Demographics
Details

Data

The data for this module is from the US Census International Database. Generally, the data for year 2005 population and fertility is good, but mortality data is less recent.

Computation

The computations are pretty simple. The population is divided into "cohorts", or age groups, male and female. Each cohort has its own fertility and mortality rate (different for males and females.) The starting size of each cohort is a given. For each step:

  1. Alter the per-cohort fertility and mortality rates, if requested.
  2. Promote each cohort (age group) up a notch. Cohort 0 becomes empty. The eldest cohort is dropped (dies).
  3. Apply per-cohort fertility rate to each cohort of females to get the overall number of kids. Apply male-female ratio to divvy up the kids. Place them in cohort 0.
  4. Apply per-cohort mortality rate.
  5. Count. Update display.
Two calculations for the display merit mention:

  1. The "r" is the percent change in population per year. There are other ways to express the rate of change. This one is like the interest rate on a credit card.

  2. The number of children per woman per lifetime is:

    Where survivex is the fraction of women who survive from birth to enter cohort x, and fertilityx is the number of children per woman during her tenure in cohort x (5 years). Population growth per year is only loosely linked to number of children per lifetime.

The simulator provides three operations on the fertility and mortality rates (button Rates):

  1. Shift fertility age (years) Y over steps N :

    Means take the current reproductive schedule and shift it older by Y years. Do this over N simulation steps (each step is 5 years.) For example, if the fertility rate of cohort 3 (15-19 year olds) is 0.5, and we shift up 5 years over 1 step, the 20-24 year old fertility rate becomes 0.5 before calculating the population for year 2010 (the simulator starts at 2005).

    The shifting is actually rather complicated to do in practice. Details on request. Suffice it to note here that if you shift far down, all reproduction ends up in the cohort aged 10-14. Also, in each of the N steps, an integer number of years is shifted. If you enter a non-integer number of years, the simulator ignores the input.

  2. Change fertility rate (+- %) RR over steps N :

    Means take each fertility rate and add or subtract RR/N % of it for each of N steps. For example, if the fertility rate of cohort 5 were 1.0 (meaning on average there's one child for every woman aged 25-29), and you told the simulator to change the rate by -50 % over 2 steps, the rate at the first step would change to 0.75 children per female, and at the second step to 0.5 children per female.

  3. Change mortility rate (+- %) RR over steps N :

    Works the same as changing fertility rate. Operates on male and female mortality. Note that a decrease of -100% means no mortality until leaving the top cohort. Everybody still dies when they exit the top cohort. An increase of 100% means to double the mortality rate. Since each rate tends to be small, this has less effect than you might have guessed.

Ginger Booth, revised March 2005, orig. December 2000, for oswald.schmitz@yale.edu