Ducwood lab
Duckweed Lab: An Experimental Study of Population Growth
Introduction (3/2 or 3/3)
How populations change over time, using genetics, allows us to understand how microevolution works. To understand the ecology of a population, we need to know how they grow or decline. There are two components that need to be considered in studying population growth. First is the data collection. Gathering data on an existing population and documenting the number of births and deaths can give us a picture of what is actually going on in the population. We can see if the population is growing or shrinking. The second component is using the data to model and predict how the population will grow or shrink in the future. Thus, understanding population growth has important implications in terms of conservation and management.
How a population grows or declines can easily be determined by counting the number of births and deaths in a given time. This can be determined by using the following equation:
∆𝑁 ∆𝑡 = 𝐵 − 𝐷
Where DN/Dt is the change in population size (N) over a given time (t). B is the number of births and D is the number of deaths, which is easy enough. However, this information is limited. It can only tell us what is going on now (what we are actually observing and what has occurred in the past), but it will not allow us to predict what will happen in the future. To be able to do this, we need to determine the birth and death rates per capita (or per individual). The per capita birth and death rates are symbolized by b and d, respectively. These rates are multiplied by the population number (N) because birth and death relies on how many individuals are in a population. Thus, the equation above can be modified to the following equation:
∆𝑁 ∆𝑡 =𝑏𝑁−𝑑𝑁
Now, the above formula can be simplified if we assume r to equal b – d as the per capita growth rate. Additionally, it would be helpful if we can determine the growth rate in very short time frames. This is because populations fluctuate regularly such that the growth rate in the first year may not the same as the growth rate in the second year. Thus, we can further modify the above equation to the following:
𝑑𝑁 𝑑𝑡 = 𝑟𝑁
Let’s assume, in a population, that the same amount of individuals are born (b) and die (d). This means that r = 0. If r = 0, then 0 * N is 0. This means that the population is not growing, and whatever N was will stay the same. If we assume that there are more individuals dying than are being born, this means that r < 0 (some negative number). This means that the population will decline. For example, if the birth rate is 0.5 and the death rate is 1, this will result in r being -0.5. This means that in a population of 100, dN/dt = -0.5 * 100 = -50, which leads to the population decreasing in size by 50 individuals (100 – 50 = 50). In contrast, if the birth rate is greater than
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Duckweed Lab: An Experimental Study of Population Growth
the death rate, r > 0. This will result in the population growing in size. If we were to graph this population over time, we would get a J-shaped curve (or an exponential growth curve). This usually happens when a population is just starting out. However, as the population increases, the curve tends to level out. This is largely because resources become limiting, but other ecological factors can apply. When this occurs, the graph will be S-shaped, which is a logistic growth curve. The population has reached its carrying capacity, which is designated by K. We incorporate K to the above equation in the following way:
𝑑𝑁 𝐾−𝑁 𝑑𝑡=𝑟𝑁+ 𝐾 -
Now, how do we determine what K is? K can be estimated from the data collected. If we observe that the population is no longer increasing or decreasing, the number of individuals in that population is K; the population has stabilized and reached its carrying capacity. Once we have all these information, we can use them to predict whether a population is decreasing, growing, or has stabilized. For the most part, ecologists are not worried about the latter two scenarios. What concerns ecologists mainly are the decreases in population size. If these patterns are observed, ecologists need to start thinking about conserving and managing the population so that it does not die out.
In this lab, we will model the growth curve of duckweed (Lemna minor), to determine what factors are necessary for its success. Duckweed is an excellent organism to examine growth because it is relatively easy to grow in a short amount of time. It is an angiosperm, but its main mode of propagation is asexual. New individuals (thallus) emerge out of existing individuals, which eventually break off and create other individuals. At some point, the population will reach its carrying capacity and we can determine what the factors are that limit its growth.
For this experiment, we will set up duckweed in two conditions: the first will consist of duckweed growing in distilled water and the second will consist of duckweed growing in distilled water with fertilizer. We will grow our duckweed populations for about a month, counting individuals twice a week. Based on this experiment setup, start thinking about what your biological hypothesis might be.
