The growth of demand will limit output growth for food over the next quarter century

The rate of growth of world food demand will be much slower for 1990–2010 than it was for the prior three decades. The major factor determining the increase in food demand is population growth. Income growth has a much smaller effect. From 1960 to 1990, population growth accounted for approximately three fourths of the growth in demand or use of grain. For 1990–2010, it is anticipated that population growth will account for nearly all of the increase in world demand for grain. The rate of population growth from 1990 to 2020 is projected to be at an annual rate of 1.3% compared with 1.9% for 1960 to 1990—a decline of more than 30%. World per capita use of grain will increase very little—perhaps by 4%. The increase in grain use is projected to be 40% less than in 1960–1990. It is anticipated that real grain prices will decline during the period, although not nearly as much as the 40% decline in the previous three decades. Concern has been expressed concerning the deterioration of the quality and productivity of the world’s farmland. A study for China and Indonesia indicates that there has been no significant change in the productive capacity of the land over the past 50 years. Contrary to numerous claims, the depth of the topsoil has not changed, indicating that erosion has had little or no impact.

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.