1. Chocolate M&M candies in “Fun-Sized” bags.
2. Appropriate plastic containers, with reclosing lids, for mixing
the candies. (We use rectangular, 14 × 10 × 7 cm containers
of 710 ml [24 oz] volume.) This size allows sufficient space
for mixing and distribution of the candies and more random
selection as students reach into containers to draw out individual M&Ms.
3. Calculation worksheets (see examples in the Appendix).
4. Pencils and calculators (if allowed and appropriate).
5. Non-toxic markers (Crayola markers work well) if the instructors do not wish students to scratch the candies to mark them.
Procedure: Lincoln-Petersen Estimate
The formula for a corrected Lincoln-Petersen estimate calculation is:
N ¼ ðMS1 þ 1Þ ×ðnS2 þ 1Þ ÷ðMS2 þ 1Þ – 1
Wherein: N = population estimate obtained from sampling efforts
on two occasions.
MS1 = all individuals of a particular species marked in Sample 1.
nS2 = all individuals of a particular species (marked and
unmarked) obtained in a second sample.
MS2 = all individuals of a particular species that were found to
be marked in the second sample.
Adding values of 1 to the sample sizes and subtracting 1 from
the total population estimate helps to correct for some bias in the
basic Lincoln-Petersen calculation.
Each color of M&M will represent a particular species population within the total community. Plain chocolate M&Ms come in
colors of blue, brown, green, orange, red, and yellow. The Mars
Corporation currently packages M&M candies according to weight;
therefore, proportions of colors in M&M candy packages are no
longer standardized and tend to vary. However, the last reported
proportions given by the Mars Corporation for M&M milk chocolate candies were 24% blue, 20% orange, 16% green, 14% yellow,
12% red, and 12% brown.
Obtaining the First Population Estimate
1. Distribute Fun-Sized bags of M&Ms to the class, and have
students work in pairs to complete the Lincoln-Petersen
and Shannon-Weaver estimates.
2. Give each student team (pair) one plastic container (with lid).
3. Student pairs will place their M&Ms into the container and
count the total number of M&Ms and total numbers of
each color in the container. For the Lincoln-Petersen calculations, each color represents a different species of M&M.
For example, each color may be a different species of mammal, butterfly, bird, or whatever the students wish to imagine the candies to represent.
4. Students record the resulting counts of the differently colored M&Ms on the provided worksheet (see student worksheet and example worksheet in the Appendix).
5. Explain to the students that, by placing the M&Ms into a
container, we have created a closed population where no
individuals will be exiting the population, reproducing, or
dying between sample events (if you can keep the students
from eating the M&Ms!). At this point, the instructor might
remind students that closed populations, short durations of
time between sampling events, and no significant changes
within the population between samplings are essential conditions that must be satisfied to obtain accurate population
estimates using the Lincoln-Petersen method.
6. Students determine which color of M&M occurs in the highest number(s). This number will then be used as the sample
size of subsequent sampling events (see student worksheet
and example worksheet in the Appendix).
7. For example, if blue M&Ms are in the greatest number in the
population, blue M&Ms will be marked if any are randomly
picked from the container in the first sampling event (MS1).
Explain to students that, in a field survey, researchers might
use tags, dyes, florescent powders, or other types of mark-ing/identifying methods to designate individuals captured in
the first sample. Also, remind students that the population
estimate will be more accurate if large sample sizes are taken.
8. Return all M&Ms to the container and gently stir or shake
the container (with the lid on, if shaken) to randomly distribute the candies in the container. Remove the lid and
have one (or both) students close or avert their eyes and
randomly draw out the same number of M&Ms as the most
numerous color (blue, in our example). Make sure students
draw out the M&Ms one at a time. This will assure equal
probabilities of capture or census. (Remind students that
this is another required condition of the Lincoln-Petersen
9. If any of the M&Ms of the highest number (blue, in our
example) are found in the sample, these candies will be
marked by gently scratching their surface. A light fingernail
scratch mark should be sufficient to identify them later.
Alternatively, if the teacher desires, a non-toxic marker (such
as a Crayola marker) may be used to mark the candies
instead of scratching. Be sure to record the number of designated M&M species (blue, in our example; see accompanying worksheet) captured in this first sample on the
provided worksheet. This is MS1.
10. Make sure all of the M&Ms are replaced into the provided
container. Place the lid on the container, and again, gently
shake the container or mix them.
11. Follow the sampling procedure describe in Step 8, have
students obtain a second sample of M&Ms, and record
the sampling result as nS2 on the worksheet.
12. Explain to the students that these particular steps are important because they allow for a random sample, wherein each
individual has an equal probability of capture. This is one of
the essential conditions that must be satisfied for an accurate
population estimate utilizing the Lincoln-Petersen method.
13. Count the number of marked individuals obtained in the
second sample; in our example, you would count the number of marked (scratched) blue M&Ms obtained in the