Names: __________________________________________________ Per: _____
Simulating Logistic Growth
Purpose: The purpose of this lab is to simulate the effects of “environmental resistance” on
population growth using a simple model.
Materials: Environment gird, a pair of dice, a container of “organisms” (beads or seeds), and a
data table
Methods: In this simulation, each organism is unable to move and occupies a unit in the
environment (a quadrant on the environment gird). Begin with a population size of 6. Roll the
dice 6 times and place the organisms at the indicated random locations on the environment
grid. (For example, if you roll 3 and a 6, place the “organism” in the 6 th box of the 3rd row,
marked “36”. If you roll a 3 and a 6 again, place the organism in quadrant “63”.) Only one
organism may occupy a quadrant in this generation. Follow the rules here to continue the
simulation:
1. Every individual will produce ONE offspring during that generation. Therefore, take 6
more organisms and place them onto the grid using the dice.
2. For the first generation only, keep adding offspring until you have 12 quadrants filled
with at least one organism. (In other words, you may have to add more than 6 offspring
to fill 12 quadrants in this generation.) No one dies of depleted resources in this
generation.
3. Count the total number of organisms on the grid and record this total as the #after
reproduction for the 1st generation. This also is your # at the start of generation 2.
4. From this point forward, every individual alive at the start of a generation will produce
ONE offspring during that generation.
5. The new offspring are placed into quadrants using the dice. Then apply the following
rule: At the end of a generation (2-11), if more than one organism is present in a
quadrant; ALL individuals in that quadrant die of resource depletion and are removed
from that quadrant.
6. Record your loss and new totals in your data table. Repeat steps 4-6 for an additional 9
generations.
Data Table:
Generation #
1
2
3
4
5
6
7
8
9
10
11
# at START of
generation
# after
Reproduction
6
12 or ____
# Lost due to
Environmental
Resistance
0
# for Next
Generation
12 or____
Analysis:
On a piece of graph paper, plot a graph of your data. The x-axis should be labeled “Generation #” and
include 12 generations. The y-axis should be labeled “Number at Start of Generation”. Use solid circles
to plot data points and connect them to make a line graph. On the same axes, plot another line showing
the population size for the first 5 generations if the population were to realize its biotic potential (i.e. 6,
12, 24, 48, etc.) using open circles for biotic potential. Title your graph and attach it to this lab sheet.
Discussion Questions:
1. Does the population grow at an exponential rate at any point in this curve? If so, when does this
occur?
2. What is the carrying capacity for the “environment” in this exercise? (Draw it on your graph & label as
“K”)
3. What is biotic potential and how does it compare to carrying capacity?
4. What does the difference between biotic potential for this population and the carrying capacity of this
environment represent?
5. What sorts of things might provide “environmental resistance” to exponential growth in natural
populations?