Honors BiologyName______

Studying Population Size LabPartner Name______

Background:

In studying a population there are two broad approaches that can be taken, a census or a sample. A census describes when every individual in the population is counted for or measured. A sample is when a subset of the population is measured or counted and then statistics are used to extrapolate from this group to the whole population. The goal is to have a representative sample, so that the measurements from the sample are applicable to the whole.

A technique called sampling is sometimes used to estimate population size. In this procedure, the organisms in a few small areas are counted and projected to the entire area. For instance, if a biologist counts 10 squirrels living in a 200 square foot area, she could predict that there are 100 squirrels living in a 2000 square foot area. One type of sampling is quadrat sampling which we will discuss later on.

Another method used to determine population size is tagging or mark recapture methods. Tagging is frequently used on species like butterflies (namely monarchs) and fish. Sometimes the “tags” are stickers (in the case of butterflies), ear clips, or notches made in fins of fish. The purpose of these tags is to track migration, health, and range as well as to help determine population numbers of species in an area. Estimating the population size requires capturing individuals, marking them, and then resampling the population to see how many out of your sample are marked. It is assumed that after tagging the individuals fully mixed with the whole population and tagged animals are not different than untagged animals.By then taking random samples and determining the percent tagged, biologists are able to hypothesize the population of that species in that area.

Objectives:

1. Read about the mark and recapture technique and the sampling technique for estimating population size.

2. Estimate the size of a sample population using the mark-recapture technique.

3. Learn how sampling size effects outcomes.

4. Determine possible factors that may influence the technique’s accuracy.

Materials: Paper, pencil, calculator, beads of two different colors, plastic cup

Part 1 Simulating Mark and Recapture Technique

  1. Obtain a plastic cup with a bag containing beads of a light color in it. Remove the bag from the cup.
  2. Without looking in the bag, randomly remove 10 light colored beads from the bag. Make a straight line using the 10 light colored beads on your lab table. These 10 beads represent the 10 captured “bird-like” animals. You must now mark these animals.
  3. In real life, you would put a physical tag on them. In this lab, you will instead replace the ten light colored beads with ten darker colored beads. The 10 darker colored beads represent the “marked animals”. Obtain ten dark colored beads from the stock container of beads. Place the 10 dark colored beads in the bag. KEEP the 10 white beads on the lab table. You will not need them.
  4. Empty the contents of the bag into a plastic cup. The plastic cup with the light and dark beads represent a population of animals in their habitat.
  5. With your eyes closed, select 15 beads from the plastic cup one at a time. This is the recapture step. Record the number of “animals” recaptured (dark beads) for Trial 1 on the data table. Once you have done this return the 15 captured animals (light and dark) to the plastic cup.
  6. Repeat step 5 until you have done 10 trials.
  7. When the ten trials are completed, enter the total number captured and recaptured on the data table provided.

Data Table

Trials / Number Captured / Number Marked Recaptured (dark)
1 / 15
2 / 15
3 / 15
4 / 15
5 / 15
6 / 15
7 / 15
8 / 15
9 / 15
10 / 15
Total:

8. Now you will learn how to estimate population size after using the Lincoln-Petersen Index. It is based on the principle that if a proportion of the population was marked in some way, returned to the original population and then, after completely mixing, a second sample was taken, the proportion of marked individuals in the second sample would be the same as was marked initially in the total population. That is,

R (marked recaptured) M (marked initially)

______= ______

T (total in trial) N (total population size)

By rearrangement we can estimate the population size, N, by solving for N. Study the equation below.

N = M*T/R

Calculate the estimated population for 10 trials. Use the total values. Show all work. Circle your answer. Show answer in a whole number and do not round up or down. Why?

9. Now physically count the number of beads in your plastic cup. What is the actual population size? ______

10. Calculate the percent error. Remember, this number is always positive. Circle answer.

%Error = Difference/Actual) x 100

Difference = (Actual Population Size - Estimated Population Size)

9. Show your teacher your calculation and then, repeat the experiment and this time add 10 more data fields to the ten trials you already have. Record the new data in the table on the right.
10. Recalculate the estimated population for 20 trials using the Lincoln Index formula. Show all work as before.
11. Calculate the percent error. Circle answer. / Trial Number / Number Captured / Number Recaptured with mark
11 / 15
12 / 15
13 / 15
14 / 15
15 / 15
16 / 15
17 / 15
18 / 15
19 / 15
20 / 15
Total: / 300 / (add original data + new data)

Part 2 Simulating Sampling

  1. Recall from the background information the description of the sampling technique.
  2. Now answer the following questions:
  3. A biologist collected 1 gallon of pond water and counted 50 paramecia. Based on the sampling technique, how many paramecia could be found in the pond if the pond were 20 gallons?
  1. If you were in charge of a team given responsibility to determine the number of oak trees in a southern forest area located in Acadia National Park, how would you accomplish this task? Describe your plan in bullet form.

Analysis: In complete sentences, answer the questions in a separate sheet of paper. Answer in complete sentences. Be ready to discuss.

  1. a) What is the estimation of the population size after 10 and 20 trials?

b) Is there a difference between the 10 trials and the 20 trials. Explain.

c) What can you say about the number of trials that should be conducted in a real mark and recapture technique?

  1. What was the actual population size?
  2. Compare the actual size to the estimated size. Explain your observation.