The increasing pressure of world population on natural resources has once again given rise to the sepctre of Malthusian stagnation. The purpose of this Artcile is to examine the Malthusian doctrine of diminishing returns to natural resources using the fisheries as a case study. For the ten stocks of fish studied, it was found that Malthusian scarcity is quite prevalent. That is, fishing productivity significantly declined with expansion in effort. This hypothesis was verified for both the steady state and stock adjustment models. Without major discoveries in controlling ocean environment, it is qutie apparent that the sea will be subject to Malthusian scarcity as the pressure of population increases.