Lotka's stable population equations (cont.)

Exercise

Interaction Chose the correct phrase on the left to describe what each of Lotka’s equations show:

  1. Lotka’s first equation  2. Lotka’s second equation  3. Lotka’s third equation 
A. Tells us how to calculate the crude birth rate in a stable population using our knowledge of its age structure
 
 
 
B. Suggests how the growth rate can be found if we know the fertility and mortality rates in the stable population
 
 
 
C. Shows us how to calculate the proportion of people by age in the stable population
 
 
 

Clear all

 

 

Reference table explaining notation

Interaction The table below is a reminder of what the algebraic symbols mean. Click on the button underneath it to open it on a pop up window. You can then keep it on your screen as a reference.

Symbol Meaning
r the stable population growth rate (the intrinsic growth rate)
t time, measured from a notional "base year" in which t=0
x age, when age is an integer it is understood to refer to age last birthday
n the size of the age group (when n=1 it may be omitted from the expression)
Wt total population at time t
Px,t the population aged x last birthday at time t
nPx,t the population in the age group  x to x+n at time t
Bt the number of births at time t
nBt the number of births in time t to t+n
nax the proportion aged x to x+n in the stable population
nLx person-years lived in the life table population between age x and x+n
lx proportion surviving to exact age x in the life table
w the last age to which anyone survives in the life table
b the crude birth rate in the stable population
fx age specific fertility rate at age x
nfx age specific fertility rate in the age group x to x+n
G mean length of the generation in the stable population
m used to denote various measures of mean age of fertility

Click to open on a pop up window external link