This is the name given to the process that has occurred during the past century, leading to a stabilization of population growth in the more highly developed countries. The Demographic Transition is shown schematically in Figure 6. It is generally characterized as having four separate phases or stages.
Stage 1. In this early stage of the demographic transition in Europe, birth rates and death rates are both high. Modern medicine had not yet developed techniques to lengthen life substantially and standards of personal hygiene were comparatively low. Both rates fluctuated depending on circumstances.No demographic transition has occured.
Stage 2. In this stage, standards of hygiene and more modern medical techniques began to drive the death rate down, leading to a significant upward trend in population size. The birth rate remained high, as much of the economy was based on agriculture. Mexico is currently between this and the following stage.Stage 2 and 3 are indicative of a partial or first demographic transition.
Stage 3. Urbanization decreases the economic incentives for large families. The cost of supporting an urban family grew and parents were more actively discouraged from having large families. In response to these economic pressures, the birth rate started to drop, ultimately coming close to the death rate. In the meantime, however, the increased population in Europe led to tremendous societal pressures that caused large scale migration (e.g., to the USA) and extensive global colonialization.
Stage 4. The last stage of the demographic transition in Europe was characterized by a higher, but stable, population size. Birth and death rates were both relatively low and the standard of living became much higher than during the earlier periods. The developed world remains in the fourth stage of its demographic transition. A good example of a country in this stage is Sweden. At stage 4, we speak of countries having completed the second or a full demographic transition.
source : http://www.globalchange.umich.edu/globalchange2/current/lectures/human_pop.html