honeysuckle to name just two. I also am seeing (native) elderberry and sumac in places where it never was before, in forest openings we've created.