Exercise C: Logistic growth rates
The biotic potential of a population is held in check by some form of “environmental
resistance”. This might include limits on food, water or habitat, or waste accumulations. In most
cases, populations tend to level off at a certain size, which is known as the carrying capacity of
the environment. This population size is characteristic of the environment in which the organism
lives and will vary among populations and among environments.
Procedure:
You can simulate the effects of environmental resistance on population growth with some
simple equipment. Use a paper with a marked grid, a pair of dice, and a container of seeds. The
squares on the grid represent an “environment” and the seeds are “organisms.” In this
simulation, each organism is unable to move and occupies a unit of the environment indicated by
the quadrants on the marked grid. Begin the simulation with a population size of 6. Roll the
dice six times to place the organisms at random locations in the pan. (For example, if you roll a
“3” and a “6”, place an “organism” in the sixth square of the third row--marked “36”.) As an
alternative to rolling two dice, you can use a table of random numbers. Follow the instructions
given to assign “organisms” to quadrants. Only one “organism” may occupy a quadrant. Follow
the rules indicated here to simulate logistic growth:
1. Every individual alive at the start of a generation will produce one offspring during
that generation.
2. The new individuals of each generation are placed in quadrants by dice or reference to
a table of random numbers (see blue sheet)
3. First place 6 organisms. If random assignment places more than one organism in a
quadrant, continue placing additional organisms until you have occupied 6 grid spaces.
4. These 6 (or more) organisms will all reproduce, each producing one offspring. Leave
the original first generation organisms in their place. Count out the number of offspring produced
and place in a pile off to the side of your workspace.
5. Roll the die, or use the random number table to assign these 6 (or more) new offspring
to a grid space. Keep going until you have 12 spaces occupied with at least 1 organism. You
may need to place additional offspring to get to 12 occupied grid squares.
4. Then apply the following rule: At the end of a generation (beginning with the end of
generation 2), if more than one organism are present in a quadrant, all individuals die of
starvation/resource depletion and are removed from that quadrant.
5. Record your observations for each generation in a table in your lab notebook similar
to the one below.
Generation # at start
# after
#
of generation Reproduction
1
2
3
4
5
6
7
8
9
10
11
12
6
____
____
____
____
____
____
____
____
____
____
____
12 or ____
____
____
____
____
____
____
____
____
____
____
Loss due to
Environmental
Resistance
__0_
____
____
____
____
____
____
____
____
____
____
# for
Next
generation
12 or ___
____
____
____
____
____
____
____
____
____
____
Analysis:
After you complete the exercise, plot a graph in your lab notebook. Use generation
number along the horizontal axis, and population size on the vertical axis. Plot one line showing
“# at start of generation” (use solid circles for each data point). Then 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, and 48, 96, etc.) (use open circles for biotic potential).
Answer the following questions in your lab notebook using complete sentences.
1. Does the population grow at an exponential rate at any point in this curve?
2. What is the carrying capacity for the “environment” in this exercise?
3. What does the difference between biotic potential for this population and the carrying
capacity of this environment represent?
4. What sorts of things might provide “environmental resistance” to exponential growth in
natural populations?