Constructing Life Tables
Objectives:
Construct a life table for humans based on data gathered from a local cemetery. Calculate a survivorship curve.
Background Information:
A life table shows for each person, at each age, what the probability is that they will die before their next birthday. You will use the date of birth and date of death on each gravestone to calculate the age of each person at death. This can then be used to construct a life table and then calculate a survivorship curve. Survivorship curves are used to show what percent of the population we expect to live to a certain age. These are used to calculate things such as average life expectancy of humans.
Questions About Survivorship Curves
There are a variety of questions that we might examine with life table data. The most obvious question that can be asked is whether the survival curves of males and females are the same or different. Evolutionary theory allows us to predict which sex should have a survival advantage. Reproduction in humans is thought to be much more costly for females because they have to carry their babies through pregnancy and then go through a period of lactation when they produce energetically expensive milk. So females of childbearing age (roughly from 1520 to 4550) should suffer higher mortality (and thus lower survival) than males of similar age. Social or political influences may also cause sexual differences in survival curves. For example, some cemeteries date back to the Civil War, and World Wars I and II. During a war, mortality should be higher and thus survival curves lower, especially for men due to the historical bias against women for combat assignments.
Another question that we might ask about lifetable from local cemeteries is whether different historical periods have had different survival curves. For example, over the past hundred years there has been a dramatic increase in the average life expectancy of an adult in western societies because of improved health attention, health care, and medical services. We should expect to see an increase in survival curves over historical time. The "health care" hypothesis predicts that cemeteries with older mean ages should have lower survival curves. So, in all, we have three hypotheses that we should be able to discriminate by their different predictions. And you should be able to think of more hypotheses.
Methods
We will take you to a cemetery where we will gather data on the birth of individuals for two time periods, 18401849 and 18501899. Work in groups of about two students. One of you can record the data, and the other can work with a calculator to find out how old each individual was when they died. The lab groups should divide up the area of the cemetery so that all areas are sampled, but none are sampled more than once. Be sure to keep a running tally of: sex of the individual, age at death, and year of birth. To determine sex, examine the individual's name. Some names are obviously male or female. For names that could be either (e.g., Leslie), keep an "unknown sex" category. Work as quickly as you can, but also be careful to show respect for where you are. Do not walk across graves! Stick to the pathways.
Data Analysis
Back in the lab we will use this information to construct an age pyramid for 1876, allowing us to characterize the population. Total up the number of deaths at each age class for everyone in your lab for the two different time periods. Remember to keep the sexes separate. Then total the number of individuals in your "male" and "female" samples. The number of individuals in each age class may be plotted as a histogram, forming a "pyramid." Age is placed on the vertical axis and the number, or the proportion, of individuals in each age class is plotted that a symmetrical, pyramidal graph results. Age pyramids such as these are useful for comparing populations from different sites, or the same population at different times of the year or from year to year. Construct an age pyramid for the year 1876. Do this by:
Table 1. Number of males and females in each age class for 1876.

# of males 
# of females 
% males 
% Females 
09 
1 
1 
2.5 
2.5 
1019 
2 
3 
5 
7.5 
2029 
1 
2 
2.5 
5 
3039 
1 
1 
2.5 
2.5 
4049 
3 
3 
7.5 
7.5 
5059 
6 
4 
15 
10 
6069 
5 
6 
12.5 
15 
7079 
0 
1 
0 
2.5 
8089 
0 
0 
0 
0 
90+ 
0 
0 
0 
0 
Total 
19 
21 


Grand total 
40 


Figure 1. Age structure diagram of Austin population in 1876. Data collected
from tombstones in Oakwood Cemetery, Austin, Texas.
Next construct a life table for both males and females living during the
year 1876. You may choose to create these tables using MS Excel. An example
follows:
Table 2. A life table for males living in 1876 and buried in Oak Wood Cemetery, Austin, Texas. 


