Population Growth In Lemna Minor
Background
A population is a group of individuals of the same type living in the same place at the same time. In
stable environments, the number of individuals in an established population remains nearly constant. In
rapidly changing environments however, many individuals may die within a short period, leaving only a
few survivors to perpetuate the species. On the other hand, populations introduced to new environments
with ideal conditions for the species, will reproduce rapidly and the population size will increase.
Population dynamics refers to changes in the number of individuals in a population and the factors that
cause these changes.
Models of population growth help scientists understand how a population’s size changes over time and
allows them to predict how populations may change in the future. These models have applications in
microbiology, wildlife management, pest management, agricultural productivity, and toxicology.
Exponential Population Growth
When resources are unlimited the number of individuals in a
population grows exponentially: 1, 10, 100, 1000, etc., as shown
in figure 1. In exponential growth, the number of individuals
increases rapidly and without limit. In exponential growth the
population does not grow by a fixed number of individuals each
generation, rather it increases by some percentage of those alive
in the previous generation. Thus, the more individuals there
are in a population currently, the more individuals there will be
added to the population in future generations (positive
feedback). This percentage is the population’s growth rate or
intrinsic rate of increase (r) and will vary from environment to
environment. In theory, there exists an environment that is
perfect in all respects for a population and in which it will
attain a maximum rate of increase. This rate of maximum
increase is a population’s biotic potential. Most environments,
however, limit growth, and the population’s rate of natural
increase is less than its biotic potential.
The following equation uses a populations intrinsic rate of increase expressed as a decimal (r), its current
size (N0), and the amount of time (t) it grows for to estimate how large the population will be at some
point in the future (Nt) if it continues to grow exponentially.
Exponential Growth Equation:
Nt = Noert
As part of this laboratory experiment you will be asked to determine the intrinsic rate of increase for
Lemna Minor under various experimental conditions and determine the conditions under which it most
closely approaches its biotic potential.
To do this you must rearrange the equation above to solve it for the intrinsic rate of increase (r). For
example, suppose there were 3 fronds on day zero and 9 fronds on day five. What is the population’s
intrinsic rate of increase over this time period? Use the formula, Nt = Noert, where Nt = 9 and N0 = 3 and t
= 5 and solve for r. Thus r = (ln 3) / 5 or r = 0.220 per day or r = 22%.
Logistic Population Growth
Exponential growth does not continue indefinitely. If it did, one population would quickly cover the entire
surface of the earth. Growth is limited by resources such as light, nutrients, and space and other densitydependent factors. The abundance of resources determines the carrying capacity (K), the number of
individuals of a population the environment can support indefinitely. The logistic population growth
equation reflects the limiting effect carrying capacity has on r and N.
Logistic Growth Equation: ∆N/∆t = rN[(K - N)/K]
In the equation above the term ∆N/∆t reads as “change in the number of individuals as time changes.”
The first part of the equation, rN, is the amount the population would increase during exponential growth
during a specified time period, but the term [(K - N)/K] modifies this to reflect that population growth
slows as population size (N) approaches the carrying capacity
(K) of the environment. In other words, when the value of N is
very small, then [(K - N)/K] is almost equal to one and the
population grows nearly exponentially. When the value of N is
almost the same as K, then [(K - N)/K] is very close to zero, and
population growth slows to nearly zero. Although individuals
in the population continue to die, and others are born the
overall population size changes very little if at all. This
pattern is called logistic population growth and is shown in
figure 2.
The population increases exponentially at first (A) when
resources are abundant. When the number of individuals
equals half the carrying capacity, the population is growing at
its maximum rate (B). Once this number is attained, the
growth rate slows (C), and the graph approaches the horizantal line whose y value is the carrying
capacity.
About Lemna Minor
Lemna Minor, or duckweed, is a
member of the family Lemnaceae.
This tiny organism is ideal for
population growth experiments
because it reproduces quickly, requires
minimal space to grow, and requires
minimal maintanence. This
freshwater plant can be identified by
its buoyant, leaf – like structures,
called fronds (see figure 3a).
