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 freefloating, 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 (r_{max}) 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.
Prelab 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 Table 3
2. Carry out the calculations necessary to complete the data table below.

Day
(#)
t

Lobes
(#)
N

Change in Number of Lobes Since Previous Count
dN

Rate of Population Growth
dN/day

Standardized Rate of Population Growth per Individual
dN/day
dN

0

3

NA

NA

NA

1

3




3

5




4

6




6

8




8

9




9

9




11

9




3. Calculate r_{max} 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 10^{8} km^{2}. 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 }km^{2} and r_{max} 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 (r_{max}), 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

Number of lobes

Change in # lobes since previous count

Change in #lobes/day

Change in (#lobes/day)/lobe

0

3

NA

NA

NA

1

3

0

0 ÷ 1 = 0

0 ÷ 3 = 0.00

3

5

2

2 ÷ 2 = 1

1 ÷ 5 = 0.20

4

6

1

1 ÷ 1 = 1

1 ÷ 6 = 0.17

3. Experimental Determination of r
Use the procedure below to determine the rate of population growth r_{max} 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 N_{t} is the number of lobes on Day 3 (N_{t} = 5), N_{o} is the number of lobes on Day 1 (N_{o} = 3), e is Euler's constant, and t is the length of the time period, 2 days.
N_{t} = 5
N_{0} = 3
t = 3
N_{t }= N_{o}e^{rt}
N_{t} = N_{o}e^{rt}
5 = 3e^{2r}
ln (5/3) = ln e^{2r }Take the natural log (ln) of both sides.
ln (5/3) = 2r Use the identity ln e^{x} = 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 rspecies or Kspecies? 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 setup 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.
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