This lab will require you to construct age-related population graphs from data collected at Hope Cemetery in Worcester. You simply need to collect data from 25 individuals who were alive in 1850, 25 individuals who were alive in 1900, and 25 individuals who were alive in 1950 (total of 75 individuals). You will need to record their first names, last names, year of birth, and year of death.

Use birth and death dates for people whose lives span the years 1850, 1900, or 1950.

1) You will then calculate the ages and determine the gender of those persons who were alive at each of the three specific time periods and plot population age distribution graphs for each of those three years. Use four-year intervals for each cohort (ie. 0-4, 5-8, 9-12 years old, etc.) to create each bar graph for each cohort and each gender of each cohort.

2) Second, you will plot a scatter plot of lifespan versus year of birth.

Answer the following questions:

3) How did age distributions in Worcester change between 1850 and 1950?
4) What pattern of life expectancy did you find?
5) Compare your data based on gender and time periods. Are the results similar or different? Why might those differences exist?
6) What underlying assumption(s) are we making regarding the individuals buried here in Worcester?

Life table
Populations have many intrinsic rates that characterize the population: birth rate, death rate, and rate of immigration and emigration.
It is often difficult to determine these rates. It usually involves following individually marked organisms through their natural lives and measuring the number of offspring produced by each organism until the death of the individual. It is often difficult to follow the individual if it is highly mobile or some of its behavior is cryptic.
To create a life table, we will use the data you (I) gathered from Hope Cemetery. The data will be available from the Blackboard website; click on the link entitled “Cemetery data”. I will have extracted the data for people born between 1900 and 1910 only to make the file more manageable and easier to work with.

7) How many people are in this sample?

This is the number living at the start of the first age class, l0.  Record the number in column 4, row 2 of Table 2.
Now we need to calculate the age at death of the people in our sample so create a new column in the spreadsheet and determine the age at death by subtracting the birth year from the death year.  Now sort the data by age at death.

8) How many people died at age 0?

This is the death rate for cohort age 0 (d0). Record the number in column 5, row 2 in Table 2.
We can calculate the number of individuals alive at the start of the second age class (l1) using the formula:
l1 = l0 – d0

Record this number in column four, row 3 of Table 2.
We can now calculate the number of individuals alive at the middle of age 0 using the equation
L0 = (l0 + l1)/2

Record this number in column 3, row 2 of Table 2.
Now we are ready to calculate the probability of dying during interval 0 (q0, also known as the age specific mortality for age 0).

q0 = d0/l0

Record this value in column 6, row 2 of Table 2.  Once we have the mortality rate, we can also calculate the survival rate of individuals in this age group (s0):

s0 = 1 – q0

Record this value in column 7, row 2.
Now repeat all of these equations for every age class in our sample.  To make things go quickly, create the life table in Excel.  Create the equations in the second row (first row should have the data labels).  Copy the equations and paste them down all of the columns.  Then, the only number you have to input is the number of people who died at that age for each row.  Excel will do the rest.  

9) Print the life table and attach it to this handout.

Age Cohort (Age Interval)
x Number in cohort
Lx Number living at the start of x
lx Number dying during x
dx Probability of dying during x
qx Probability of surviving interval x
sx
0-1 0
1-2 1

Table 2: Life table for a sample of humans born between 1910 and 1919 and buried in Hope Cemetery in Worcester, MA. (Continued in Excel)

Survival curve (Survivorship Curve)
Using the data in the life table, we can create a survival curve, which graphs the logarithm of number of survivors (lx) vs. age (x).
The survival curve for a species can take three general shapes, as depicted in figure 1. In type 1, there is a high survival rate of the young and low survival rate after a particular age. In type 2, the rate of death is constant for all ages. In Type 3, there is high juvenile mortality but relatively low mortality after a certain age.

Figure 1: Types of survival curves.

10) What type of curve do you think humans have? Do you think the shape of the curve has stayed the same or changed over the last century?

To create a survival curve for our data, create a new column in the life table and calculate the log of lx.  To create the survival curve, use the chart wizard to create an XY graph of log of number surviving (log lx) vs. age.  Be sure to label the x- and y-axis and title the graph.

11) Print the graph and attach it to this handout (It’s easier than it seems: simply plot # survivors versus age at death; you will start off with 100% of the cohort born in the 1900-1910 time interval and, as individuals die at certain ages, that number will go down and down until no one remains after the oldest individual to have lived)

12) Go to Blackboard and download the pdf’s for survivorship data from three locations:

  a)  Newberry, South Carolina (a southern rural town of about 10,000, collected by   an ecology class);
b)  Collegeville, Minnesota (The data are from 4 small cemeteries on the campuses of    St. John's University and the College of St. Benedict in central Minnesota. One data set    is from the local community, while the other is from the brothers and sisters of the    monastic communities. The second makes quite a contrast to usual cemetery data  because these people led a very different life style and were not born into their   communities.);
c)  Georgetown, Texas (These data were collected from a small cemetery by an    upper-level ecology class at Southwestern University).

The data available on Blackboard have been collected from local cemeteries by students in ecology courses from colleges and universities around the U.S. Each data set contains summarized data: for each decade of birth, there are the number of deaths by decade of age for both men and women. Some information is also given about the community from which the data were collected and the date of the data set.  Compare and contrast all of these data sets, and create survivorship curves for each data set to facilitate your answers to this comparative analysis.

EXTRA CREDIT: Provide me with complete data from gravestones of Alfred Madden Tracy, Caroline Tracy, Florence Clinton, or Frank Clinton (all relatives of Dr. Tracy born between 1850 and 1900). They all are buried in Hope Cemetery and their data (and images of headstones) all can be found online!