Duckeweed plants have one root which
hangs free in the water. Duckweed is
the smallest flowering plant and can
reproduce sexually by flowering and
releasing seeds, but seldom does.
More often, they rereproduce
asexually by vegetative budding (see figure 3b). New buds develop into fronds, sprout a root, and then
separate from the parent plant to produce a new plant. Therefore, the growth of a duckweed population
is best monitored by counting the number of fronds present. Lemna is found in still waters from
temperate to tropical zones, though it prefers waters around 25˚C.
On average fronds live four to five weeks. Due to its rapid growth rate, duckweed is utilized in a variety
of governmental and commercial practices. For example, The U.S. EPA requires companies that make
pesticides to determine how the chemicals affect aquatic plant biology. Many companies use duckweed
as the model plant, measuring a pesticides toxicity by observing its effect on the growth rate of the
duckweed.
Duckweed is also used to remove nitrogen and phosphorous from wastewater. Nitrogen and phosphorous
are plant nutrients that in high concentrations (as in wastewater) promote rapid plant growth. When
wastewater is released into the environment untreated, new plant growth can quickly clog waterways and
cause eutrophication. To remove nutrients from wastewater, Lemna plants are added to treatment tanks
to act as natural filters. As the plants grow, they take up nitrogen and phosphorous 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 water purification.
Procedure
During this lab, you and your classmates will test Lemna Minor’s population growth rate and carrying
capacity in a variety of growing treatments. The treatments that will be studied are conditions that may
exist in natural waterways where Lemna Minor is naturally found. Your class will test the following
conditions: salinity, phosphate levels, nitrate levels, growing space, and amount of shade. All groups will
also maintain a control that is standardized to a common set of growing conditions throughout the class.
Setup
Please see Mr. Britton to sign up for one of the available experimental treatments in order to ensure all
variables are tested by groups in your class. Once you have signed up for a variable, work with your
partner(s) to formulate a hypothesis stating the effect of your experimental conditions on the growth rate
of the duckweed population. Then work with other groups studying the same experimental treatment to
design an experiment to prove/disprove your hypothesis and write the procedure you and the other groups
will follow to conduct this experiment. All procedures must be written and approved before beginning
your experiment. Data that all groups must collect in order to compare how each experimental treatment
effects the various Lemna Minor populations is shown in the sample data table below. You will need to
construct separate data tables that are similar to this for each level of experimental treatment tested.
Each table will need to accommodate up to 15 days of data.
Sample Data Table
Treatment: 500% Salt
Day #
Daily Frond
Count
Trial #: 3_
New Frond
Growth
Days Since
Previous Count
Starting Date: 12/25/13_
Change in the # of
Fronds per Day
Change in the
number of Fronds Per
Day per Frond
0
3
1
3
0
1
0
0.00
3
5
2
2
1
0.33
4
6
1
1
1
0.20
Each day, count the number of fronds in each of your test tubes and record this as the “daily frond
count” for the day in your appropriate data table. Then calculate the difference between the daily
frond count and the previous count. Record the result as “new frond growth.” Divide the number in
the “new frond growth” column by the “number of days since previous count.” Record the result in the
column “Change in the number of fronds per day.” Divide the number in the “Change in the number of
fronds per day” column by the “daily frond count” total from the previous day. Record this data in the
column “Change in the fronds per day per frond.”
Tips for Designing Your Experiment
1. Make sure to maintain a control population to compare the results of your experimental
populations to.
2. Make sure you vary (manipulate) only one factor, in order to see what effect this one variable
has.
3. Test the effect of your chosen experimental condition over a range of values (at least three
values in addition to the control) but within a reasonable range. (For example testing salt
concentrations of 50% is unrealistic, since seawater has a salt concentration of 3.5%)
4. Align the values you choose to test with other groups testing the same type of experimental
treatment so that we end up with multiple trials at each experimental level for that
experimental treatment. (for example all nitrogen groups should test the same three nitrogen
concentrations in addition to a control.
