Student teams will enter their previous, total counts of the M&M
species in the provided worksheet and complete calculations for the
Shannon-Weaver diversity index for their simulated community (see
student worksheet and calculation examples worksheet in the Appendix). The teacher might remind the students, as mentioned earlier,
that this index is a measure of uncertainty and, the closer the obtained
value is to 0, the more certain you become of sampling the same species (color) of M&M from the community each time that a sample is
taken. The closer the value is to 4, the less likely you would obtain
the same species of M&M candy from differing samples.
Extending our activity by having students calculate diversity
indices for their M&M communities provides greater depth, practice, and reasoning into the biological and ecological concepts. Students learn techniques that researchers utilize in real-world
estimates of biological community structure and abundance. The
M&M methodology might also be incorporated into lessons and
demonstrations concerning adaptation, cryptic or non-cryptic coloration, and basic genetics lessons. Instructors can design many lessons incorporating biological and mathematical concepts and
critical thinking skills with the M&M model, therefore, in a manner
of speaking, the lessons are already “in the bag”!
Brady, J. K., & Brady, J. C. (2009). Using field experiences to study the land-use legacy. American Biology Teacher, 71(7), 419–423.
Greenwood, J. J. D. (1996). Basic Techniques. In W. J. Sutherland (Ed.),
Ecological Census Techniques a Handbook (11–110). Cambridge:
Cambridge University Press.
Jungck, J. R., Gaff, H. & Weisstein, A. E. (2010). Mathematical manipulative
models: In defense of “Beanbag Biology.” CBE Life Science Education, 9,
NGSS Lead States. (2013). Next Generation Science Standards: For states by
states. Washington, DC: National Academies Press.
Smith, R. L. (1996). Ecology and Field Biology (5th ed.). New York:
HarperCollins College Publishers.
Steen, L. A. (Ed.). (2001). Mathematics and Democracy: The case for
quantitative literacy. National Council of Education and the Disciplines
(NCED). Woodrow Wilson National Fellowship Foundation.
Whiteley, A. R., Woolf, J., Kennedy, K., Oberbillig, D., & Brewer, C. (2007).
Classroom mark-recapture with crickets. American Biology Teacher,
JIM R. GOETZE ( email@example.com) is Professor of Biology and
Chairperson in the Natural Sciences Department, Laredo College, West End
Washington St., Laredo, TX 78040-4395. MARISELA RODRIGUEZ (marisela.
firstname.lastname@example.org) is Dean of Arts and Sciences, Laredo College, West
End Washington St., Laredo, TX 78040-4395.
Appendix: Lincoln Petersen Estimation and Shannon-Weaver Calculation Student Worksheet
A particular color of M&M will represent a distinct species within a hypothetical community. Plain Chocolate M&Ms come in
colors of blue, brown, green, orange, red, and yellow.
Please count the number of M&Ms of each color in your sample (combine two Fun-Sized bags of Chocolate M&Ms) and
record the total numbers of each color below:
Total Number of M&Ms in sample (the total population) =
Lincoln Petersen Estimation Calculation
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 [includes 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.
Blue = Brown =
Green = Orange =
Red = Yellow =