WLF 448: Fish & Wildlife Population Ecology
Lecture Notes IV, Fall 1996

 

Mean Expectation of Life:

Data from Quick, H. F. 1974. Population Ecology. Pegasus Books, Indianapolis. Appendix B, pp. 192-185.

x dx d'x lx qx Lx ex
1 5 333 1000 0.333 833.5 1.83
2 4 267 667 0.400 533.5 1.48
3 3 201 400 0.505 299.5 1.16
4 2 133 199 0.669 132.5 0.84
5 1 66 66 1.000 33.00 0.50

Calculating Mean Expectation of Life

To calculate ex, first an auxiliary column, Lx, must be derived from the 1x column. Lx is a symbol for expressing animal-years lived, and is used for estimating how much longer an animal can be expected to live if it reaches a particular age. Similar to saying “so many animals lives so many years,” or something like man-hours worked.

The figures in this column are obtained by adding the number of survivors shown in the lx column for two successive age classes, and dividing by 2. Thus, 1000 +667 ÷ 2 = 833.5 animal-years, on the average, were lived during the first year of life by the cohort of 1000 that began life together. In other words, 1000 began life in the first year, but only 667 finished the full year. Since there is no age class after the last one, a zero is assumed because the census did not find animals alive after that age. In this example, then, 66 is averaged with 0, and 33 is entered as the average number of survivors of this last age to live halfway through this time period.

After the L values are obtained, we can obtain the mean expectation of life (ex). Before a mean expectation of life can be calculated for a cohort, the last member must live out its life span in order to show how many animal-years this last member contributed to the overall average life span of the whole cohort. Therefore, the expectation of further life for a particular age class depends on the whole life history of the cohort to follow this particular age class. Therefore, calculations begin from the bottom of the L column and work up to each successive age class until ex for the youngest cohort is computed.

ex = (Ln + all L's up to a given age x) ÷ lx , where n = oldest age class

Example:

e3 = (L5 + L4 + L3) ÷ l3 = (33.0 + 132.5 + 299.5) / 400 = 1.16 years

Return to Lecture Notes IV. Estimation of Population Parameters - II.

 

Updated 29 July 1996