I have a very rudimentary understanding of Locke's labor theory of property. The key argument is expressed in Chapter 5 of Book II of the Two Treatises of Government:
Though the earth, and all inferior creatures, be common to all men, yet every man has a property in his own person: this no body has any right to but himself. The labour of his body, and the work of his hands, we may say, are properly his. Whatsoever then he removes out of the state that nature hath provided, and left it in, he hath mixed his labour with, and joined to it something that is his own, and thereby makes it his property. It being by him removed from the common state nature hath placed it in, it hath by this labour something annexed to it, that excludes the common right of other men: for this labour being the unquestionable property of the labourer, no man but he can have a right to what that is once joined to, at least where there is enough, and as good, left in common for others.
This is, appropriating something (e.g. land) is valid as long as it comes from its own work and there is sufficient left for others.
The issue for which I have found no clarification in the text is the following. Say that a boat with 100 people crashes into a deserted, isolated island. Each one appropriates a 100th of the land. A few years later, another boat with 100 people crashes into the island. Since these people have no land, they must rent a place from the landowners. Yet, if the original 100 individuals would have appropriated half of the land, they would have left space for the rest to also own some land. Thus, is the original appropriation of land not in line with Locke's conditions?
It might seem evident that Locke's condition about being enough for others refers to contemporary fellow men, and not a future with larger population. But can we simply dismiss the problem I am raising as such? This is, can we just say that, because a resource was divided in a time when population was small, there is no injustice in any sense by any subsequent situation where just a small proportion of the larger population owns the resource? Had Locke something to say on this respect? Maybe in another text of him?