Field Sampling/Ecology Name______________________

Regents Biology Per ________ Date___________

Lab # _______ Using Random Sampling

Introduction

A population is a group of organisms of one species living together in the same place at the same time. Scientists often study the number of organisms in a specific population. Population size is important for understanding how:

1. the distribution of the population is influenced by biotic (living) or abiotic

(non-living) factors

2. disturbance (from pollution, human interference, fire, weather…) affects

       a population
   3. to properly set hunting restrictions (fish, deer, turkey)
   4. to restore a damaged ecosystem or manage an existing ecosystem

Scientists cannot possibly count every organism in a population. Instead, the size of a population can be estimated by random sampling (gathering data from a randomly selected portion of a larger area or group). One way of taking random samples is by using the grid method. This involves dividing the entire study area into a grid (network of evenly spaced squares). A portion of the grid is sampled by choosing some of the squares at random. Only the organisms in these squares are counted, and the total population is calculated based on these squares.

Scientists must make certain assumptions when using this method. An assumption is something accepted as true that may or may not actually be true. The main assumptions of the grid method are that:

1. organisms do not move from one square to another.

2. squares are chosen randomly.

3. the sample taken is an accurate representative of the whole population.

The first assumption is valid if the grid method is used to measure sessile (stationary) populations such as plants and some animals (ex. barnacles), since they cannot move from one square to another. The second assumption is valid if the procedure ensures that each square has an equal chance of being chosen. The purpose for collecting the samples randomly is to avoid biasing the data. Bias is a tendency to favor something. Accuracy is the closeness of a measurement or estimate to the actual or true value. Since the accuracy of an estimate increases with the number of samples taken, the third assumption is valid if the sample size is large enough. On the other hand, very large samples take a long time to count, which can be a disadvantage.

In this activity, you will use the grid method to determine the number of wild lupine plants (Lupinus perennis) in a meadow and look at how data obtained by random sampling compare with data obtained by an actual count. You will use paper squares with numbers and letters to randomly select and count squares in the grid.

Wild lupine is a perennial plant in the pea family with beautiful pink to blue flowers. Its habitat is dry, sandy soils in sunny to partially shaded areas. The Karner Blue

butterfly (Lycaedes melissa samuelis) is an endangered species (both Federal

and NY State) which is dependent on the wild lupine plant.

Many of the lupine habitats, both in NY and other states, can no longer support lupine. Natural replacement of lupine by taller shrubs and trees (succession) and urbanization has reduced lupine numbers.

Karner Blue butterflies are completely dependent on lupine. In April, caterpillars hatch from last year's eggs and they feed on lupine leaves. When the caterpillars pupate, and become adult butterflies in May or June, they feed on nectar from lupine and lay their eggs on the plant. When the eggs hatch, they feed on lupine and the cycle continues.

The Karner Blue is experiencing a decline from lupine habitat destruction primarily due to human activities such as agriculture, urbanization, and fire suppression. Extinctions of entire populations of the Karner Blue have occurred around large cities both within NY State and other parts of the US. The most stable populations in NY State are in Saratoga County. In fact, we have a population of wild lupine growing in the meadow behind Shenendehowa. Methods used to establish or restore appropriate habitat conditions for wild lupine and the Karner Blue include mowing, controlled burning, and protecting habitat from development. Knowledge of population size of both wild blue lupine and Karner Blue butterflies help scientists and environmentalists make the best management decisions.

References:

US Fish and Wildlife Service NY State Dept of Environmental Conservation

http://www.fws.gov/ http://www.dec.state.ny.us/index.html

Purpose

The purpose of this activity is to investigate the effect of sample size on accuracy by:

using random sampling (by the grid method) to estimate the number of wild lupine plants in a meadow
conducting two trials to obtain estimates based on two different sample sizes.
determining the true (accepted) value by actual counting
comparing the two estimated values to the true value by calculating % error.

Materials

2 sets of paper squares (10 with numbers, 10 with letters)

2 cups/bags/envelopes

Procedure

The grid shown below represents a meadow measuring 10 m on each side. Each square in the grid is 1 m x 1 m. There are 100 squares in the grid. Each black dot represents one wild lupine plant.

Random Selection of Grid Squares to be Counted:

1. For Trial #1, you will sample and count only 5 squares (out of 100). To do so,

randomly remove one paper square from each container (one number and one

letter). Record the letter-number combination that you selected in Table 1. Return

all paper squares to the appropriate containers, shake to remix, and repeat this

process 4 more times. Record the five letter-number combinations in Table 1.

2. For Trial #2, repeat step 1, but this time count 10 squares (out of 100). Record the

ten letter-number combinations that you selected in Table 2.

Counting Plants (dots) in Grid Squares:

3. For each randomly selected letter-number combination (in both trials), find the

corresponding grid square in the diagram (on p.1) and count the number of plants

(dots) in that square. Record the number counted for each grid square (for both trials)

in Table 1 and Table 2.