Materials
· lab coats
· gloves
· plastic cups (x7)
· labeling tape
· marker
· distilled water
· fertilizer
· disposable pipette
· duckweed
· toothpick
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Updated 12/03/20 Alejandrino 2
Methods
Duckweed Lab: An Experimental Study of Population Growth
1. Form a group of either three (3) or four (4) individuals.
2. Wear lab coats and gloves.
3. For the labeling, be sure to use the labeling tape so that we can use the cups more than
once.
1. Label three (3) of your cups with “A,” “B,” and “C.” These will represent the
control or distilled water treatments.
2. Label three (3) of your cups with “D,” “E,” and “F.” These will represent the
fertilizer treatment.
3. Label the last cup as the “counting cup.”
4. Except for the counting cup, fill the cups with 200 ml of distilled water and use a marker to indicate the water level on the outside of the cup.
5. For the three (3) fertilizer cups, add five (5) drops of liquid fertilizer using the disposable pipette. The fertilizer tends to settle, so you might want to shake the container, keeping in mind that the lid is on tight (note: the fertilizer smells really bad and you don’t want to get it on you).
6. Except for the counting cup, add 15 individuals of duckweed to the cups using a toothpick. If a thallus is white, it is dead. Try not to put them in the cups. If they are attached to a green individual, you can put them in the cup, but don’t count them. “Baby” thalli do not count unless they are about half the size of an “adult.”
7. Set your cups on a bench space along the side or back of the lab. In the counting cup, place your toothpick and disposable pipette so that you can use them again.
8. In three days (outside of scheduled lab times), your group is to count the number of thalli in each cup and record them in Table 1. Remember to count only the green ones as the white ones have died. You may take the dead ones out of the cups as long as there is no live ones attached.
9. Once you have finished counting your duckweed, refill the water up to the line you marked previously. Do not fertilize the treatments. They will only be fertilized once a week i.e., your scheduled lab day.
10. Continue this procedure for three weeks. Be sure you are wearing close-toed shoes, long pants, gloves, and a lab coat whenever you are working with your plants.
11. On the fourth week, count your duckweed populations one last time and record them into Table 1.
Table 1: Data sheet for recording duckweed population growth. A, B, and C represent the control or distilled water treatments, while D, E, and F represent the fertilizer treatments. Twice a week, count the number of individuals (N) in each cup and record them below.
control or distilled water distilled water with fertilizer GroupDayA B C D E F
0 3.5 7
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Duckweed Lab: An Experimental Study of Population Growth
10.5 14 17.5 21 24.5 28 K r
Data Calculations (3/30 or 3/31)
On 3/30 or 3/31, you will receive your group’s complete data from your professor. Now, you need to estimate K (the carrying capacity) and calculate r (the intrinsic rate of increase) for each of your population.
12. K is estimated by averaging the last two or more counts where the population has stopped growing and leveled off. If it seems like the population has not leveled off, use the last count as K. Do this for each of your population and record K into the “Group Duckweed Data” Excel spreadsheet.
13. To calculate r, remember that the basic logistic population growth equation is 𝑑𝑁 𝐾−𝑁
𝑑𝑡=𝑟𝑁+ 𝐾 -
If we solve for r, the equation can be rewritten as 𝑟=+𝑑𝑁-+1-+ 𝐾 -
or
𝑟=+ ∆𝑁 -+ 𝐾 - 𝑁∗∆𝑡 𝐾−𝑁
Remember that DN/Dt is the change in population size (N) over a given time (t). Thus, we are multiplying it to the inverse of the population size with respect to K. Now, r can be calculated for multiple, specific time intervals and averaged (see Table 2). Below are the detailed instructions to calculate r for one population.
𝑑𝑡 𝑁 𝐾−𝑁
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Duckweed Lab: An Experimental Study of Population Growth
1. Using Excel or some other spreadsheet program, create a table similar to Table 2 for each of your populations. The first column should be the days we collected data. For our lab, keep in mind that we collected data every 3.5 days. To simplify the work, assume that each 3.5-day interval is one (1) day. We can make adjustments later by multiplying 1 day by 3.5.
