  We introduce a population-age-time (PAT) model which describes the temporal
evolution of the population distribution in age. The surprising result is that
the qualitative nature of the population distribution dynamics is robust with
respect to the birth rate and death rate distributions in age, and initial
conditions. When the number of children born per woman is 2, the population
distribution approaches an asymptotically steady state of a kink shape; thus
the total population approaches a constant. When the number of children born
per woman is greater than 2, the total population increases without bound; and
when the number of children born per woman is less than 2, the total population
decreases to zero.
