Several independent trajectories of subsistence intensification, often leading to agriculture, began during the Holocene. No plant-rich intensifications are known from the Pleistocene, even from the late Pleistocene when human populations were otherwise quite sophisticated. Recent data from ice and ocean-core climate proxies show that last glacial climates were extremely hostile to agriculture—dry, low in atmospheric CO2, and extremely variable on quite short time scales. We hypothesize that agriculture was impossible under last-glacial conditions. The quite abrupt final amelioration of the climate was followed immediately by the beginnings of plant-intensive resource-use strategies in some areas, although the turn to plants was much later elsewhere. Almost all trajectories of subsistence intensification in the Holocene are progressive, and eventually agriculture became the dominant strategy in all but marginal environments. We hypothesize that, in the Holocene, agriculture was, in the long run, compulsory. We use a mathematical analysis to argue that the rate-limiting process for intensification trajectories must generally be the rate of innovation of subsistence technology or subsistence-related social organization. At the observed rates of innovation, population growth will always be rapid enough to sustain a high level of population pressure. Several processes appear to retard rates of cultural evolution below the maxima we observe in the most favorable cases.