a. Each team also calculates the mean and standard error
of the speed of their new generation for comparison
with the parent generation (Table 2).
9. Using their second generations, teams play the second
round of the simulation like the first (steps 3–8).
10. Once the third generation is established, one individual
from the prey population receives a beneficial mutation
that increases its speed to one number above the highest
number in the population.
a. To simulate this, the prey team haphazardly pulls one
card from their third generation and replaces it with a
“wild” UNO card or a card with a number one higher
than the highest in the population.
11. Following the simulated mutation, the prey team recalcu-
lates the mean and standard error of the speed of their pop-
ulation in the third generation, which now includes one
a. The predator team does not experience a mutation, so
their mean speed and standard error remain constant
i. It is best if members of the predator team par-
ticipate in the mutation process with the prey
12. Thereafter, a third and (if time allows) fourth round of the
simulation are run.
13. After the fourth simulation, students also calculate the
characteristics of the fifth generation.
Our lab periods are 110 minutes, and the majority of student
groups complete four rounds and calculate speeds of a fifth generation within that time. If less time is available, the main trends are
visible in fewer rounds (Tatina, 2007), but at least four rounds are
needed to include the mutation simulation (Table 2 and Figure 1).
It is also possible to play the game in stages (say, from one class
period to another), until several rounds are completed.
The analytical results are means and standard errors of running
speeds per generation (Table 3). However, students also report
card-number frequencies as part of their calculations, which helps
clarify the mechanism of natural selection. The calculations slow
some student groups at first, but once they master them in the first
round, groups typically are proficient in subsequent rounds. This
meets our goal of strengthening quantitative skills and reducing
We suggest that students form groups of four or five so that at
least two students collaborate on each prey and predator team.
Teamwork allows students with more confidence to coach and
assist others needing help. Students can also cross-check each
other’s calculations within and among teams to reduce the errors.
As increased engagement is one goal of active-learning pedago-gies (Nelson, 2008), it is important to note that students generally
enjoy this simulation. It consistently keeps students engaged for an
Table 3. Mean (X̅ ) and standard error (SE) of running speed for each generation based on a simulation run
using the starting populations in Table 1. Generations with an “m” notation (e.g., 3m) are those in which a
beneficial mutation occurred for one prey individual (in this case, a mutation converted a 5 to an 8).
SE X̅ SE
1 5.0 0.16 5.0 0.37
2 5.4 0.14 5.6 0.34
3 5.8 0.12 6.4 0.16
3m 5.9 0.13 6.4 0.16
4m 6.7 0.08 6.6 0.16
5m 7.1 0.03 7.0 0.00
Figure 1. Graphed results from Table 3 showing mean
running speed with standard error as required for homework.
Students graph their own results. Results vary depending on
THE AMERICAN BIOLOGY TEACHER A QUANTITATIVE SIMULATION OF COEVOLUTION WITH MUTATION USING PLAYING CARDS