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The cyclic rise and fall in population size that has been observed in animal and pre- modern human populations reflects sequential phases of population growth and decline. Disregarding the possible selective influences of migration, these cyclic movements must ultimately be accounted for in terms of the range of variation in fertility and mortality. No downward trend in mortality is apparent in any country before the middle of the eighteenth century, about the same time that population growth began to demonstrate an exponential curve. The initial period of sustained population growth in nearly every country for which reliable data are available corresponds with at least two decisive changes in the death rate. First, the fluctuations in mortality became less frequent and less drastic. Second, the initial, slow--sometimes imperceptible--decline in mortality gradually gained momentum and eventually stabilized at relatively low levels in the twentieth century. Thus, steady increases in life expectancy, progressively diminishing death rates and more stable and predictable mortality patterns have accompanied the persistent increments in world population. In England and Wales , Japan , Ceylon and Chile an exponential pattern of population growth has accompanied the downward trend in mortality. In England and Wales , where the transition from high to low vital rates occurred over two centuries, the exponential growth curve was attenuated only after fertility fell and approached the low level of mortality; this pattern was less apparent for Japan , where an accelerated transition occurred over several decades. Although data concerning the relative effects of mortality and fertility on population growth are incomplete for the early transitional period, it seems likely that a significant though temporary increase in fertility may have added momentum to the population explosion set off by steady improvements in survivorship. The influence of fertility is particularly apparent in the rapid population growth of currently developing nations that have not yet completed their transitions, for example, Chile and Ceylon . In most of these developing countries, the death rate has declined rapidly in recent years, especially since World War II, and the birth rate has remained high with minor fluctuations. This sudden widening of the demographic gap has produced unprecedented high rates of population growth.