In a life table (Table 2), various statistics are compiled for each age class, or cohort (designated as x). Data are commonly collected as numbers of individuals in each age class. L_{x} is the number of individuals in age class x. It is assumed that L_{x} is the number alive at the middle of age class x (for example, in the above table, 33 individuals are assumed to be 5 years old, even though the true ages of the 33 might range between 0 and 10 years old).
We designate l_{x} as the number of individuals alive at the beginning of age class x. Thus, L_{x} may be defined as
L_{x} = ( l_{x} + l_{x+1})/2 and,
l_{x} = 2L_{x}  l_{x+1}
For example, in Table 2, L_{0} = 33, L_{1} = 16, L_{2} = 9, L_{3} = 4, L_{4} = 1, L_{5} = 0.
Since L_{5} = 0, we can set l_{5} = 0. Then by applying the above equation,
l_{5} = 0
l_{4} = 2(1)  0 = 2
l_{3} = 2(4)  2 = 8  2 = 6
l_{2} = 2(9)  6 = 18  6 = 12
l_{1} = 2(16)  12 = 32  12 = 20
l_{0} = 2(33)  20 = 66  20 = 46.
The number of individuals in the population that die during interval x is:
d_{x} = l_{x}  l_{x+1}
Note that the sum of the_{ }d_{x} values must equal l_{0}; in our example 46.
The agespecific mortality rate (q_{x}) is the proportion of individuals at the start of age interval x who die during that age interval:
q_{x} = d_{x} / l_{x}
also expressed as the probability of an individual dying during the interval. The agespecific survival rate (s_{x}) for age interval x is the proportion of individuals alive at the start of the interval who do not die during the interval period. In other words, s_{x} is the probability of surviving age interval x:
s_{x} = 1  q_{x}
We can calculate agespecific life expectancy (commonly done for human populations) as follows. Let us define T_{x }as the number of time units left for all individuals to live from age x onward; this is obtained by summing L_{x} values as follows:
T_{x }= L_{x }+ T_{x+1}
and expressing T_{x} in time units; so
T_{4 }= L_{4} = 1
yr
T_{3 }= L_{3} + T_{4 }= 4 + 1 = 5 yr
T_{2 }= L_{2} + T_{3 }= 9 + 5 = 14 yr
T_{1 }= L_{1} + T_{2 }= 16 + 14 = 30 yr
T_{0 }= L_{0} + T_{1 }= 33 + 30 = 63 yr
Then, the life expectancy for an individual of age x is
e_{x} = T_{x}/l_{x}
Life expectancy represents the average additional length of time that an individual will live, once it has reached age x. To compare different populations, the numbers dying (d_{x}) or surviving (l_{x}) are often expressed as number per 100 or per 1000 individuals entering the population at age 0; that is l_{0} is set to 100 or 1000, and all other lifetable entries are expressed relative to this value. For the example in our table, we have l_{0} = 46 and l_{1} = 20. If we set l_{0} = 100, then we would have an l_{1} value of (20/46)(100) = 43.5. In other words, for every 100 individuals born into the population, 43.5 survive to age 1.
Various types of graphs may be constructed from life table data, including mortality rate curves, life expectancy curves and survivorship curves. Most widely used among ecologists, the survivorship curve is prepared by plotting the of the number of survivors against age (sometimes this done on semilogarithmic paper). From this graphical presentation, three basic types of curves are recognizable, as discussed in lecture.
We will construct percentage survivorship curves by age for both males and
females living during each of the two time periods, 18001849 and 18501899.
Using the data sheet for the survivorship, determine the number surviving to
each age for males and females. Calculate the age class, number that died,
percent surviving. Using these data, plot the survivorship curve for each
gender (male or female) for each time period. What can you say about survival
and life expectancies during these two time periods?
To calculate percentage survivorship by age:
Calculate cumulative number of dead at each age class from total # of
individuals counted for each gender (male or female).
Example:
Total # females counted in survey = 1000.
Total deaths before age 10 = 50.
For age class #1 (0  9 years), total percent surviving 1000  50 = 950/1000 =
95%.
Total deaths in 1019 age class = 50.
For age class #2, total percent surviving:
Subtract Age class 1 (50 deaths) + Age class 2 (50 deaths) from total no. of
individuals counted: 1000  100 =900 (or 90%).
Example:

Figure 2. Survivorship curve for females living between 18001849.

18001849 
% 


Age Limit at Death 
Questions
1. Take a close look at your survivorship curves. How might you explain their general form or appearance? Are factors in the ecological or social environment important to the shape of survivorship curves?
2. Are there "wiggles" in your survivorship curves? What sorts of factors, real or artifact, might cause variations in survival schedules? How would you go about testing the influence of such factors.