Solution-Determine the population of dandelions in your yard

Population Density Lab

NOTE: You will need a TI-83 or 84 graphing calculator for this lab. If you don’t own one, try to borrow one. If you cannot borrow one, there are free TI-83 calculator downloads online here:

Although density is usually an important population characteristic in ecological studies, it is often difficult to accurately measure. There have been many techniques designed for estimating population density, each with their own particular strengths and weaknesses. In this lab, we will examine two techniques for density estimation: “mark and recapture” and quadrat sampling. These are most appropriately used for mobile animal populations and sessile animal or plant populations, respectively.

Part A: Mark and recapture techniques

In these techniques, a sample of organisms, usually mobile animals, is captured from the population whose density we wish to estimate and an identifying mark is applied to them. In practice, these marks can be of many types, including radio collars in large mammals, leg bands in birds, fin clipping in fish, etc. The marked animals are released back into the original population, and after a period of time a second sample is captured. The size of the population is related to the fraction of individuals in the second sample that carry marks.

Slightly different mark-recapture techniques must be applied to populations that are open(meaning that individuals may migrate into and out of the population, be born, or die) orclosed (where the population does not change size during the study period).
You will be using a simulation to complete the mark and recapture activity.


1. Go to this link to complete the mark and recapture of rabbits:

2. Click “Trap and Mark”. Then “Retrap”. Then “Check Traps”.

3. You have caught an initial population of 10 rabbits and then retrapped. You will now tally the number of marked and unmarked rabbits in the 10 traps.

4. In question 1 of the Moodle lab report, indicate how many rabbits were marked and how many were unmarked in the entire population found in the 10 traps.

5. Using the values, calculate the original size of the rabbit population in the area by using the following formula:

M = number initially marked
CwM = number caught with marks
Cw/oM = number caught without marks

Calculated Population Size = M x (CwM + Cw/oM) / CwM

6. Record the calculated population size in question 2 of the Moodle lab report. Click on the “actual size” button at the bottom of the rabbit screen once all the traps have been opened. Record the actual population size in question 2 of the Moodle lab report. Answer question 3 in the Moodle lab report.

Part B: Quadrat techniques

For immobile animals or plants, our job of estimating density is made somewhat easier. Here, we could simply count up the number of organisms within our known study area and directly calculate the actual population density. In practice, however, it is usually impractical to count an entire population, so we usually do counts in a number of replicated small areas known as quadrats and use the average density in these quadrats as ourestimated (but not necessarily “real”) density.

1. Tear a sheet of paper into 20 slips, each approximately 4cm x 4 cm.

2. Number 10 of the slips from 1 to 10 and put them in a small container.

3. Label the remaining 10 slips from A through J and put them in a second container.

The grid shown below represents a meadow measuring 10 m on each side. Each grid segment is 1m x 1m. Each black circle represents one sunflower plant.

4. Randomly remove one slip from each container. Record the number-letter combination and find the grid segment that matches the combination. Count the number of sunflower plants in that grid segment. Record this number on the data table 1 in question 4 in the Moodle lab report. Return each slip to its appropriate container.

5. Repeat step 4 until you have data for 10 different grid segments (and the table is filled out). These 10 grid segments represent a sample.
Table 1.

Random Sampling Data

Grid Sigment (number – letter)

Number of Sunflowers





















Total Number of Sunflowers


Average (divide total by 10)


Total number of plants in meadow (multiply average by 100)


6. Find the total number of sunflower plants for the 10 segment sample. This is an estimation based on a formula. AID all the grid segment sunflowers together and divide by ten to get an AVERAGE number of sunflower plants per grid segment. Record this number in the table. Multiply the average number of sunflower plants by 100 (this is the total number of grid segments) to find the total number of plants in the meadow based on your sample. Record this number in your data table.

7. Now count all the sunflower plants actually shown in the meadow. Record this number in the data table. Divide this figure by 100 to calculate the average number of sunflower plants per each grid.

8. Answer questions 5-7 in the Moodle lab report.

9. In Table 2, questions 8 in the Moodle lab report, calculate the mean density per quadrat, and the variance in density per area. See the calculator supplement below for help on how to do this with your Ti83..


Sunflower Area

Mean # per quadrat




Mean # per m2


Variance per  m2


Ti 83 Instructions For Mean and Variance

Click “Stat”.
Click “Edit”.
Clear any data that’s in the calculator.
In L1 insert 12,2,3….10
In L2 Insert the number of sunflowers you found in each of the quadrat at that tree.
Click “Stat”.
Arrow over to “Calc”.
Choose option 1
Click “Enter”
Click “2nd”
Click L2 (This is the 2 key).
Click “Enter”_
X = mean
Sx= Variance

Part C Dispersion patterns

In aIDition to giving us information regarding population density, quadrat studies can also tell us something about the way the population is spatially distributed. In an evenly distributed population, each quadrat should contain roughly the same number of individuals. Thus the variability in the counts (as measured by the standard deviation or variance) should be close to 0 and the ratio of variance/mean should be close to 0 as well. Conversely, some quadrats scattered through clumped populations should have a large number of individuals (if you happen to “hit” a clump), while others will have very few. Thus, quadrat counts for a clumped population should have high variability and the ratio of variance/mean will be > 1. Randomly distributed populations follow a statistical distribution called the Poisson distribution in which the variance of measurements is equal to the mean of the measurements. In this case the variance in quadrat counts would be equal to the mean count and the ratio variance/mean ? 1. Thus, we can determine the spatial pattern of a population simply by knowing the mean number and variance found in counts of its density:

Variance/mean ratio Dispersion pattern

? 0 uniform
? 1 random> 1 clumped


Using your quadrat counts from the previous section, determine how the sunflower population is distributed. Answer questions 9 and 10 in the Moodle lab report.


1. How many rabbits were marked and unmarked after checking the traps?

2. What is the calculated population size? Round to the nearest whole number and show your work.

What is the actual population size?

3. Compare the calculated to the actual population size. Explain why they may not agree exactly.

What changes to the procedure would improve the accuracy of the activity?

4. Table 1.

Random Sampling Data

Grid Sigment (number – letter)

Number of Sunflowers





















Total Number of Sunflowers


Average (divide total by 10)


Total number of plants in meadow (multiply average by 100)


Total number of Sunflowers –

(count by hand)

Average number of Sunflowers –

(divide total by 100) Per grid

5. A lazy ecologist collects data from the same field, but he stops just on the side of the road and just counts the 10 segments near the road. These 10 segments are located at J 1-10. When he submits his report, how many sunflowers will he estimate are in the field? Show your work.

b. Suggest a reason why his estimation differs from your estimation.

6. Population Sampling is usually more effective when the population has an even dispersion pattern. Clumped dispersionpatterns are the least effective. Explain why this would be the case.

7. Describe how you would use Sampling to determine the population of dandelions in your yard.

8. Table 2: Average quadrat densities


Sunflower Area

Mean # per quadrat




Mean # per m2


Variance per  m2


9. Distribution of the sunflower population from your calculations.

Mean density =
Variance =
Variance/Mean =
Distribution Pattern =

10. What dispersion pattern did you find for the sunflower? Why do you think this is the pattern you see?

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