Life tables are used to describe and understand the population dynamics of a species. This information is important in conservation studies (reintroduction of species), agriculture (reduction of pest species), and human health (following epidemics). Using reintroduction of a species as an example, life tables can indicate when a breeding population has been established.

There are two types of life tables, based on the method of data collection. Age-specific life tables are based on the fate of a real cohort (group of individuals). Group members belong to the same generation and the population may be either stable or fluctuating. Age specific life tables are also known as horizontal or cohort life tables.

Time-specific life tables are based on an imaginary cohort. Researchers collect data and determine age structure at a point in time. The population is assumed to be stationary. Time-specific life tables are also known as vertical or static life tables.

Calculations

Table 1. Life Table for a Barnacle population.

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 1.:

Figure1. Survivorship curve for Balanus glandula

Figure 2. The three types of survivorship curves.

There are three possible types of survivorship curves (Figure 2). A type I survivorship curve is characterized by having most of the mortality among the older individuals. A type II curve has a constant rate of mortality, while a type III curve has most of the mortality among the young. Humans in developed nations have a type I curve. Most birds are type II. Fish, insects, many marine invertebrates, and parasites are characterized by a type III curve.

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.
• Pyramids and population demographics are here.

Human Life Table

Human Life Table Assignment

You can get a Word copy of this laboratory here. For this exercise you will create human life tables using both historical and current data. Current data is collected from the obituary section of the Louisville Courier Journal. You can find back issues of the Courier at the library. As you collect your data (working backwards through the obituaries), record the age and sex of the person that died. You will need 100 males and 100 females for your study. If you cannot tell the gender of the person from their name, skip them. Group your data into five-year age categories (0-4yr, 5-9yr, etc.). For each age category you will have a count of the number of people that died.

Now for the fun part! Historical data is collected from a local cemetery that dates back at least 100 years (such as the Cave Hill Cemetery). Remember to check the closing time for the cemetery; we’ve had students locked in several years ago (before they put the razor wire up on the fence. Starting in 1900, collect age at death and gender data for 100 males and 100 females as before. Group your data into five-year age categories.

Optional Data Set: If you'd rather not collect historical data, and would rather collect data on a third-world country, please feel free to do so. Also, if you want, you can use the Internet to collect either of your databases.

Calculations

An Excel-based worksheet for the human life table assignment can be found here.  A widget for doing the same calculations over the internet is here (use whichever you are most comfortable with). Enter your data in either the second or the third column. The spreadsheet will calculate the life table for you. Enter separate data for recent males and females and historical deaths separated by sex (you’ll have 4 spreadsheets). Print out your results. You can save your spreadsheets to your local drive or to a floppy disk. You can not save to the server.

Report

1. Compare and contrast the survival curves and life table data between males and females. Do this for both the historical data and recent deaths. Are the any differences either historically or recently between the sexes?
2. Compare survivorship curves and life table data for recent male deaths as compared to historical deaths of males. Do the same for females.
3. Did you notice a "blip" in the historical data for 1918-1919? What caused this "blip" (a clue is found here. More is here).
4. What type of survivorship curve is seen for the human data? Under what conditions would you expect to see a type I or type II curve for a human population? What type of survivorship is shown in the barnacle?
5. Run the demographics simulator found here. Only pay attention to the lower pyramid graph (current birth rate).. Some explanations from the simulations are shown below. You can keep both windows open as you run the simulation. Also, check out this discussion on HIV/AIDS covered in this simulation. Run through several countries comparing industrialized and third world. Include some countries where AIDS is at epidemic levels.

Explanation for the graph.

• Males are on the left; females on the right. Note the differences in the proportion of males and females in the population; especially when we get older (look at the 80-90 cohorts).

• Age groups are in intervals of 5 years. The beginning of this simulation begins at age 0-5, after five years these first newborns and toddlers are now in the 5-10 age group.

• "Children" is the average number of offspring per female. As usual, only the female part of the population matters and males can be safely ignored (just like real life). The replacement rate for industrialized countries is about 2.1 children per woman.

• The lighter blue and pink bars represent the current distribution of the population (at the start of the simulation. Note the bulge between 30-50. This age group is part of the baby boom. The simulation runs for 100 years (until the 0-5 cohort reaches the top of the graph)

• The darker blue and red represent the male and female distributions 100 years from now. Note that we expect more older people in the population as compared to middle-aged persons in today's population.

• Magenta bars at the top are the 85-90 year old survivors from today's 0-5 age group.

• The lighter magenta are the children of today's 0-5 age group.

Example Demographics

• USA

  • From the lighter colors note that today's population is mostly composed of of people aged 0-around 50. Starting at 50, people start dieing (so, I guess I'm on schedule ). Therefore, a large percentage of the population can support people over 65.

  • The projected population demographics for 2100 shows that there will be a far greater number of people surviving after age 50. This is mainly because the replacement rate is near to 2.1 children per woman.

• Italy

  • Already, Italy had a bulge above the 0-20 year olds.

  • That's only exasperated 100 years from now. Note that the number of children per female is well below the replacement rate of 2.1.

• China

  • Today's population is composed mainly of younger people.

  • The future population is even more inverted much like Italy. Note the replacement rate.

• India

  • Compare today's Indian demographics to that of current USA. Notice the greater proportion of younger people.

  • Even though the number of children per female is larger than that in the US, the future population is not as evenly distributed as ours. This is because they are starting with a greater proportion of young people.