ECOLOGY I: ANALYSIS OF ABUNDANCE.

 INTRODUCTION

You can get a Word-formated document of this page by clicking here. Additional information can be found here and here. Yet another growth model is found here (you can run or download the program). During this laboratory session you will explore the rate of growth in a simple ecosystem (rising bread) and will study a mathematical model of population growth. In addition, a method for determining the size of a natural population will be demonstrated.

EXERCISE 1 Population Growth.

All species have a high reproductive potential (capacity for population growth). Insects and fish, for example, typically lay several hundred eggs, while clams can release several thousand eggs. Normally, this huge potential is kept in check by the carrying capacity of the environment (when resources become too scarce to support further growth).

MATERIALS:

For the entire class: 1 package of dry yeast, 1/4 cup lukewarm water, 1 1/2 cups cool water, a teaspoon or so of sugar, 5 cups of flour, test tubes (one per student), rulers (one per student), vegetable oil, marking pens.

Calculators.

PROCEDURE:

1- Population Growth in a Simple Ecosystem. Your instructor has prepared a stiff dough by first adding a package of dry yeast to 1/4 cup of lukewarm water and sprinkling about 1/4 teaspoon of sugar into the mixture to get yeast growth started. After 10 min or so, the yeast mixture was added to 5 cups of flour and most of the remaining 1 1/2 cups of water was added to make a very stiff dough.

2- Obtain a test tube, ruler, and a small portion of the dough from the supply desk. Put a drop or two of vegetable oil in your test tube and roll the tube to distribute the oil on the interior wall. Pack a centimeter of dough in the bottom of the tube.

3- Record the starting time and dough height for the tube in the results section. For the remainder of the laboratory measure and record the height of the dough at 15-min intervals. The rising of the dough is caused by accumulation of carbon dioxide generated by the yeasts. Since the rate of carbon dioxide production is proportional to the yeast population size, the height of the dough is an indirect measure of yeast growth. If your laboratory is short and/or the room temperature is cool, your instructor may require you to continue your recording outside of the laboratory.

4- Graph the growth of your yeasts in the results section. Compare the shape of your population curve to the mathematical model outlined in Box 5.1.

EXERCISE 2 Mark and Recapture Techniques for Determining Population Size.

MATERIALS:

Classroom-Based Exercise: 500 - 750 dried beans of one color in a three pound coffee can with a lid. Your group will be assigned 50, 100, 150, or 200 beans of a contrasting color.

Field-Based Exercise: Forested site with appropriate species (pill bugs or snails work well), paint brushes, enamel paint (color coded by lab section if multiple sections will use the same site), meter tape, plastic Petri dishes.

Calculators.

Often it is not possible to directly count all of the organisms in a habitat to determine the size of a population. In these cases an estimate of the population size can be made by marking a segment of the population at one time and later recapturing the organisms (hence "Mark and recapture techniques"). The ratio of marked to unmarked individuals in the second sample can then be used to estimate the total number of organisms in the population. In this section of the laboratory we will simulate a population of organisms to demonstrate the methods used in a mark and recapture experiment. If time and climate permit, your instructor may have you perform the experiment at a field site.

BOX 1 POPULATION GROWTH CALCULATIONS.

Although the factors that control a population's growth are fairly complex, ecologists have found that some relatively simple equations do a reasonable job of modeling population growth. Many models have been put forward, but one of the more commonly-used equations is the logistic equation of population growth:

Where: N_t+1 is the change in population size (N) for the next generation.

r is the innate capacity for increase (a reproduction rate). It is equal to the birth rate minus the death rate (b-d).

Nt is the population size for the current generation.

K is the maximum size the population can attain (Sometimes called the carrying capacity).

The program used to generate the following figures is Populus. Click here to run the program and try your own population parameters. If you get an error message (Runtime error 200) click here. You can get your own version of Populus to run at home by clicking here. Indicate that you want to DOWNLOAD the file (not open it). Then choose or create a directory to save the file (usually \populus). Run pop34p in that directory and it'll unpack the Populus files. Then run populus.exe on your system. NOTE: Some new versions of Windows 95 and all versions of Windows 98 will not run populus. If you get an error message (Runtime error 200) click here. NOTE: If you hand in your Populus homework over the internet, you can copy the populus graphs by pressing Alt-PrintScreen to put the graph on the clipboard, and then paste it into your homework document.

The following figures show the effects of varying r while holding the starting population size (N0) and carrying capacity (K) constant. In (a) the population has a reproductive rate of 0.5 and smoothly approaches the carrying capacity in an S-shaped curve.

Figure (b) shows the effects of doubling the reproductive rate to 1.0. Note that the curve is still S-shaped, but that the population reaches its carrying capacity in fewer generations.

When rm is again doubled to 2.0, the population oscillates around the carrying capacity (c). Note that, although the oscillations are damped (they get closer and closer to K), the population doesn't settle down even after 200 generations (it still oscillates between 99 and 101).

