An 
table is a tabulation of numbers which is used to calculate life expectancies.
 |  |  |  |  |  |  |  |
| 0 | 1000 | 200 | 1.00 | 0.20 | 0.90 | 2.70 | 2.70 |
| 1 | 800 | 100 | 0.80 | 0.12 | 0.75 | 1.80 | 2.25 |
| 2 | 700 | 200 | 0.70 | 0.29 | 0.60 | 1.05 | 1.50 |
| 3 | 500 | 300 | 0.50 | 0.60 | 0.35 | 0.45 | 0.90 |
| 4 | 200 | 200 | 0.20 | 1.00 | 0.10 | 0.10 | 0.50 |
| 5 | 0 | 0 | 0.00 | -- | 0.00 | 0.00 | -- |
 | 1000 | 2.70 |
: Age category (
, 1, ..., 
). These values can be in any convenient units, but must be
chosen so that no observed lifespan extends past category 
.
: Census size, defined as the number
of individuals in the study population who survive to the beginning of age category
. Therefore, 
(the total population size) and 
.
: 
; 
. Crude death rate, which measures the number
of individuals who die within age category 
.
: 
. Survivorship, which measures the proportion
of individuals who survive to the beginning of age category 
.
: 
; 
. Proportional death rate, or "risk," which
measures the proportion of individuals surviving to the beginning of age category
who die within that category.
: 
. Midpoint survivorship, which measures the
proportion of individuals surviving to the midpoint of age category 
. Note that the simple averaging formula must be replaced by
a more complicated expression if survivorship is nonlinear within age categories.
The sum 
gives the total number of age categories lived by the entire study population.
: 
; 
. Measures the total number of age categories
left to be lived by all individuals who survive to the beginning of age category
.
: 
; 
. Life expectancy, which is the mean number of age
categories remaining until death for individuals surviving to the beginning of age
category 
.
For all 
,
. This means that the
total expected lifespan increases monotonically. For instance, in the table above,
the one-year-olds have an average age at death of 
, compared to 2.70 for newborns. In effect, the age
of death of older individuals is a distribution conditioned on the fact that they
have survived to their present age.
It is common to study survivorship as a semilog plot of 
vs. 
, known as a survivorship
curve. A so-called 
table can be used to calculate the mean generation time of a population. Two 
tables are illustrated below.
Population 1
 |  |  |  |  |
| 0 | 1.00 | 0.00 | 0.00 | 0.00 |
| 1 | 0.70 | 0.50 | 0.35 | 0.35 |
| 2 | 0.50 | 1.50 | 0.75 | 1.50 |
| 3 | 0.20 | 0.00 | 0.00 | 0.00 |
| 4 | 0.00 | 0.00 | 0.00 | 0.00 |
 |  |
 |  |  |
(1)
|
 |  |  |
(2)
|
Population 2
 |  |  |  |  |
| 0 | 1.00 | 0.00 | 0.00 | 0.00 |
| 1 | 0.70 | 0.00 | 0.00 | 0.00 |
| 2 | 0.50 | 2.00 | 1.00 | 2.00 |
| 3 | 0.20 | 0.50 | 0.10 | 0.30 |
| 4 | 0.00 | 0.00 | 0.00 | 0.00 |
 |  |
 |  |  |
(3)
|
 |  |  |
(4)
|
: Age category (
, 1, ..., 
). These values can be in any convenient units, but must be
chosen so that no observed lifespan extends past category 
(as in an 
table).
: 
. Survivorship, which measures the proportion
of individuals who survive to the beginning of age category 
(as in an 
table).
: The average number of offspring produced
by an individual in age category 
while in that age category. 
therefore represents the average lifetime number
of offspring produced by an individual of maximum lifespan.
: The average number of offspring
produced by an individual within age category 
weighted by the probability of surviving to the beginning
of that age category. 
therefore represents the average lifetime number of offspring produced by a member
of the study population. It is called the net reproductive rate per generation and
is often denoted 
.
: A column weighting the offspring
counted in the previous column by their parents' age when they were born. Therefore,
the ratio 
is the mean generation time of the population.
The Malthusian parameter 
measures the reproductive rate per unit time and can be calculated
as 
.
For an exponentially increasing population, the population size 
at time 
is then given by
 |
(5)
|
In the above two tables, the populations have identical reproductive rates of 
. However, the shift toward later
reproduction in population 2 increases the generation time, thus slowing the rate
of population growth. Often, a slight delay
of reproduction decreases population growth
more strongly than does even a fairly large reduction in reproductive rate.
