(The post title just refers to the problem of initial acquisition by another name.) I've been having a rather unproductive discussion over at Not PC on this issue, and thought I would try to clarify matters in this new post. To recap: the question is how one can rightfully appropriate (i.e. acquire absolute ownership rights over previously unowned) land or other natural resources. (An excellent real-life example is provided by PC's own discussion of claiming ownership over whales.)
The problem for the libertarian here is that any such appropriation necessarily violates the liberty of others, for it prevents them from making use of what they previously had free access to. (As previously noted, the enforcement of property rights involves physical coercion, and thus conflicts with others' freedom from interference.) For example, if I appropriate the only local food source, and refuse anyone else access to it, then my actions have clearly harmed them -- indeed, a consistent libertarian ought to say that I have violated their rights.
So it seems that the only way you could acquire an absolute right over a natural resource would be if everyone else consented to the appropriation, i.e. if they voluntarily sacrificed their liberty for your sake. (Perhaps you could offer them some incentive, e.g. a share of the profits, in exchange for this sacrifice.) But since the "everyone" in question includes future generations, this is a condition that can never be met.
Put another way: we have a moral obligation, when taking from the world's natural resources, to leave "enough and as good" for others. This 'Lockean proviso' would prevent any absolute property rights from ever being granted, once we took future generations into account. At best, one might acquire a conditional property right that limited the ways one could dispose of the resource -- it might require responsible and sustainable consumption, or the subsequent transference of the right to others in greater need, and so forth. One could appeal to utilitarianism to establish such a (prima facie and conditional) right. After all, we'd all soon die if we were never allowed to use natural resources such as food sources. But such a foundation will also justify redistribution of surplus wealth to the needy, so that won't help the libertarian.
PC instead employs the standard libertarian argument that individuals own their labour and thus rightfully own the products of their labour. But their work products are not created ex nihilo, so this begs the question of how they could come to own the natural materials that went into the finished product.
Absent any other explanation, we must conclude that they don't have the prerequisite natural right over the natural materials used. As such, the acquisition violates others' rights. This provides a libertarian justification for a universal basic income: it is the 'ground rent' or compensation that is owed to each human being for the land and natural resources that have been deprived them by others' illicit appropriations. All property derives from these ill-gotten gains, and compensation must be paid accordingly.