Lincoln Index

The Lincoln index is a statistical measure used in several fields to estimate the population size of an animal species. Described by Frederick Charles Lincoln in , it is also sometimes known as the Lincoln-Petersen method after C.G. Johannes Petersen who was the first to use the related mark and recapture See more. Consider two observers who separately count the different species of plants or animals in a given area. If they each come back having found species but only particular species are found by both observers, then each See more. Sampling Theory Drake equation German tank problem Inter-rater reliability See more. Lincoln, Frederick C. May . Calculating Waterfowl Abundance on the Basis of Banding Returns. Circular. Vol. . Washington, See more. The Lincoln Index formalizes this phenomenon. If E and E are the number of species or words, or other phenomena observed by two See more. The Lincoln Index is merely an estimate. For example, the species in a given area could tend to be either very common

1. Lincoln Index

ESTIMATING POPULATION SIZE

2. BACKGROUND:

* The best way to measure the size of a population
is to count all the individuals in that population.
When determining the population sizes of trees
or other relatively immobile organisms, this
method is, indeed, practical. If the organisms
were mobile, however, such as fish, counting
every individual would be difficult. Some
individuals might be counted twice or not at all,
since the experimenter would not know which
fish had been counted and which had not.
Ecologists use a method called the Lincoln Index
to estimate the size of a population.

3. BACKGROUND:

* In this experiment, you will model a
population of mobile organisms, capture and
mark a sample of the population, and then
capture a second and third sample. You will
then estimate the size of the model
population using the Lincoln Index. The
accuracy of the Lincoln Index will be inferred
by counting the model population.

4. * To use the Lincoln Index, scientists capture a
sample of the population they want to
measure. They mark these individuals and
release them. After waiting several days, the
scientists return and capture another sample.
These individuals are not marked; however,

some of the individuals in the second capture

5. The scientists then use the following formula to
estimate the size of the population.
# Marked in 1” Sample = # Marked in 2" Sample

Total Population Total Caught in 2 Sample

6. The Lincoln Index makes several assumptions
that must be met if the estimate is to be
accurate. These assumptions are:

A.) The population of organisms must be closed,
no immigration or emigration.

B.) The time between samples must be small
compared to the life span of the organism

C). The marked organisms must mix completely
with the rest of the population during the time
between sampling.

7. Copy the following down in your

journal:
N1=
N2= N2= N2= N2=
R= R= R= Re

Note: N1 will be the same for all 4 trials

Total Population = (N2)(N1)
(R)

8. MATERIALS: paper bags, dry beans,

markers

PROCEDURE:

EXPERIMENT 1

1.) The paper bag represents the habitat of your model
population. Add several handfuls (3-4) of dry beans to the
habitat. The beans represent your organisms in your habitat.
NOTE: Do not try to count the exact number of beans until
the end of the experiment.

2.) Remove a small handful of beans from the model habitat.
This handful will be your first sample. The sample should be
at least 20 beans but less than half the total population.

3.) Using a colored marker, mark all organisms in this first
population. Mark them well enough to be easily identified if
recaptured. Count the beans and record this number as N1
for all trials on the data sheet. Let the marks dry on the
beans.

9. 4.) Place the beans from your first sample (N1)
back into the habitat. Mix them well.

5.) Without looking, one member of the group
should remove another handful of beans. The
sample size should be about the same as the
original. Count the total number of beans in the
second capture. This is your N2 value for trial 1.
Notice that some of the beans will have the
marking from the first capture. Count these
organisms and record this number as R for trial 1.
6.) Return the organisms to their habitat. Mix well.
7.) Repeat steps 5 and 6 three more times giving
you a total of four trials or four recaptures.

10. POST LAB QUESTIONS:

Answer these in your lab journal.

1. Calculate the average for your N2 and R values.

2. Use your data to estimate the size of the
population in the model habitat. Use the Lincoln
Index formula for your calculation. Show your
work using the average of N2 and R.

Total Population = (N2)(N1)
(R)

11. POST LAB QUESTIONS:

Answer these in your lab journal.

3. Compare the population estimates calculated
with the Lincoln Index to the actual size of the
population. (Count the total number of beans in
your population!) Calculate a percent error.

Percent error= Lincoln Index—Actual x 100
Actual

12. POST LAB QUESTIONS:

Answer these in your lab journal.

4. Compare your results with other groups. Which
group’s estimates was most accurate?

Compare the sample sizes of the groups. Is there an
inference you can draw about the size of the
samples/populations and the accuracy of the
Lincoln Index?

5. Why is it important that the time between first
and second samples be a short time compared to
the organism’s life span?

13. POST LAB QUESTIONS:

Answer these in your lab journal.

6. How can a data collector determine whether the
population being studied is growing or declining?

7. The United States conducts a national census of its
people every ten years. Numbers collected from this
census are used to determine many things in each
state from the number of seats awarded in the
House of Representatives to amounts of federal
dollars for that state. Could a sampling technique
such as this be used to calculate the population of
the United States?

Explain: