Keith Montgomery
Department of Geography and Geology

In order to fully understand the demographic transition there are some terms and concepts we should know. The following terms are defined and discussed below:
Birth rate
Death rate
Natural change
Replacement fertility
Doubling time
Survivorship curve
Population pyramid
Population momentum

Birth Rate:

The Crude Birth Rate represents births in a given year for every 1000 persons.

By expressing births in this manner we can compare countries of greatly differing populations. For example, in The United States there were a total of 3.78m births in 1998. Given a total population of 270m the rate of birth was therefore 14/1000. In Guatemala, on the other hand, there were a total of 0.43m births in 1998. However, given a total population of only 12m, this represents a rate of birth of 36/1000 -- a much higher rate than that of The United States, as we might expect.

Strictly speaking this is a "crude" rate of birth because it is averaged across the entire population, regardless of age or sex! And neither is it adjusted for the age structure of the population. Thanks to the post-war "baby boom", 25% of the US population is female and in childbearing years, compared to 23% in Guatemala. More specifically, then, for every 1000 women of childbearing age (15-49 yrs) in Guatemala there were 153 births in 1998, compared to 54 in The United States -- this is an even greater contrast in reproduction than crude birth rates alone indicate, and this is so because there are relatively less women of childbearing age in the Guatemalan population . This measure of birth rate is also sometimes called the "general fertility rate" or the "age-specific birth rate".

Nevertheless, it is the Crude Birth Rate that is most commonly quoted and compared and this is the figure we will use. The CBR is controlled mainly by the fertility of the population (see below) and by the number of women of childbearing age in the population (see population pyramid below).

Death Rate:

The Crude Death Rate represents deaths in a given year per 1000 people.

By expressing deaths in this manner we can compare countries of greatly differing populations. For example in The United States there were a total of 2.43m deaths in 1998. Given a total population of 270m the rate of death was therefore 9/1000. In Guatemala, on the other hand, there were a total of 0.08m deaths (80,000) deaths in 1998. However, given a total population of 12m, this represents a rate of death of 7/1000 -- perhaps surspisingly, a lower rate than that of The United States.

However,  this is a "crude" rate of death because it is averaged across the entire population, regardless of age (or sex, or ethnicity). Clearly, for example, one's chances of dying in The United States are considerably more or less than 1% depending on whether one is 90 yrs old or 9 yrs old! Or whether one is a white male or a black male. And neither is it adjusted for the age structure of the population. This is the key to understanding how a Third World country can have a lower death rate than a developed country (not all do).

In the US, 9.5% of the population is elderly (>65 yrs), whereas in Guatemala only 3.1% are over 65 yrs. thanks to recent growth and declines in childhood mortaility. So, although childhood mortality is still higher in Guatemala, the much higher proportion of young persons still resulted in relatively fewer deaths in 1998 (63% of Guatemala's population is less than 25 yrs, compared to 35% in The United States).

The issue of age structure becomes all the more interesting if we compare population over time. In 1940 the CDR of the US was about 10.8. In 1998 it stood at around 9.0. Thus, one might be inclined to think that not much progress has been made in the past 58 years. However, the population of The United States is much older in 1998 and so the slight decline actually represents a considerable advance in health care and longevity. Adjusting for the age difference (akin to adjusting for inflation when comparing dollars costs -- "constant dollars"), the death rate age-adjusted to 1940 was about 5.0 in 1998 -- less than half the 1940 rate. (In fact, that might be a more realistic figure to compare to Guatemala in 1998).

Nevertheless, it is the Crude Death Rate that is most commonly quoted and compared and this is the figure we will use.

Natural Change and Rate of Natural Change in Population:

Natural change in population is the difference between births and deaths. It does not include the effects of migration.  Including the effects of migration (both in and out) would give us Total Change. The difference between natural and total change can be important in countries that are experiencing significant migration and one should be careful when reading data to be sure which they represent.

In 1998 in The United States there were  3.78m  births and  2.43m  deaths. The natural increase was therefore 1.35m  persons. However, in order to compare change among countries of differing population size we reduce this change to a rate per thousand (as with births and deaths, above). Therefore, given a population of 270m, the rate of natural change in 1998 in The United States was 5/1000, or 0.5%.  This compares to Guatemala as follows: 0.43m births -  0.08m deaths =  0.35m increase; total population 12m therefore rate = 29/1000, or 2.9%.

