Practice question

Longer travel time between patches increases the optimal residence time within a profitable patch under the marginal value theorem. Travel is an unavoidable period with no food gain, so frequent departures would devote a large fraction of total foraging time to transit. A forager should therefore exploit each reached patch more thoroughly, remaining until its declining marginal gain rate equals the lower habitat-wide average created by the greater travel cost. Graphically, increasing travel time moves the tangent’s origin farther left on the cumulative gain curve and shifts the tangency point to a later departure time. This does not mean that total patch gain alone is maximized; the decision maximizes long-term gain per total time, including travel. Shorter residence would worsen the transit penalty, while increased patch discovery is unlikely when travel itself is longer. Risk can modify the prediction if travel or patch residence differs in danger, but risk is not the mechanism in the basic theorem. The result follows from diminishing returns combined with time lost between patches.