In figure (d) the reproductive rate is increased to 3.0 and the population fluctuates wildly around the carrying capacity. These divergent oscillations eventually cause the population to go extinct.

BOX 2 ESTIMATING POPULATION SIZE BY MARK AND RECAPTURE.

The procedure for estimating population size begins with the capture of individuals at the study site. The organisms are then marked in some way so that they can later be identified by the investigator. Typical marking methods include ear tags, leg bands, dyes or paints, and clipping of fins or toes (ouch!). These animals are then returned to the habitat and allowed sufficient time to mix with the other members of the population, thus establishing an as yet unknown ratio of marked to unmarked animals in the total population. After an appropriate period of time, a second sample is collected to determine the ratio of marked to unmarked animals in the total population. Since a record is kept of the number of marked individuals in the first sample and the number of marked and unmarked animals in the second sample, this information can be used to estimate the total number of individuals in the population by the following formula:

N = Mt (Uc + Mr) Where: N = The estimated population size.

Mr Mt = The number of organisms marked, then released during the first sampling interval.

Uc = The number of unmarked individuals captured during the second sampling interval.

Mr = The number of marked individuals in captured during the second sampling interval.

As an example, assume that 50 animals were captured, marked, and returned to a population during the first sampling period (Mt = 50). On returning to the field, 60 animals are captured. Of these 60, 55 are unmarked (Uc = 55 and Mr = 5). Plugging these values into our formula:

N = Mt (Uc + Mr) = 50 (55 + 5) = 3000 = 600

            Mr                          5                  5

The estimated number of animals in the entire population is 600. 

PROCEDURE:

1- Laboratory Simulation. Work in groups of two or three, as indicated by your instructor. To simulate a mark and recapture experiment, your group has been provided with a coffee can with 500 or more dried beans. Your instructor will also give you 50 to 200 colored beans. Your job is to estimate the size of your population in the coffee can habitat using the methods described in Box 2.

2- Simulate the first sampling period by removing the same number of unmarked beans from the coffee can as you have marked beans. Keep these unmarked beans separate from the rest of the sample. Return a like number of marked beans to the coffee can and close the lid.

3- Shake the can to mix the beans in the habitat to simulate dispersal of the marked individuals among the rest of the population. Without looking, extract 50 beans from the can one at a time, shaking the can occasionally to maintain a good mix. Record the number of marked and unmarked individuals. Extract another 50 individuals and record the total number (out of the 100 you have extracted) that are marked and unmarked. Extract another 50 and record the proportion of marked for a total of 150 individuals. Use the formula in Box 5.2 to calculate the population size if 50 specimens for most species and study sites. When you return to the laboratory your instructor will collect your data and provide you with a total class count.

7- The following week you will return to the same site to re-collect animals. As before, move through the study site disturbing it as little as possible. Keep a count of both the marked and unmarked individuals as they are collected. If animals are marked with more than one color, count as recaptured only those marked with your section's color (animals with only another lab section's color should be counted as unmarked).

8- When you return to the laboratory your instructor will pool your class results and will give you the class totals for marked and unmarked animals. Estimate the number of animals in your sample using technique outlined in Box 5.2. Determine the population density by dividing the population estimate by the area (in square meters).

 REPORT SECTION _________________________ __________________

(Name)                      (Date/ Lab Section)

RESULTS AND DISCUSSION

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EXERCISE 5.1- Population Growth (Yeast Growth). Enter the height of the dough column in the following table. Then graph the shape of the population curve in the provided space.

Yeast Growth vs Time

EXERCISE 1- Population Growth (Mathematical Model). Run Populus to determine the changing rm, K, and N0 on the shape and final outcome of the population curve. Use both continuous and discrete models. Which variable seems to be most important in controlling the rate of population increase?

EXERCISE 2- Mark and Recapture Techniques for Determining Population Size (Laboratory Simulation). Enter the estimated population size in the provided blanks. Include both your own group's analyses and those of other class members to complete the following table

Mark and Recapture Simulation

Actual number of beans in the original population:_______

How does the amount of effort a researcher exerts during the initial marking of individuals affect the accuracy of a population estimate? Is there a similar exertion effect when organisms are recaptured during the second sampling day?

In an real experiment, the choice of the sampling interval is important. If the sampling interval is too short, the marked animals may not disperse into the general population. If too long, migration may affect results. What other factors do you think may affect the results if the sampling interval were either too long or short and what would these effects do to the population estimate (increase or decrease it)?

EXERCISE 2- Mark and Recapture Techniques for Determining Population Size (Field Study). Enter the your field data in the following table.

Species Sampled: _______________

Area of Study Site: _________ mฒ

Mark and Recapture Field Study (Your Data)

Mark and Recapture Field Study (Class Data)

Estimated Population Size: ______________

Estimated Population Density: ___________

What types of preliminary research do you think an ecologist should do before starting a sampling experiment?