We can arrive at the same answer using just the rates alone:
 (1998 data)
United States Guatemala
CBR per 1000
CDR per 1000
Rate Natural Increase
per 1000 (CBR-CDR)
Percent Rate Natural Increase

Generally we are most interested in natural change, but total change is interesting. In 1998 the US population increased by a total of 0.9% which reflected a net in-migration of 1.08m persons. In Guatemala, on the other hand, total change was 2.7% (i.e. less than natural change), and this reflects a net out-migration of 0.026m persons (mainly young persons in search of greater opportunities in The United States). 


The total fertility rate is the average number of children that would be born  to a woman during her lifetime if she were to pass through her childbearing years conforming the age-specific fertility rates of the year in which she turned fifteen. Fertility  in 1998 in Guatemala and The United States was 4.8 and 2.1 per woman, respectively.

Fertility across the world is correlated with a number of factors. These include: age of marriage; female literacy; childhood mortality. We can also state more subjectively that there exist in different societies values and norms that support childbearing and these may be stronger in some societies than in others. Indirectly, the desire to have a male child may also force the issue in parts of South and East Asia. Contraceptive use is highly correlated with fertility decrease but this is more likely an effect of decisions taken to limit fertility that reflect positive changes in the previous factors listed. Religious affiliation has no clear relationship with fertility. Among Christians, religiosity (church-going) is more of a factor than whether or not one is nominally Protestant or Catholic.

Fertility refers to numbers of children being born and is related to social behaviors and personal decisions. This should not be confused with  fecundity, which refers to the biological capability and capacity of bearing children. In common discourse the former term is often confused with the latter.

Replacement fertility:

The level of fertility at which a cohort of women on the average are having only enough children to replace themselves and their partner in the population. By definition, "replacement" is considered only to have occurred when the offspring reach 15 yrs. In The United States and other industrialized countries, a TFR of  2.1 is considered to be replacement level (more than 2.0 to allow for childhood mortality).

Doubling time:

Doubling time is the number of years it will take to double the present population given its present rate of growth. This time is approximated by dividing "70" by the percent rate of increase. For example, at a rate of growth of 0.5% it would take 140 years to double the population of The United States (i.e. 70/0.5 = 140). Guatemala would double its population in 70/2.9 = 24 yrs!

This calculation is only approximate and is used as a rough guide in comparing population change. One crucial assumption in the method is that growth starts at the rate given and remains unchanged throughout the time period (so, it is open-ended exponential growth and not complete logistical S-shaped change). 

Survivorship curve:

Survivorship curves keep track of the fate of any given birth cohort. They show the percent still living at a given age. Nowadays in the developed world few children die before reproduction. In The United States in 1998 only 1% of all children born alive died by the age of five (compared to 6.7% in Guatemala). However, 300 years ago it was quite a different matter, as the graph below illustrates. In the City of York (England) in the 17th. Century, fully 60% had died (graph shows about 40% survival), and only 30% made it to the threshold of reproduction (15 yrs.). Only 20% remained alive by the age of twenty. With so few females living to reproduction, only a high fertility rate could maintain the population.

Upper curve: Late 20th.C. developed country.
Middle Curve: 19th. C. developed country/20th.C. less developed country.
Lower Curve: City of York (England), 16-17th.C.

Population pyramid:

A bar chart that shows the age and sex distribution of members of a  population. The age divisions are referred to as "cohorts" and may be in 5 or 10 year increments, depending on the level of detail desired. By convention, females are always plotted to the right, males to the left. The units across the base may be either absolute numbers or percent of the population.

Population momentum:

Population momentum refers to the  tendency for population growth to continue beyond the time that replacement-level fertility has been achieved because of a highly relatively high concentration of people in the childbearing years. Population momentum occurs towards the end of Stage Three of the Demographic Transition.

This growth can be seen on the diagrams below to be due to a large, younger generation (the product of Stage Two growth) replacing a smaller, older generation. But note that this requires 50-60 years to happen -- therefore substantial growth continues even after replacement fertility has been attained. Once momentum has stopped then births (additions at the base of the pyramid) equal deaths (losses primarily at the top of the pyramid) and growth ceases. We are then truly in Stage Four of the Demographic Transition.