Life Tables and Demographics

Table 1 shows an example life table for the barnacle, Balanus glandula. Unlike most animals, barnacles are sessile as adults (they remain plastered down in a single place and do not move). This makes them easy to follow over long periods of time. During the first year researchers mapped out the distribution of 142 animals on a rocky coastline. They then return to the site for nine years and determined which individuals died (any missing from the map were known dead since barnacles cannot move as adults. Their data are shown below. 

• The first column (x) is the age of the animals in years. Depending on the beast, this may change. Mice, for example, may be better followed on a monthly basis, while long-lived animals (such as ourselves, crocodiles, and turtles) may be better followed in five-year intervals.
• The observed number of alive (n_x) is the actual number of barnacles counted each year (x). The researchers used half-counts during years 4 and 6 since they determined that the animals recently died (within the past week). They could determine this since there were "scars" still visible at the map positions of the individuals.
• The third column (l_x) is the number of surviving individuals adjusted to a standard population size of 1000. The value at 1 year is calculated as the current n_x divided by the original population size, then multiplied by 1000. For example, year 1 is (62/142)*1000 while year 2 is (34/142)*1000. The values are rounded to the nearest whole number.
• The number dying (d_x) represents the change in population size from year x to year x+1. The number dying during year 0 is 1000-437=563. For year 1 the number dying is 437-239=198.
• The mortality rate (q_x) is calculated by dividing the current year’s d_x by the current year’s l_x. For year 0, 563/1000=0.563. For year 1 the mortality rate is 198/437=.453.
• The average number alive during any particular year (L_x; don’t confuse with the number surviving) is calculated by adding together l_x +l_x+1 and dividing by 2. Thus, for year 0 the average number alive is (1000+437)/2=718.5! For year 1: (437+239)/2=338.
• The seventh  column (T_x) is an intermediate value for calculating the life expectancy. It is calculated by cumulatively adding the L_x values from the bottom up. Thus, for year 8, T₈= L₈+L₉ (T₈=0+7=7). For year 7, , T₇= L₇+L₈ (T₈=14+7=21).
• The life expectancy (e_x) is the average life expectancy of barnacles of age x in barnacle-years. It is calculated by dividing T_x by l_x. For year 0, the average barnacle is expected to live for only another 1.577 years (1577/1000). If they survive the first year, their life expectancy is an additional 1.9 years (858.5/437). Note that once the animals get past the first few years, the ones that survive get to live for a longer time.
• The last column is used to calculate a survivorship curve. It is simply the log of the number surviving (log(l_x)). The graph for the above data is shown in figure 5.:

A live calculation worksheet in Excel format can for the Balanus population can be found here. A further discussion on life tables is at this link. The human life table assignment is here!