As children, our earliest steps forward in awareness take us into demography, as we number our birthdays, put numbers on the ages of people around us, number the others in our family, our town, our country, and our planet, as we learn that the years we will have to live are numbered.

As adults, we cope with a world whose problems and opportunities are shaped by demography. Low growth rates and high growth rates form the backdrop to the contrasts between rich nations and poor nations, peace and conflict, environmental protection and degradation that form the stuff of each evening’s...

The most basic demographic equation is the “Balancing Equation”. The Balancing Equation for the world as a whole from 2010 to 2011 takes the form

K(2010) +B(2010) −D(2010) =K(2011)

Here,K(2010) is the world population at the start of 2010,B(2010) are the birthsduring2010,D(2010) are the deaths during 2010, andK(2011) is the population at the start of 2011. The letter “K” is traditionally used for population instead of “P”, to avoid confusion with probability, which also starts with p. Estimated values for the numbers that go into the balancing equation for 2010 are...

We have managed to develop our model for exponential population growth with no reference to the most important word in demography, the wordage. In effect, the exponential model treats all people as if they were alike. As we shall see, it can be expanded into a model formulated in the language of probability theory in which all members of a population have identical constant risks of dying or of producing offspring without reference to sex or age. But of course in any real population, even one for which the exponential model gives a good approximation of population growth, the...

We begin our study of mortality by focussing on cohorts. We look at the lifelines and the deaths that occur in the diagonal stripe on the Lexis diagram that represents a particular cohort’s experience, and we introduce measures of survival and probabilities of dying as a function of age for the cohort. We could, instead, look at the rectangle on a Lexis diagram that represents some period and consider the lifelines that cross the rectangle and the deaths that fall inside it. That is more complicated, because in that case the people at risk of dying at different ages are...

In our studies so far we have dwelt mainly on the beginning and ending of lifelines on a Lexis diagram, on the start of life when one is born into a cohort and on the end of life when one takes one’s exit by dying. Indeed, on our Lexis diagrams we have been marking nothing at all along the lifeline, as if nothing happened in between. It is reminiscent of a modern poem in which the poet thinks of her father and the inscription on his tombstone: a date of birth, a date of death, and nothing in between but...

Transition matrices are tables used for population projection. Official presentations of projections are often filled with disclaimers cautioning the reader that projections are not predictions. They do not tell us what the worldwillbe like but only what the worldwouldbe like if a particular set of stated assumptions about future vital rates turned out to be true. The assumptions may or may not bear any relation to what actually happens.

Such disclaimers are disingenuous. Projection is not just a game with computers and pieces of paper. We do projections for a purpose, and that purpose is to...

It is now time to take an important step forward in the kinds of measures that we calculate. Up to now, we have been studyingcohortmeasures like theNRRand the expectation of life at birth, based on observations of the life experience of cohorts. Now, we shall consider how to calculate versions of these measures based onperioddata. Alongside a “cohortNRR” we shall have a “periodNRR”. Alongside a “cohort lifetable” we shall have a “period lifetable”.

The concepts of all these measures are fundamentally cohort concepts. They describe features of the life course of individuals....

Our approach to building period lifetables is essentially the same as our approach to period fertility measures. We make the assumption that the age-specific rates for the period continue unchanged into the future. We work out the lifetable that an imaginary cohort of newborn babies would experience under this idealized, neutral assumption about the future. This imaginary cohort is oursynthetic cohort.

With fertility measures, the age-specific rates enter directly into the calculations, and we simply substitute the period rates for the cohort rates in the formulas. The situation with lifetables is a bit more challenging, because we have not...

Most of the methods in earlier chapters have been applied to one population at a time with interest in one outcome at a time. We take, for example, a cohort of men or of women, making no distinctions among the different cohort members, and we study the outcome “death”, making no distinction among different kinds of deaths. Or we take women of a given age and study the outcome of next childbirth, making no distinction among different women and no distinction among different kinds of births. We assume a homogeneous population and a homogeneous outcome. When data are plentiful, we...

Marriage is full of complexities, not only for humans who enter into it, but also for demographers who study it. Not all models of population growth and change include marriage as a component. There is no explicit mention of marriage in the Balancing Equation. But marriage enters implicitly into all models through its impacts on other processes. Marriage obviously affects fertility, initiating exposure to significant risks of childbearing for many. Marriage also affects mortality. Married people live longer than nonmarried and never-married people. It remains a question whether this effect occurs primarily because marriage enhances chances of survival by providing...

We turn now to the study of age structure. There is a very full and satisfactory theory which accounts for the relative numbers of young and old men and women in a population. The basic idea is to obtain formulas for how a population will be distributed by age if the population has been closed to migration and if its birth and death rates have been unchanging for a long time. The actual age distribution of the population naturally differs from this theoretical age distribution. Each of the deviations is explained by reference to particular events of migration and particular...

People are found in places and move from place to place. All the processes we have been studying occur within space as well as across age and time. In this chapter we turn to methods of spatial demography. We leave behind the fiction of closed populations. In open populations, people enter and exit not just by being born and dying but also by crossing borders or changing categories of legal status. Migration across borders is a major component of population growth in many countries, especially the United States, influencing population composition, politics, economics, and social harmony. Great migrations are part...

In this book we have only been able to focus on the most essential demographic methods. What we have covered provides a foundation for studying other fascinating areas. Stable population theory has many further ramifications. Newer work in mathematical demography, not yet comprehensively treated in textbook form, includes random population models, population feedback and homeostatic control, and models with population, economy, and environment intertwined.

In the last few years, active collaboration between demographers, biologists, and geneticists has led to the new field of “Biodemography”. Careful measurement and modeling of old-age mortality for nonhuman species as well as humans are leading...