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2.1 Estimating Population Sizes


Goals & Objectives:

After completion of this activity students will be able to:

  1. define population;
  2. differentiate between methods for estimating the size of a populations of mobile and sessile organisms;
  3. use quadrats to estimate the sizes of sessile populations;
  4. identify the appropriate quadrat size and sampling frequency for different organisms or environments; and
  5. use equations to calculate sizes of mobile organisms.


Environmental scientists often want to know the population size of a given species. A population is a group of organisms of the same species living in the same area at a given time. A species is a population or group of populations of a particular type of organism whose members share certain characteristics and can breed freely with one another and produce fertile offspring. This information can help to determine whether the population is stable, growing or declining. Knowing about populations can enable scientists to compare different ecosystems and allow policy makers to make better decisions such as whether to list a species as threatened or endangered.

Parameters that are critical to population studies are population size, the total number of individuals in the population, and population density, the number of individuals per unit area.  The most direct way to determine population size is to count all of the individuals, but for most populations a complete count is either not possible or not practical.  Several methods have been devised to estimate population size by sampling a portion of the population.  These methods vary depending on whether the organism being studied is sessile, unable to move from place to place (plants and some animals), or mobile, able to move around freely in the ecosystem (like most animals). For sessile animals or plants, estimating population size is somewhat easier than for mobile organisms.

Several techniques exist for estimating population size and density by counting the individuals in a sample, a small part of the total population, and extrapolating to the entire population.  One way to sample a large population is to use a quadrat, an ecological sampling unit of known area.  A square or rectangular sampling device may be used for small quadrats.  In general, we use the quadrat to limit our counting area to a manageable size.  A study will use a quadrat multiple times to perform counts in the region of interest.  The average density of individuals in these quadrats is used to estimate the population size in the area of interest.

In deciding how to sample a population, some choices must be made.  First, increasing the number of quadrats sampled will increase the accuracy of our estimate. But, we can only do so by spending more time and money.  Thus, we must make a tradeoff between the number of samples taken and the time and money spent.  Most researchers will base the number of quadrats they sample on how sparse or dense they expect the population to be and other factors about the biology of the organism of interest.  Usually at least 10 but as many as 30 quadrats are sampled.

The second choice deals with the size of the quadrats themselves.  They must be an appropriate scale.  Think about the size of quadrat you would want for a survey of dandelions compared to a survey of oak trees.  Would the same size quadrat be appropriate for both surveys?  Another consideration with the size of the quadrat deals with statistical methods.  In environmental science, statistics are used to define our confidence in the results of our studies and experiments.  The more accurate the samples are, the stronger the evidence of actual differences between sampled areas.  This is true for all types of samples, whether quadrats or the mark-recapture studies that are discussed later.  Accuracy in quadrats is often directly related to quadrat size.  As before, there is a trade-off between the accuracy provided by larger quadrats and time spent counting individuals in the larger quadrats.

The most commonly used method to estimate population sizes of mobile organisms is called mark and recapture.  There are several variations available, but we will use the simplest one, called the Lincoln-Peterson Index (so called because it was derived independently by Peterson in 1894 for estimating fish populations and by Lincoln in 1930 to estimate duck population sizes from hunters’ returns of leg bands). For this technique, a sample of the population to be studied is captured, marked and released to rejoin the population.  This establishes a ratio of marked animals to total animals in the population as shown in Equation 1.  A second sample of the population is then made.  The ratio of marked (recaptured) animals to unmarked animals in the second sample should equal the ratio of marked to unmarked animals in the whole population:

Eqn. 1



M = the number of animals marked and released

N = the size of the population

r = the number of marked animals re-captured in the second sample

s = the size of the second sample including both marked and unmarked animals.


Because you will know M, r, and s, you can calculate N, the size of the total population as shown in Equation 2.

Eqn. 2

Some important assumptions are necessary for this ratio to hold true:

  1. Marked individuals become randomly mingled with the rest of the population.
  2. Losses from or gains to the population due to deaths, births, immigration, or emigration between sampling periods are negligible.
  3. All individuals are equally likely to be caught.  That is, being captured once does not affect the probability of an individual being caught again.
  4. Marking does not affect the individuals.
  5. Samples are taken randomly.


It is often useful to know how different an estimated value (in this case, population size) is from the actual value. Percent error (also called percentage error) is often used. This is the difference between the estimated and actual values expressed as a percentage of the actual value as shown in Equation 3. To calculate the percent error for population estimates, find the difference between the actual population size and the estimated population size by subtracting the smaller of the two values from the larger. Divide the difference by the actual population size and multiply by 100. Note that this only works when the actual population size is known.

Error   Eqn. 3

Exercises 1 demonstrate2 techniques for determining the size of sessile organisms. Exercise 4 demonstrates techniques for determining the size of mobile organisms.

Activity 1:  Estimating population size of dandelions


The Dandelion grid can be found on Page 8 of this lab.

