Scenario 3: Imagine instead of an environmentally conscious vegetarian pair of Cains, the human population of the island is a pair, let's call them Mr and Mrs Raton, who are even more rapacious and consuming than Abel is. However, unlike Abel, they do plan to bear children and perpetuate their lineage. They are completely unconcerned for the sustainability of their lifestyle, and all the food sources they live off will be depleted before any of their children possibly reach adulthood.(The pair's name is a nod to the way ships' rats, in the days of European sea exploration, would come ashore onto islands with populations evolved to meet local/specialized pressures and wipe them out completely. These populations of rats would grow exponentially as long as the prey was easy; but as it was soon obliterated, the rats themselves died off when what they could eat was no longer available.)
So we naturally ask ourselves, is this behavior by the Ratons moral? Do they have the right to pass on a blighted and arid landscape to their own offspring?
I contend that their behavior is immoral, and moreover that they do not have such a right. To have full responsibility for and (some measure of) full control over a person's life and well-being (as parents do over their children) includes the obligation to not willfully deprive that person of the means of life. Additionally, it makes no difference whether these children are only as-yet-hypothetical or whether already alive: I'm viewing their whole planned path as a unit, one where (in this case) the order certain pieces occur in is irrelevant to the general cruelty and depraved indifference of the whole.
Naturally, the difference between Scenarios 2 and 3 is not a binary, on-off matter. I've written Scenario 2 so that the Cains' offspring will enjoy all the resources they do, but I don't mean to argue that all usage of nonrenewable resources is immoral. Leaving the world to the next generation in as good condition as you found it is, of course, exemplary, but the welfare of the future generations is not the only criterion on which morality is to be judged. (That way lies infinite regress, as well as any number of paradoxes involving nonconvergent integrals.) However, ones own wanted and freely chosen children have a claim upon one's labor so long as they are too young to take care of themselves -- this is a principle I have never heard a libertarian argue against -- and as a corollary one wrongs one's children if one depletes the resources they will need to survive and thrive.
In the context of the actual modern world, this principle is what justifies removing children from abusive parents: saying that parents have no right to abuse their children is equivalent, under the definition I'm working under, to saying that it is not wrong for others (in this case, the state) to prevent a parent from abusing a child.