## Info

distribution when given a starting distribution and the intrinsic rate of increase of the population.

The steady-state age distribution is easily computed from mortality. A basis population must be assumed for the first age group, such as the number 1000 used for n0 in Table 14.6. Then successive age group populations are computed by rearranging equation (14.11):

The age distribution is often presented as a histogram, as in Figure 14.13. This can be compared to a steady-state life table histogram. Populations with relatively large numbers of young and of individuals of offspring-producing age will tend to be increasing.

To compute unsteady-state changes, the mortality is simply applied to each age group at time step j to find the population entering the next age group:

The population of the first age group is obtained from the natality of each population, bt:

Table 14.7 shows several generations that result based on the given starting population distribution and the life table in Table 14.6. Figure 14.14 is a plot of the total population over 45 generations of the organism.

Note the "baby boom'' caused by the large number of young in the starting population. Eventually, the oscillations die out as the population assumes a stable age distribution. This approximates the steady state because natality exceeds mortality and the population is growing. Note that the population distribution at 45 days is still not at steady state. In fact, steady state is never reached. This population is growing exponentially, because birth exceeds mortality.

When the oscillations die out, the total population, N, increases in a constant proportion, l, or geometrically, with each generation:

where Nt is the total population at time t and N0 is the initial population. If population growth can be assumed to be continuous, growth can be described by the familiar firstorder growth equation giving the rate of increase as being proportional to the current population:

dt where r is called the intrinsic rate of increase. This is a the rate of increase normalized by the population (dN/dt)/N. The case of equation (14.17) in which r has a constant value is the exponential growth rate model. Figure 14.13 Population histogram for three different growth scenarios. Kenya represents a country with a high growth rate, 2.5% per year. The U.S. growth rate is moderate, 1.0% per year. Italy is a country with a low growth rate, 0.3% per year, which is expected to begin to decline over the next several decades. Each bar represents a cohort of five years of age. (From U.S. Census Bureau, 2004.)

Figure 14.13 Population histogram for three different growth scenarios. Kenya represents a country with a high growth rate, 2.5% per year. The U.S. growth rate is moderate, 1.0% per year. Italy is a country with a low growth rate, 0.3% per year, which is expected to begin to decline over the next several decades. Each bar represents a cohort of five years of age. (From U.S. Census Bureau, 2004.)

TABLE 14.7 Population Distribution Changes Based on Life Table from Table 14.6°

i