Life Expectancy
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 chosenso that no observed lifespan extends past category 
. - : Census size, defined as the number of individuals in the study population who survive to thebeginning of age category . Therefore,
(the total population size) and 
. - :
; 
. Crude death rate, which measures the number of individualswho die within age category . - :
. Survivorship, which measures the proportion of individuals who survive to thebeginning of age category . - :
; 
. Proportional death rate, or ``risk,'' which measures the proportion ofindividuals surviving to the beginning of age category who die within that category. - :
. Midpoint survivorship, which measures the proportion of individualssurviving to the midpoint of age category . Note that the simple averaging formula must be replacedby a more complicated expression if survivorship is nonlinear within age categories. Thesum 
gives the total number of age categories lived by the entire study population. - :
; 
. Measures the total number of age categories left to belived 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 survivedto 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.
| |  | |  |
| 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 |
 |  |
 |  |  | |
 | |  |
| | | | |
| 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 |
|  |
| |  | |
| |  |
- : Age category (, 1, ..., ). These values can be in any convenient units, but must be chosenso that no observed lifespan extends past category (as in an table).
- : . Survivorship, which measures the proportion of individuals who survive to thebeginning of age category (as in an table).
- : The average number of offspring produced by an individual in age category while in that agecategory.
therefore represents the average lifetime number of offspring produced by anindividual 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.
thereforerepresents the average lifetime number of offspring produced by a member of the study population. It is calledthe net reproductive rate per generation and is often denoted 
. - : A column weighting the offspring counted in the previous column by their parents' age when theywere 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 givenby
In the above two tables, the populations have identical reproductive rates of
. However, the shift towardlater 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 fairlylarge reduction in reproductive rate.See also Gompertz Curve, Logistic Growth Curve, Makeham Curve,Malthusian Parameter, Population Growth, Survivorship Curve- Pyramidal Frustum
- Pyramidal Number
- Pyritohedron
- Pythagoras's Constant
- Pythagoras's Theorem
- Pythagoras Tree
- Pythagorean Fraction
- Pythagorean Quadruple
- Pythagorean Square Puzzle
- Pythagorean Theorem
- Pythagorean Triad
- Pythagorean Triangle
- Pythagorean Triple
- Pépin's Test
- Pépin's Theorem
- Pólya-Burnside Lemma
- Pólya Conjecture
- Pólya Distribution
- Pólya Enumeration Theorem
- Pólya Polynomial
- Pólya's Random Walk Constants
- Pólya-Vinogradov Inequality
- Pósa's Theorem
- Q
- q-Analog