biologists. Our exercise is based upon the biological content areas of
ecology, population biology, and diversity. In turn, these content
areas of biological sciences are an underpinning for students’
understanding of natural selection and evolutionary processes—the central, unifying theme(s) of modern biology.
Use of the packaged M&M candies provides some advantages
in a large classroom setting or when use of live specimens is not
possible. One advantage is that the M&M candies can be easily
explained as a “closed population” because the candies are
already, literally, enclosed within a bag. Also, the candies are of
several different colors, making them distinct for the counting/
marking purposes necessary to obtain data utilized in calculation
of the Lincoln-Petersen population estimate and Shannon-Weaver
diversity index. Another advantage is that students are able to literally see the entire, simulated community and the differently colored species within this community. This allows visualization of
the mathematical results of their sampling activities, as explained
below. An additional advantage, if your students do not have
food allergies, is the experimental subjects are edible and, if handled with care during the experiments, may be presented to the
students at the end of the lesson as a reward.
We explain to students that scientists, researchers, and consultants need to know the various types and species of organisms
present in natural communities and ecosystems. Additionally, to
make informed decisions related to the well-being of the natural
community or particular species within that community, scientists
also need to know (or be able to approximate) the population size
of the various species. It would be helpful if, prior to conducting
the activities, students were able to distinguish between populations, communities, and ecosystems.
Our technique involves an application of the Lincoln-Petersen
method of population estimation and calculation of a Shannon-Weaver diversity index value to our classes utilizing plain, chocolate
M&Ms as our different species within a hypothetical community.
Each different color of M&M represents a different species of animal.
For example, the teacher might explain that, due to difficulties of
travel, equipment, and time, we will use each different color of
M&M to represent a different species of mammal that we could
not ordinarily study. The blue M&M candies might be Meadow
Voles, the green M&Ms might be Least Shrews, the yellow M&Ms
might be Wolves, the brown M&Ms might be White-Tailed Deer,
etc. The teacher may leave the composition of the simulated community up to the students. We explain that knowledge of the number of
a particular species within a community is essential for a working
biologist to make informed decisions regarding management and
conservation of that species within its community.
We explain that the Lincoln-Petersen method is the most basic
population estimation method and involves one session of capture,
marking, and release of individuals of a particular species (or in
our simulation, a particular color of M&M) within a study commu-
nity, and a second, recapture session (Greenwood, 1996). In
essence, the Lincoln-Petersen method estimates the population size
of a particular species as the ratio or proportion of recaptured
marked individuals compared to all individuals of that species
(marked and unmarked) captured during the two sampling sessions.
For the Lincoln-Petersen estimate to be accurate, the study popula-
tion must be closed, at least during the study session. This means
that no individuals die, leave, or are born within the populations
and community during the study period. Also, all individuals of
a particular species under study must have an equal probability of
capture or census. Additionally, identifying marks used on captured
individuals must remain distinguishable throughout the brief study
We point out to our students that the Lincoln-Petersen tech-
nique is most accurate for large sample sizes of a particular species,
assuming that the overall population size of a species within a com-
munity is fairly large. Researchers have determined that, if the
number of marked individuals obtained in the second sampling
event is less than eight, the Lincoln-Petersen population estimate
will be biased. Confidence limits calculated from Lincoln-Petersen
estimates have been found to be reasonably accurate if the number
of marked individuals found in the second sample is greater than
50 (Greenwood, 1996).
The Shannon-Weaver diversity index calculation requires that
the researcher be able to identify different types of individuals
within a community. In a biological context, this might mean that
the researcher is able to identify and classify individuals to the spe-
cies level, or at least, be able to confidently separate the community
into different, distinct, groups.
Before beginning this portion of our activity, we explain to
students that the Shannon-Weaver index is a simple, common
way in which researchers can determine the richness and even-
ness of species’ distributions within natural communities. The
greater the number of species within a particular community
(species richness) and the more evenly they are distributed
throughout the community is a good measure of community sta-
bility. The Shannon-Weaver index is based upon information the-
ory and is, essentially, a measure of uncertainty in a system/
community. Calculated values of the Shannon-Weaver index will
range from 0 to 4. A value of 0, or close to 0, indicates a high
probability that your next result will be the same as the previous
result. For instance, if you chose a blue M&M from the sample
container, there is a high probability that your next choice will
also be a blue M&M. However, if the value is the opposite—a
value of 4 or close to 4—this means that there is a low probabil-
ity of obtaining the same color of M&M in your next choice. In
other words, when the calculated value is close to four, the com-
munity or system under study is much more diverse. In a biolog-
ical context, this means that many different kinds of species
would be found within this community. Also, a value closer to
4 would indicate that the individuals within the community are
evenly distributed throughout this community (Smith, 1996).
The most important requirement for calculation of the Shannon-
Weaver index is that individual species or types of organisms
within a community be distinguishable from each other, as are
our differently colored M&Ms.
All of these aforementioned conditions are satisfied well by
our simulated M&M community. Additionally, use of the candies
would also allow instructors to impose effects of natural selection
on the community (adding or removing M&M candies, for
instance) in order to have students analyze these effects upon
their resulting population and community diversity estimates.
With this prior knowledge, students are prepared to engage in
the activities as teams of two partners. A detailed description of
the activities follows, with examples and worksheets in the
Appendix to this article.