5. Make sure that others that are testing the same experimental variable and levels are starting
with the same number of duckweed individuals in their initial populatojns.
6. Make sure everyone in the group knows what you are measuring/counting so that everyone will
make the same measurement(s) / counts, in the same way, each time.
7. Label your containers with your group name, period number and the experimental condition
being tested in the container. Consider making your labels visually unique so they are easy to
find each day when you need to record data and check on them.
Data Analysis
Estimating Intrinsic Rate of Increase (r) and Biotic Potential (rmax)
Create another set of data tables to record daily mean values for all trials conducted by your group and
any other group that tested the same experimental variable at the same levels of experimental treatment.
Use the mean values in these data tables to complete the calculations below.
1. Use the exponential growth equation to calculate the mean r-value for each of the duckweed
populations growing at each level of your experimental treatment for the entire duration of this
experiment. Show all calculations in the data and analysis part of your lab report.
2. Identify the interval of time when the growth rate is the highest for each treatment level (i.e. the
time when the # of new fronds per day per frond was the greatest). Highlight this value in each of
your data tables. This represents the period of time when your population was closest to its biotic
potential.
3. Use the exponential growth equation and this interval of time to calculate the estimated biotic
potential (rmax), for each level of experimental treatment for your groups experimental variable
Experimental Determination of K
1. Graph the mean number of fronds vs. time for each level experimental treatment.
2. The carrying capacity, K, is the point where the number of fronds appears to reach a constant
value.
3. Draw a horizontal line on your graph from the point on your graphed line back to the y-axis and
label this K for each population
Summarize your Calculated Data Values
Create a separate data table showing the mean r, mean rmax, and mean K values for level of experimental
treatment.
Class Data
Treatment
Type
Treatment
Level
r
rmax
K
Salinity
Phosphate (PO43-)
Nitrate (NO3-)
Treatment Type
Light
Space
Treatment Level
r
rmax
K
Post Lab Questions
Answer the following question at the end of your lab report.
1. Review yours groups growth curves for each level of treatment. Compare the growth rate between
levels of treatments.
a. Based on the differences in growth rates, what can you conclude about the effect of your
treatments on the duckweed population?
b. Label a point on the control group curve where the population growth rate was:
i. Exponential
ii. Increasing at a decreasing rate
2. Look at the class data table
a. Which habitat treatment is most conducive to fast population growth? Support your choice
with evidence from the data table.
b. Which habitat is most conducive to high carrying capacity? Support your choice with
evidence from the data table.
3. Based on the class data table, identify the treatment level for each environmental parameter that
is optimal for Lemna Minor.
4. Does a population’s intrinsic rate of increase (r) change with habitat, or is it an inherent
characteristic of the species? Explain using data from the class data table to support your answer.
5. Explain how birth and death rates are accounted for in population growth equations?
6. Nitrate and phosphate are both important nutrients for organisms. Does one of these nutrients
seem to have a greater effect on populations of Lemna Minor than the other? Support your
conclusion with references to the data and explain why you think one had a greater effect than the
other.
7. Review the class data to answer the following questions.
a. Which experimental treatment and what level of that experimental treatment produced the
greatest intrinsic rate of increase (r)?
b. Which experimental treatment and what level of that experimental treatment produced the
lowest intrinsic rate of increase (r)?
c. Imagine two populations of duckweed that start with ten individuals and grow for 100 days.
One population grows under the conditions identified in part a and the other is grown
under conditions described in part b. What is the difference in their population size after
100 days? Show your work.
Use the article to the right to help answer questions 8 – 9.
8. What evidence from your lab supports the articles assertion
that “conditions in Oso Lake do favor duckweed
populations”?
9. The article states, “…if the spread is not checked, the
takeover will negatively impact wildlife and other plant
species.” Describe one specific, negative impact one fish
and other aquatic vertebrates and explain how duckweed
could cause this effect.