Population Estimation
Please do not write on this lab sheet
Background
The ability of scientists to accurately estimate the total population of a target organism is
fundamental to any ecological study. Species and resource management is closely tied to
population size counts performed in the field. Because counting every individual in a population
can be impractical and very difficult, field biologists have developed a variety of techniques and
mathematical formulas for estimating populations. Several of these methods require counting a
portion of the population while others involve successive captures of individuals.
Part 1
Mark and Recapture Method
One common population sampling technique is the mark-recapture. This technique involves
capturing a number of individuals in such a way as to identify them if recaptured, and then
releasing them back into the population. A subsequent capture is performed, and the ratio of
marked to unmarked individuals is noted. Typically, several recaptures are performed. Ultimately
the total population of the target species is estimated on the basis of this ratio.
Assumptions must be made for all types of population estimates, and it is a valuable exercise to
think about some of the assumptions required to ensure the validity of a given sampling method,
as well as some of the circumstances that might cause these assumptions not to be met (e.g., are
individuals from outside the sampling area likely to move into the area during the sampling
period?). The following conditions were assumed to be true in deriving the mathematical formula
used to determine the mark-recapture population estimation. If the following conditions do not
apply to a particular population, the mark-recapture method will not provide a reliable population
estimate.
Assumptions:
The ratio of the actual population to the number of captured individuals is the same as the ratio of
the number of released, marked individuals to the number of recaptured, marked individuals.
 Each individual in the population has an equal and independent chance of being captured.
 Except for the effects of trapping, the population is not increasing or decreasing in size during
the sampling period.
Biologists conducting a population census will probably not have proof that these conditions are
met. Field biologists study situations carefully and learn all that they can about the target
organisms to ensure that the assumptions are reliably met. In situation in which the assumptions
are in question, other methods must be found for estimating populations, or less trust must be
placed on the accuracy of the estimate.
During this section of the lab, you and your partners will use the mark-recapture method to
estimate a population. Whereas a fisheries biologist might use this method to estimate the
population of largemouth bass in a pond, you will be using the method to estimate the number of
beans in a beaker.
A simple formula for estimating a population using the mark-recapture technique is:
Where:
N= m s
t
N = Estimated Population Total
m = number of individuals marked from 1st capture
s = number of individuals captured each round
t = number counted that were marked during the recapture
Procedure – Part 1
1. Put at least three handfuls of red beans in a paper bag.
2. By sight, write down and estimated guess as to the population of beans in the bag
3. “Capture” a sample (at least one handful or small beaker-full) from your population
4. Count the number captured and record this number in your data table as “m.”
5. Replace the beans captured with the same number of “marked” beans (represented by white
beans). Bring the removed red beans to the front so they do not get mixed in with the
population again.
6. Shake up the bag to distribute the marked individuals among the population
7. “Capture” another sample from the population.
8. Count the beans and record this number in your data table as “s” #1.
 Of these beans, count the number of “marked” beans, and record this number as “t” #1
 Using these values and the “m” value, calculate “N” and record this as “N” #1.
9. Return all of the ”captured” beans to the population, shake up the beaker and repeat steps 6
and 7.
10. When your group has completed ten recaptures, average all of the population estimates (N)
together and enter this value in the data table.
_____________________________________________________________________________
Part 2
Quadrant Method
The mark and recapture method may not always be an appropriate means to estimate a
population size. Sometimes it may work better to simply examine a relatively small area in which
the population exists and applying the findings to the entire area. There are three variations of
this method. First, several same-sized areas can be arbitrarily chosen and marked off in which
the population can be found. After counting the number of individuals in each area, an average
can be found. By multiplying the average number of individuals to the size of the area the
population exists, a population can be estimated. A better use for this method is to estimate the
number individuals/m2. A second version is to mark a grid covering the area the population
inhabits. By counting the individuals in certain squares of the grid and comparing those numbers
to the entire area, a population can be estimated.
A plant ecologist may use one of the quadrant methods to estimate the population of a particular
species of tree in a forest. During this section of the lab, your group will be using the second
variation of the quadrant method to compete a second estimation of the population of beans.
Procedure - Part 2
1. Dump the beans onto an empty desk and randomly spread them out. They do not need to be
spread evenly. Be sure the beans are not stacked. Do not move or touch beans until the
completion of this method of estimation.
2. Using a ruler and sections of string, make a grid over the entire desk by taping the sting down.
Be sure the desk is divided evenly by the strings.
 Measure the length of the desk and determine how you can divide it evenly in to several
columns. Repeat the same process to the width of the desk.
 Make sure the measurements are even at both ends of each column and each row.
3. Based on estimation, classify each square in the grid as having a “high”, “medium”, or “low”
density of beans. It might be a good idea to use an eraser to mark
4. Once each square has been classified, pick a square that best represents each classification
Count all the individuals in each of the three squares and record the number in the data table.
5. Count the number of square of each type of density and record the number in the data table.
Once both methods of population estimation are complete, hand count ALL the beans in
your population and record this number in BOTH data tables.
To calculate the percent error between the estimate and the actual number, use the following
formula.
(Actual number - the average N / by the actual number) x 100
Be sure to answer ALL questions on the data sheet!
Name _____________________________ Pd. ______
Visual estimation: ______________
Part 1 - Mark and Recapture Method:
m=
Trial
s
t
N
1
2
3
4
5
6
7
8
9
10
Average N =
Actual N =
Percent error =
1. How would it be possible to decrease the percent error using this technique?
2. List three additional populations for which this technique would work well.
3. List three populations for which this technique would not work well.
Part 2 - Quadrant Method:
Density
Representative #
High
Medium
Low
Estimated Total
Actual Total
Percent Error
# of Squares
Total
X
=
X
=
X
=
1. How would it be possible to decrease the percent error using this technique?
2. List three additional populations for which this technique would work well.
3. List three populations for which this technique would not work well.
General
Which method was more accurate? Why?
Why might it be useful to know the population of a species? Name and describe at least two
applications for estimating a population.