BY 450 - ECOLOGY



BY 450 - ECOLOGY SPRING 2005

LABORATORY EXERCISE

INTRODUCTION TO LIFE TABLES

In this lab, we will construct life tables using demographic data. You will use demographic data compiled from human birth and death rates on cemetery headstones to estimate survivorship rates in human populations and construct a life table similar to the ones we have discussed in class. You should realize that this is a highly artificial situation. In normal populations, we would estimate survivorship using information about age structure, age at death, etc. Most organisms don’t have headstones.

Use this information to complete the life table.

Recall that:

ax = the total number of individuals observed in the population in stage x.

lx = survivorship to stage x.

dx = proportion of the original cohort dying during stage x.

qx = mortality rate for individuals in stage x.

kx = killing power of stage x (log10 ax – log10 ax+1)

Fx = number of offspring produced in stage x.

mx = offspring produced per surviving individual in stage x.

Human Demographics as Estimated from Cemetery Headstones

Locate a large cemetery (one which is accessible to the public, and one which has a minimum of ghosts, demons, etc.) Choose (as randomly as possible) 100 headstones and record the birthdate, deathdate (year alone is sufficient), sex (if apparent) and name (just to avoid duplication). Bring your datasheets to the lab and enter the data in a spreadsheet. We will then calculate the age at death and group the entries in 5 year categories (0-5, 6-10, etc.). Then, calculate survivorship as follows.

We will calculate some of this information a little differently, and will draw some different types of information from the data.

Set survivorship for age category 0 at 1.0. In other words, everyone reaches this category. Signify survivorship for age class 0 as l0. To calculate l1, survivorship from age 0 to age 5, subtract the proportion of the population dying during that interval from 1.0 (i.e., l1 = l0 - proportion dying during interval 0). To calculate survivorship for age group 2, subtract the proportion dying during period 2 (6-10 years) from l1. Continue in this manner until the survivorship column is complete. You should, in all likelihood conclude with a 0 in this column.

Consider the following sample:

| | | | |

|AGE GROUP |YEARS |# DYING (OUT OF 100) |lx |

| | | | |

|0 |0 |0 |1.00 |

| | | | |

|1 |0-5 |8 |0.92 |

| | | | |

|2 |6-10 |6 |0.86 |

| | | | |

|3 |11-15 |4 |0.82 |

At this point, lx may be viewed as the probability that an individual will survive to the end of the xth interval.

We will now calculate the average life expectancy remaining to an individual at each age interval. To do this, first determine the average survivorship for overlapping age intervals, Lx, from age x to age w:

Add this column to your life table. Sum these (it’s easiest to start from the bottom of the table and work upward) and place the results in the ΣLx column. Now divide ΣLx by lx for each age interval to determine life expectancy (ex). You may want to go ahead and multiply this by five to convert from age intervals to years. Remember, each of your intervals represents five years.

Now, use the following fecundity schedule (number of female birth per five years per female) to complete the life table.

| | | | | | | | | | | |

|AGE |0-10 |11-15 |16-20 |21-25 |26-30 |31-35 |36-40 |41-45 |46-50 |51+ |

| | | | | | | | | | | |

|mx |0.000 |0.002 |0.166 |0.424 |0.348 |0.193 |0.094 |0.026 |0.002 |0.000 |

These fecundity values are from the 1940's, and have no doubt changed over time. They should, however, serve well for our purposes.

Now, add another column to the life table, lxmx. For this calculation, assume that your data are good estimates of female survivorship. Realize that this column is calculating the contribution of an individual female to population growth and utilizes information both about survivorship to a particular age and fecundity during that age interval.

Calculate R0, the replacement rate, as:

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and G, the generation interval as:

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and r, the intrinsic rate of population growth as:

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When calculating these intervals, remember that your data were analyzed in five-year increments, so your intervals must be multiplied by 5 to equate to years. The same applies to life expectancy.

Using the methods above, complete the following life table for your human survivorship data. Then, use your newly acquired knowledge to complete the following.

1. Use EXCEL to produce a surivorship curve and attach it to this lab report. Comment on

the type of survivorship curve observed. At what age does median life expectancy (lx = 0.50)

occur?

2. Can you make any predictions about human population growth from your data? If this were a

representative sample, is human population growing, declining, or remaining stable. Based on

your knowledge, does your data model the real world?

3. How many years are between generations in your data? Does this seem to be representative?

4. How might your data differ if your limited your observations to headstones for people born

before 1850? What other limitations can you suggest to this technique?

|Age |Interval |Number Dying |lx |Lx |Σ Lx |ex |mx |lxmx |xlxmx |

| | | | | | | | | | |

|0 |0 | | | | | |0 | | |

| | | | | | | | | | |

|1 |0-5 | | | | | |0 | | |

| | | | | | | | | | |

|2 |6-10 | | | | | |0 | | |

| | | | | | | | | | |

|3 |11-15 | | | | | |.002 | | |

| | | | | | | | | | |

|4 |16-20 | | | | | |.166 | | |

| | | | | | | | | | |

|5 |21-25 | | | | | |.424 | | |

| | | | | | | | | | |

|6 |26-30 | | | | | |.348 | | |

| | | | | | | | | | |

|7 |31-35 | | | | | |.193 | | |

| | | | | | | | | | |

|8 |36-40 | | | | | |.094 | | |

| | | | | | | | | | |

|9 |41-45 | | | | | |.026 | | |

| | | | | | | | | | |

|10 |46-50 | | | | | |.002 | | |

| | | | | | | | | | |

|11 |51-55 | | | | | |0 | | |

| | | | | | | | | | |

|12 |56-60 | | | | | |0 | | |

| | | | | | | | | | |

|13 |61-65 | | | | | |0 | | |

| | | | | | | | | | |

|14 |66-70 | | | | | |0 | | |

| | | | | | | | | | |

|15 |71-75 | | | | | |0 | | |

| | | | | | | | | | |

|16 |76-80 | | | | | |0 | | |

| | | | | | | | | | |

|17 |81-85 | | | | | |0 | | |

| | | | | | | | | | |

|18 |86-90 | | | | | |0 | | |

| | | | | | | | | | |

|19 |91-95 | | | | | |0 | | |

| | | | | | | | | | |

|20 |96-100 | | | | | |0 | | |

R0 = ________________________________

G = ________________________________

r = ________________________________

DATASHEET FOR HUMAN LIFE TABLE

| |NAME |SEX |BIRTH YEAR |YEAR OF DEATH |AGE AT DEATH |NOTES |

|1 | | | | | | |

|2 | | | | | | |

|3 | | | | | | |

|4 | | | | | | |

|5 | | | | | | |

|6 | | | | | | |

|7 | | | | | | |

|8 | | | | | | |

|9 | | | | | | |

|10 | | | | | | |

|11 | | | | | | |

|12 | | | | | | |

|13 | | | | | | |

|14 | | | | | | |

|15 | | | | | | |

|16 | | | | | | |

|17 | | | | | | |

|18 | | | | | | |

|19 | | | | | | |

|20 | | | | | | |

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