Rules:

You may chose the same letter or number twice (so return paper squares back to container before you make your next selection)
Count all black dots that are in the grid square or on the top or right lines, but do not count black dots on the bottom or left lines.

Example:

5 dots should be counted in this grid square.

4. Find the total number of wild lupine plants in your sample for Trial #1 by adding up the

numbers you counted and recorded in Table 1. Record this number in the space

provided.

5. Find the total number of wild lupine plants in your sample for Trial #2 by adding up the

numbers you counted and recorded in Table 2. Record this number in the space

provided.

Data, Observations, and Calculations

Table 1 – Trial #1 Sampling Data (Sample Size = 5 Randomly Selected Squares)

*Letter*	*Number*	*Number of plants*

Trial #1 Total = ______________

Table 2 –Trial #2 Sampling Data (Sample Size = 10 Randomly Selected Squares)

*Letter*	*Number*	*Number of plants*

Trial #2 Total = ______________

6. In Trial #1, you determined the number of wild lupine plants in a sample of 5 grid

squares. To calculate the estimated total number of plants in the entire meadow

(which contains 100 squares), multiply Trial #1 Total by 20 as shown below:

Estimated total # of plants in meadow = # of plants in sample (5 squares) X 20

= _________ X 20 = Also record this

(total from Table 1) number in Table 3

This is your estimate of the total number of plants in the meadow based on random

sampling (of 5 squares). Record this number in Table 3.

7. In the Trial #2, you determined the number of wild lupine plants in a sample of 10

grid squares. To calculate the estimated total number of plants in the entire meadow

(which contains 100 squares), multiply Trial #2 Total by 10 as shown below:

Estimated total # of plants in meadow = # of plants in sample (10 squares) X 10

= _________ X 10 = Also record this

(total from Table 2) number in Table 3

This is your estimate of the total number of plants in the meadow based on random

sampling (of 10 squares). Record this number in Table 3.

8. Now, count all the wild lupine plants actually shown in the meadow. This is simply

actual counting (of 100 squares). Record this number in the space below. This

will be the true or accepted value. (If time is running short, ask your teacher what the

accepted value is).

Suggestion: mark each black dot as you count to avoid double counting or missing any black dots

Accepted Value* (Total # of plants in meadow by actual counting) =

* Also record this number in Table 3

9. Summarize your data by completing Table 3 below.

Table 3 - Comparing Sampling and Actual Counting

Method

Total number of wild lupine in Meadow (100 squares)

Percent Error

(see Q #10-11 below)

Trial #1

Estimated value based on Random Sampling of 5 squares (from Q #6)

Trial #2

Estimated value based on Random Sampling of 10 squares (from Q #7)

Accepted value based on Actual Counting of 100 squares (from Q #8)

10. What is the percent error in your Estimated Value for Trial #1? Use the formula

below to calculate percent error. Please show your work by filling in the

appropriate boxes. Also record your answer in Table 3 above.

% Error = Estimated Value (by random sampling) – Accepted Value (by actual counting) X 100

Accepted Value (by actual counting)

Note: the numerator (top number in your fraction) should be a positive number (absolute value; ignore negative sign if there is one). Your % error answer should contain a maximum of 3 numbers (round).

–

= X 100

= __________ X 100 = %

(for Trial #1; record in Table 3)

11. What is the percent error in your Estimated Value for Trial #2? Use the same

formula and procedure as for Trial #1. Also record your answer in Table 3 above.

% Error = Estimated Value (by random sampling) – Accepted Value (by actual counting) X 100

Accepted Value (by actual counting)

–

= X 100

= __________ X 100 = %

(for Trial #2; record in Table 3)

Discussion: Answer the following questions in complete sentences in the space provided.

1. a) What is a population?

___________________________________________________________________

b) Name 2 reasons why a scientist would want to count the number of organisms in a

population.

___________________________________________________________________

2. a) Define assumption.

___________________________________________________________________

b) What are the 3 main assumptions of the grid method of random sampling?

___________________________________________________________________

c) What requirements must be met in order for each of these assumptions to be valid?

___________________________________________________________________

3. What is the scientific name of wild lupine?

___________________________________________________________________

4. Describe the habitat of wild lupine.

___________________________________________________________________

5. Explain how Karner Blue butterflies are dependent on wild lupine.

_________________________________________________________

___________________________________________________________________

6. In New York State, where are the most stable populations of Karner Blue butterflies

(and wild lupine) found?

___________________________________________________________________

7. Name 3 methods used to establish or restore appropriate habitat conditions for wild

lupine.

_____________________________________________________________________

8. Define bias. ___________________________________________________________

9. Why did we use paper squares with letters and numbers in cups to select grid squares?

_____________________________________________________________________

10. a) Define accuracy. ____________________________________________________

__________________________________________________________________

Note: wait until we compare results with the other groups in the class before you answer the rest of this question.

b) Overall, which trial resulted in greater accuracy (lower % error)? _______________

c) Explain these results. _________________________________________________

__________________________________________________________________