Brits Losing After American Invasion

According to recent reports red squirrels in Britain are facing extinction. There may be only 30,000 left in England, 10,000 in Wales, 10,000 in Northern Ireland, and 121,000 in Scotland [Red Squirrel Facts]. The European Red squirrels (Sciurus vulgaris) are being out-competed by American or Eastern gray squirrels (Sciurus carolinensis) introduced into Great Britain in 1876.

Human Brits are banding together to help the red squirrels fight off the foreign invasion [Friends of the Red Squirrel] but the prospects are dim. It looks like curtains for the reds.

This clearly has something to do with evolution. When one species out competes another and drives it to extinction we think of this as part of the process of evolution. But which process is it? It doesn't really count as natural selection, strictly defined, since that process involves differential success of individuals within a population. What do we call it when two species go head-to-head and only one survives?