On reading The Origin of Species (p 126)

The dependency of one organic being on another, as of a parasite on its prey, lies generally between beings remote in the scale of nature. This is often the case with those which may strictly be said to struggle with each other for existence [...] But the struggle almost invariably will be most severe between the individuals of the same species, for they frequent the same districts, require the same food, and are exposed to the same dangers.

This is the start of the central point of chapter 3 - The Struggle for Existence. He goes on to point out that the struggle between varieties will be almost as severe, and (I am guessing, now, as I have not read much further yet) so decreases as you move further away on the 'tree of life'.

The struggle for existence has previously in the chapter been demonstrated to be the major check on population; different species competing for the same resources, and particularly how different species which were previously deprived of a share of the resources available by a more successful organism, when that organism is removed, begin to thrive.