Population Studies using Lemna
Background Information
Lemna minor is a member of the family Lemnaceae (duckweed family). This tiny
organism is ideal for population growth experiments because it reproduces quickly,
requires minimal space to grow, and requires no maintenance. The free-floating,
freshwater plant consists of a green elliptical lobe (frond) with one root and is found in
still waters, from temperate to tropical zones. The plant reproduces by vegetative
budding, although it may flower. On average, lobes live for four to five weeks.
lobe
Figure 3 - Lemna minor
Due to its rapid growth rate, duckweed finds wide use in governmental and commercial
applications. For example, the US EPA requires companies that make pesticides to
determine whether their chemicals affect the growth of aquatic plants. Many companies
use duckweed as a test plant. In the test, the pesticide is applied to duckweed's growing
medium and any effects on the duckweed's growth rate are taken as a measure of the
pesticide's toxicity.
Some companies use duckweed to remove nitrogen and phosphorus from their
wastewater. Nitrogen and phosphorus are plant nutrients that in high concentrations (as in
wastewater) promote rapid plant growth. If wastewater were released into the
environment untreated, new plant growth would clog waterways and cause
eutrophication. To remove nutrients from the wastewater, Lemna plants are grown in it.
As the plants grow, they naturally take up nitrogen and phosphorus from the wastewater.
When the duckweed plants die, they are harvested, composted, and used as mulch. The
treated wastewater continues to the next stage of purification.
The high nutrient content of duckweed also makes it a viable alternative to existing
livestock feed. Duckweed can even offer advantages in some cases. For example, poultry
feed requires expensive supplemental pigments that occur naturally in duckweed.
Although duckweed is a freshwater plant, its range has extended beyond earth's terrestrial
limits. In 1982, the space shuttle orbiter Columbia carried an experiment to study the
effects of microgravity on duckweed growth.
In this experiment, the maximum rate of population growth (rmax) for Lemna minor in
different types of growing media will be determined. This will involve calculating the
number of lobes (daughter plants) present in a sample population over a several weeks.
Pre-lab Questions
1. Compare and contrast exponential and logistic population growth. Include the
respective rate equations as part of the answer.
Note: See Example
Calculations in Data
2. Carry out the calculations necessary to complete the data
Table 3
table below.
Day
(#)
Lobes
(#)
Change in
Number of
Lobes Since
Rate of
Population
Growth
Standardized Rate
of Population
Growth per
Individual
Previous Count
t
N
dN
dN/day
dN/day
dN
0
1
3
4
6
8
9
11
3
3
5
6
8
9
9
9
NA
NA
NA
3. Calculate rmax using the values in the data table above.
4. Sketch a graph of “Day Number” versus “Number of Lobes” using the data table
above. Then, use the graph to determine the carrying capacity (K) of the population.
5. The surface area of the earth is approximately 5.1 x 108 km2. How many days would a colony
of three lobes of Lemma minor require before they covered the earth's surface? Assume the
surface area of one lobe is 2.25 x 10-12 km2 and rmax is 0.288 lobes per day.
Structured Inquiry
Hypothesis
Predict what effect you think the variable will have on the growth of the duckweed population.
Procedure
Each lab group will set up five cups: one control group and four experimental groups
with different concentrations of the variable. Each group constitutes one trial and class
data can be pooled to yield multiple trials.
1. Data Table 1
Construct a data table to collect the following information in each of your group’s cups (5
copies needed – one for each cup).


Day Number
Number of Lobes
2. Data Table 2
Construct a data table to collect and average the multiple trials (class data) for each
cup (5 copies needed – one for compiling average data in each cup). The data table
should encompass the following information. Note: Data may be collected using an
Excel spreadsheet.



Day Number
Number of Lobes in Each Group
Average Number of Lobes
3. Data Table 3
Construct a data table that has 5 columns for each cup (5 copies needed – one for the
average data of each cup). Give the columns the headings bulleted below. The heading
for this table will be "Duckweed Growth Data".





Day Number
Average Number of Lobes (from multiple trials)
Change in the Number of Lobes since the Previous Count
Change in the Number of Lobes per Day
Change in the Number of Lobes per Day per Lobe.
4. Data Table 4
Construct a data table that has 3 columns to summarize the calculations made in the
control and experimental trials (1 copy needed – to summarize the calculations made
on each cup). Label the columns with the headings bulleted below.



