It also turns out to be a fairly thorny one to solve. Think of a tropical forest scattered with groves of banana trees, and imagine some forager who consumes the low-hanging fruit of one grove. After a while, this hypothetical forager faces the decision of leaving to find another grove or climbing the trees to get harder-to-reach bananas. Mathematically, it does not seem to be possible to make generalizations about which strategy is the best if the forager walks randomly until they stumble upon a new patch, Redner says; the forager can take almost any path through the environment, and very quickly the possible routes diverge enormously, so it winds up being very difficult to say anything conclusive.
However, in a recent paper in the journal Physical Review E, Redner and his collaborators find that if you think about a one-dimensional situation—with the metaphorical banana groves spread out in a line—then it becomes tractable. The decision now is between climbing the trees of the current grove or moving down the line to the next grove in the distance. In this situation, the forager can tell how far away the next opportunity is; all the uncertainty that remains is whether it is worth it to keep exploiting the resources they have right now or strike out for the next destination. Redner and colleagues found that in this case, the optimal survival strategy is to leave the grove when the time needed to continue to exploit it matches the time that would be required to reach the next one.