2. N are the population (size) counts per day. You can copy these over from the “Group Duckweed Data” Excel Spreadsheet.
3. DN represents the change in population size from the previous day to the current day. You can think of this as
∆𝑁 = 𝑁0 − 𝑁012
where Nt is the current day and Nt-1 is the previous day. Enter these differences
into the third column.
4. The fourth column is a division of DN from the third column by the product of
the population from the previous day (Nt-1, second column) and Dt, which is 1.
5. The fifth column incorporates the carrying capacity (K) that you averaged for the population. K is divided by the difference between K and the previous day’s population size (Nt-1). There is no need to calculate the last row of the fifth
column because this usually results in a large number, which can skew the data.
6. Finally, r (the intrinsic rate of increase, Column 6) is the product of the fourth and fifth columns. At the bottom of the column, average all the r values for the
population and enter it into your “Group Duckweed Data” Excel spreadsheet.
7. Repeat this process for the rest of your group’s populations.
Table 2: An example for calculating r based on the data collected, where Dt = 1 day and K = 337, which an average of the population size from Day 3 through Day 6.
Day
0 1
2 3 4 5 6
N D N D N/(Nt-1*D t) K/(K-Nt-1) r 15 - - - -
22 22-15=7 7/(15*1)=0.47 107 85 3.86
355 248 2.32 308 -47 -0.13 339 31 0.10 346 7 0.02 - -
0.47*1.05=0.49 1.07 4.13
337/(337- 15)=1.05
1.47 3.40 -18.72 2.48 11.62 1.17
r (average) 2.33 14. Once you have recorded all of your group’s populations’ K and r, upload the completed
file into the Group Duckweed Data link on Moodle.
Statistical Analyses (4/6 or 4/7)
Thus far, each group has uploaded their completed duckweed data onto Moodle. For statistical analyses, these data should be compiled together and reorganized. As with the previous lab, I have done the former but you have to do the latter. Before you begin, download the Class
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Duckweed Lab: An Experimental Study of Population Growth
Duckweed Data Excel spreadsheet from Moodle. Also make sure that K and r were calculated correctly.
15. First, calculate the average population of all groups’ Treatment 1 (all control; A, B, and C together) from the initial day.
16. Then, repeat the process for each day of Treatment 1. You should have a total of nine averages.
17. Do the same for Treatment 2 (fertilizer treatments or D, E, and F together).
18. Then, graph the growth curve of Treatment 1 and Treatment 2 using the class averages. Remember which axis the independent variable goes. The graph should have two growth
curves, which are Treatment 1 and Treatment 2 averages per day.
19. Next, perform an ANOVA comparing K between the treatments and construct a graph
that shows this comparison with the appropriate error bars.
20. Finally, perform an ANOVA comparing r between the treatments and construct a graph
that shows this comparison with the appropriate error bars.
Specific requirements for the final paper
Introduction: Below is an outline of how the Introduction for this paper should be organized and what information should be included. Be sure to use scientific literature to support your explanations.
· Start with a paragraph that broadly explains what the experiment is about. What is the main idea of the experiment and why is it important to test? Think about the big picture of this second part of the class.
· The next paragraph should be about growth curves. Explain what growth curves are and how they relate to the main idea of the experiment.
· The third paragraph should introduce the experimental system. Why is Lemna minor an ideal organism for the experiment? What can it tell us about growth curves and the main idea? How might the treatments affect the growth curves?
· The last paragraph should explain how experimenting on Lemna minor will help us understand growth curves and the main idea (What is your objective?). Don’t forget to include your biological hypothesis and make sure your references in the previous paragraphs back it up.
Results: Below is a list of specific figures that need to be included in the final paper.
· A figure showing the class average growth curves of Treatment 1 and 2.
· A figure comparing the class average of K between Treatment 1 and 2. Be sure to include
the appropriate error bars that match the results of the ANOVA.
· A figure comparing the class average of r between Treatment 1 and 2. Be sure to include
the appropriate error bars that match the results of the ANOVA.