Population Dynamics

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POPULATION DYNAMICS

Population dynamics refer to the way in which the size and age structure of populations change over time and the characterization of that change in mathematical terms. This article is a basic introduction to the topic, largely avoiding the mathematics.

Population Growth/Decline

Population growth (or decline) is the net balance of births, deaths, in-migration and out-migration. If growth is assumed to occur on a discrete basis, usually annually, and if the rate of growth is constant, population size at a future time t, P(t), can be related to population size at time 0, P(0), by the geometricequation P(t) = (0)(1 + r)^t where is the rate of growth. In practice, demographic events are spread throughout the year so that growth is usually smooth enough to be described by a continuous variable over time. If the rate of growth is constant, P(t) can be related to (0) by the simple exponentialequation P(t) = (0)e^rt.

A convenient measure of population growth is doubling time, or the time that would be needed for population size to double at the current rate of growth. The doubling time is calculated by solving the above equation for in the case where P() = 2P(0). Hence the doubling time is the natural logarithm of 2 (about 0.693) divided by the rate of growth (equivalent to dividing 69.3 by the percentage rate of growth). For example, if the annual rate of growth is 2 percent, the doubling time is 69.3 ÷ 2 or just under 35 years. The higher the rate of growth, the shorter the doubling time.

Balance Equation

Changes in population size are a function of the three constituent components of population change: birth, death, and migration. Change is expressed in discrete terms by the balance equation:

P(t+1)–) = B, D+1) + I(t, +1)–O+1)

where B(t, +1) is the number of births occurring during the interval t to +1 (usually a year), and D, I, and O are corresponding numbers of deaths, inmigrants, and out-migrants. When age is taken into account, this equation expresses the changes occurring to cohorts (persons of the same age in years at time) alive at time. For example, the number of

children in the cohort aged 2 at time t+1 will be equal to the number aged 1 at t, minus deaths occurring to the cohort during the interval from t to +1, plus net migrants of the same age cohort arriving or departing during this interval (note that B is zero). These demographic accounting equations are used in assessing data quality, in estimating net migration, and, in populations closed to migration, as the basis for demographic estimation using indirect methods.

Age Structure

The age structure of a population is determined by the relative size of past successive cohorts at birth and subsequent changes in size because of death and migration. The numbers of births, deaths, and migrants in the present year (or other time interval) are determined by prevailing fertility, mortality, and migration rates and the existing age structure of the population, which in turn is a result of previous demographic rates and structures. Thus the present age structure is a function of current and past demographic rates–that is, of the population's demographic history. Past changes in demographic rates lead to changes in age structure over time.

Usually, the most significant factor in determining population structure is fertility and, in particular, changes in fertility over time. High-fertility populations are characterized by a population pyramid with a wide base relative to older ages, whereas lowfertility populations have a much narrower base. A rapid change in fertility, whether an increase or a decrease, can lead to dramatic changes in both population structure and growth. An example of such a change is the post–World War II increase and subsequent decrease in fertility in many Western countries, resulting in the period of large birth cohorts known as the "baby boom." A large birth cohort appears as a bulge that "ripples" through the population age structure toward older ages over time. As this cohort passes through the childbearing ages, it produces a secondary large birth cohort (large relative to adjacent cohorts and for given fertility rates), which will itself produce a further large cohort a generation later. The effect–sometimes described as an echo–is progressively dampened as a consequence of the wide age range of childbearing and gradually disappears. Thus, through the initial effect on population structure, an increase in fertility, even if temporary, affects population size and structure for many years into the future.

More permanent changes in fertility and changes in mortality and migration have similar effects. Age-and sex-specific effects caused by war, major epidemics, and large-scale migration can have a marked effect on population structure, with consequent effects on future births and hence on population growth and structure.

Population Momentum and Aging

The effect of age structure on population growth is referred to as population momentum. Even if fertility were to change immediately to the level that would just ensure the replacement of each generation (that is, a net reproduction rate of 1), the population would continue to grow (or decline) for as long as structural effects remain in force. Thus, for populations that experienced fertility declines from high levels to near replacement levels in the latter decades of the twentieth century, the age structures are such that substantial further growth will occur for many decades into the twenty-first century. (Momentum effects can also perpetuate population decline, despite a fertility increase, after a long period of below-replacement fertility. This has not yet been observed.)

A consequence of changing age structure is uneven growth across age groups. This is easily seen in the ripple effect of the baby boom. In many populations, past declines in fertility accompanied by increases in longevity have resulted in the aging of the population. An aging population experiences increases in the size of the older population (for example, persons aged 65 and over) relative to the total. In contrast, population rejuvenation occurs when the younger population (for example, persons aged 0 to 14) increases in relative size, normally because of falling infant and child mortality or increased fertility. Growth in the size of different age groups can be compared across ages and populations. For example, during the period from 1950 to 2000, the population of India aged 0 to 14 years increased by a factor of 2.5 compared with a factor of 3.8 for the population aged 65 and over, while the total population increased by a factor of 2.8. This compares with the more rapidly aging population of Singapore, which has corresponding factors of 2.1 at age 0 to 14,12.0 at age 65 and over, and 3.9 for the total population. By 2050, the populations aged 65 and over in India and Singapore are expected to have increased (since 1950) by factors of 18 and 55 respectively, compared with factors of only 4 or 5 for the total populations, illustrating both the magnitude of growth at this age and the wide variation between populations. The disparity is caused by the different speeds at which fertility declined and mortality improved in the two populations: rapidly in Singapore and only moderately in India.