Life Table Example: Stable Age Distribution
 
Age: 

(yr.) 

x

 No. Alive: 

nx

 Proportion surviving to start of age x: 

lx

 Fecundity: 

  

bx

   

  

lx bx
         
0 1000 1.0 0 0
1 500 0.5 1 .5
2 250 0.25 2 .5
3 125 0.125 1 .125
4 0 0.0 0 0
  S lxbx=NRR=R0=1.125 / gen (population increases 12.5% per generation)
Generation time » 1.667 yr
r = ln(R0)/G » ln(1.125)/1.667 = 0.07067 / yr
l = Nt+1/Nt = er » 1.07323  (population increases 7.3% per year)
  Population dynamics:
 
Time n0 n1 n2 n3 N=S n Nt/Nt-1
             
0 100 0 0 0 100 --
1 50 50 0 0 100 1.0
2 75 25 25 0 125 1.25
3 75 37.5 12.5 12.5 137.5 1.1
4 81.3 37.5 18.8 6.2 143 1.04
5 87.7 40.7 18.8 9.4 156.6 1.095
6 93.8 43.8 20.3 9.4 167.3 1.068
7 100.9 46.9 21.9 10.2 179.9 1.075
8 108.2 50.4 23.4 11.0 193 1.073
9 116.2 54.1 25.2 11.7 207.5 1.075
etc. etc. etc. etc. etc. etc. etc.
             
Proportion of pop. in each age-class=ni/N .56 .26 .12 .057   Growth rate converges on:
l = 1.074 / yr
or
r=.0714 / yr
 

1) Stable Age Distribution occurs after only a few generations.

2) Once SAD is achieved, the population grows at a constant rate (and you can apply the exponential growth model). Each age-class grows at this same rate, which is why the SAD is maintained.