Does The Grey Squirrel Attack The Red?

Contrary to English Folklore in which Gray squirrel attacks and even kills Red Squirrels, the two actually do not have any direct violent conflicts. The reason for the disappearance of the Red Squirrel is the ability of The Eastern Grey Squirrel to out-compete it. Acorns have always been aplenty in Britain. However, the Red Squirrel cannot digest them while the Grey Squirrel can. The squirrel parapoxvirus is a deadly disease for red squirrels while infected Grey Squirrels do not appear to be affected (in terms of health). The worst factor is probably that Red Squirrels under pressure do not breed as often.

In the Early 20th century Grey squirrels were introduced into England. They soon spread across the country and invaded Wales and parts of southern Scotland where they practically eradicated the native Red Squirrel.

It deals with territory claimed by one over the other. For they are competing for the same food. By your question the grey squirrel wins. Well in Florida the Red Fox Squirrel is three times as bigger and always wins, unless out numbered! However is less aggressive.
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Aye mate it does