Sample Cup
Carrying Capacity (in lobes)
Intrinsic Rate of Increase (per day)
5. Prepare one set up of the control and each of the four variable concentrations. Make
sure all your cups have your team ID on them.
Control –Spring Water
Measure 90mL of spring water in a graduated cylinder and pour into a cup. Using a
toothpick, carefully transfer one colony of three lobes and two colonies of two lobes
(total of seven) to the cup. Cover the cup with plastic wrap and secure it with a
rubber band. Poke five small holes in the plastic wrap and label the cup “Control”
Place the cups in a lighted plant rack.
Experimental - Fertilizer
Obtain four cups. Place 90mL of 0.5% fertilizer into one cup, 90mL of 1.0%
fertilizer into another cup, 90mL of 2.0% fertilizer into another cup, and 90mL of
4.0% fertilizer into another cup.
Using a toothpick, carefully transfer one colony of three lobes and two colonies of
two lobes (total of seven) to each cup. Cover the cups with plastic wrap and secure
them with rubber bands. Poke five small holes in each cup’s plastic wrap. Label the
cups Exp 0.5%, Exp 1.0%, Exp 3.0%, and Exp 4.0%. Place the cups in a lighted
plant rack.
6. On a daily basis (or every other day basis), count the number of lobes in your cups and
record the data in your table. Count only live (green) lobes. Lobes that are totally yellow,
clear, black, or white are dead. The experiment may continue for 3 to 4 weeks.
Data Analysis
1. Compile Average Data
First, compile the data from all the multiple trials and calculate average data of each
trial. This should be done in the five copies of Data Table 2.
2. Prepare Average Data for Calculations
To estimate the biotic potential (rmax), several calculations must be made from the
average data collected in the five copies of Data Table 2. Place these calculations in the
five copies of Data Table 3.
For example, suppose you collect the following data. On the first day of the
experiment, Day 0, you place 3 lobes in the cup. The next day (day 1), the number of
lobes is still 3. Two days later (day 2), there are 5 lobes. Four days later (day 4), there are
6 lobes.

First, complete the column "Change in the Number of Lobes since the
Previous Count." On Day 0, there is no change because there was no previous
count. On Day 1, the previous count was made on Day 0. The number of
lobes, 3, did not change and a 0 is recorded in the column. On Day 3, the
number of lobes increased to 5 from 3, so a 2 is recorded in the column, and
similarly for Day 4.

Second, complete the column, "Change in the Number of Lobes per Day."
This value equals the value from column three, the number of new lobes in that
day's count, divided by the number of days since the previous count. On Day
3, there were 2 new lobes since the previous count on Day 1. Thus, the change
in the number of lobes per day equals 2 divided by 2, which equals 1.

Finally, the last column, the number of new lobes produced per day per lobe,
equals the number in the "Change in the Number of Lobes per Day" column
divided by the number of lobes from the previous count. For example, on Day
3, the change in the number of lobes per day was 1, and there were 3 lobes on
the previous count, Day 1. Thus, the change in the number of lobes per day per
lobe is 1 divided by 3, or 0.33.
Example - Data Table 3
Day number
0
1
3
4
Number of
lobes
3
3
5
6
Change in #
lobes since
previous count
NA
0
2
1
Change in
#lobes/day
NA
0÷1=0
2÷2=1
1÷1=1
Change in
(#lobes/day)/lobe
NA
0 ÷ 3 = 0.00
1 ÷ 5 = 0.20
1 ÷ 6 = 0.17
3. Experimental Determination of r
Use the procedure below to determine the rate of population growth rmax for each of the cups.
Obtain the necessary values from each of the 5 copies of Data Table 3. Then, summarize the
values calculated in Data Table 4.
Use the maximum figure from the "Change in the Number of Lobes per Day per Lobe" data,
to begin calculating the population's intrinsic rate of increase. If there are two maxima, choose
the one that occurs first in time. In the example above, the maximum occurred on Day 3. Use
the exponential growth formula where Nt is the number of lobes on Day 3 (Nt = 5), No is the
number of lobes on Day 1 (No = 3), e is Euler's constant, and t is the length of the time
period, 2 days.
Nt = Noert
Nt = 5
N0 = 3
Nt = Noert
5 = 3e2r
ln (5/3) = ln e2r
t=3
Take the natural log (ln) of both
sides.
ln (5/3) = 2r
Use the identity ln ex = x
r = 1/2 ln (5/3)
r = 0.255 lobes per day
4. Experimental Determination of K
Use the procedure below to determine the carrying capacity (K) for each of the cups. Obtain
the necessary values from each of the 5 copies of Data Table 3. Then, summarize the values
calculated in Data Table 4.
To determine each cup's carrying
capacity, graph the "Number of
Lobes" against the "Day Number" to
obtain a logistic population growth
curve. Eventually, the number of
lobes reaches a constant value. This
number is the cup's carrying
capacity.
Analysis Questions
1. Based on your data and calculations, is Lemna an r-species or K-species? Explain your
answer.
2. Why does the rate of population growth for Lemna change as the experiment
progresses?
3. Based on the data, what is the affect of fertilizer on the carrying capacity of a Lemna
population?
4. Based on the data, what is the affect of fertilizer on the rate of population growth of a
Lemna population?
5. Create a graph with standard error bars for the Control set-up that plots time vs.
number of lobes.
6. Carryout appropriate statistical analysis to determine if there is a statistically
significant difference between the number of Lemna present in the control cup and the
experimental cup with 0.5% fertilizer on day 15 of the experiment.