It’s important that quadrats be selected at random so that you don’t bias your sample.

If you have an application that allows you to generate random numbers, set it for a maximum of 150 and number the quadrats on the dandelion page from 1-150. Use your application to choose the number of quadrats specified in each activity. You can find a random number generator online.

If you do not have a random number generator available, you’ll need to follow these directions:

  1. Cut 25 slips of paper, each about the size of a postage stamp. Mark 10 slips A through J and put them into a container. Number the other 15 slips 1 to 15 and put them into a second container.
  2. The attached Dandelion Population Map grid represents your study area: a field measuring 10 m by 15 m.  Each grid segment represents a quadrat measuring 1 m on each side.  Each black dot represents a single dandelion plant.
  3. Randomly remove one slip from the letter container and one from the number container.  Record that letter-number combination in the data table below.  Find the grid segment that matches the combination and count the number of dandelion in Table 1.  RETURN THE SLIP TO THE APPROPRIATE CONTAINER! Shake the containers to randomly re-distribute the number and letter.
  4. Repeat step 3 until you have data for 5 different grid segments.  These 5 grid segments represent your sample for part 1. Record your results in Table 1 in the Data Sheets and Analysis section.

Dandelion Methods, part 2:

To examine the effect of increasing the number of samples taken on accuracy of the study your random number generator to select 20 grids (repeat step 3 from part 1 twenty (20) times), giving you samples for twenty grid segments.  These 20 grid segments represent your sample for part 2.  Record the data in Table 2 in the Data Sheets and Analysis section.

Activity 2: Birds at CCBC Essex

Dr. David Thorndill banded birds at CCBC Essex from 1982 until his retirement from CCBC. Data from these studies can be used to estimate the population size of dark-eyed juncos near Cub Hill in 1999. Dark-eye juncos are song birds that are more common in Maryland during the winter months. In Dr. Thorndill’s studies, birds were captured then released into the population. Each time birds were captured, additional birds were added to the banded population. For example, on 11 January, 8 new birds were caught and banded changing the total to 47 previously banded birds for the 16 January sample.

This table is repeated as Table 6 on the last page of the Data and Analysis section. You will calculate the total number captured and estimate the population size based on each day’s capture. The total number captured equals the number captured that were already banded plus the newly captured individuals. Use equation 2 to determine the estimated population size.


Table 5: Mark-recapture data for dark-eyed juncos in 1999
Date Previously banded (M) Caught, already banded ( r) Caught, new individual
11-Jan 39 14 9
16-Jan 48 4 7
23-Jan 55 2 8
30-Jan 63 8 2
6-Feb 65 6 5




Activity 1:  Estimating population size of dandelions


Table 1: Dandelion population survey, part 1

Sample number

Grid coordinates Number of dandelions in quadrat
Letter Number


Table 2: Dandelion population survey, part 2
Sample number Grid coordinates Number of dandelions in quadrat Sample number Grid coordinates Number of dandelions in quadrat
Letter Number Letter Number
1       11      
2       12      
3       13      
4       14      
5       15      
6       16      
7       17      
8       18      
9       19      
10       20      

Analysis Questions:

  1. How many quadrats are there in total? _______
  2. What is the actual number of dandelions? _______
  3. Calculate the average number of dandelions in each grid for the 5- and 20-quadrat samples. Although you didn’t count partial plants, round to the nearest 0.1 plants.

5 quadrat average: ________      20 quadrat average: ________

  1. Calculate the population estimates based on the 5- and 20-quadrat samples. Multiply the number of dandelions per quadrat by the number of quadrats.


Population estimate 5 quadrats: ______ Population estimate 20 quadrat ______


  1. Calculate the percent error for the population estimates.

Percent error for 5 quadrats  _______    Percent error for 20 quadrats  _______

  1. Compare the population estimates for the 5 sample and the 20 sample methods. Which was more accurate?  Why would this sample size be more accurate? Did your results match your expectations? Explain.
  2. Why is it important to choose quadrats randomly?
  3. What changes could you make to the procedures to reduce the error percentage?


Activity 2: Birds at CCBC Essex

Analysis Questions:

  1. Calculate the total number of juncos caught during each month and the estimated population size and record them in Table 5.


Table 5: Mark-recapture population estimates for dark-eyed juncos in 1999
Date Juncos previously banded (M) Captured, already banded ( r) Captured, new individual Total number captured on that date (s) Estimated population size (N)
11-Jan 39 14 9    
16-Jan 48 4 7    
23-Jan 55 2 8    
30-Jan 63 8 2    
6-Feb 65 6 5    


  1. What could you do to increase the accuracy of the estimated population size?


  1. The dark-eyed junco is a common bird.  However, if we were concerned about conserving its populations, what problems do you think would arise from the range of population estimates figured above?  In general, what do you think is the importance of accurately measuring population sizes?


  1. How realistic do you think the assumptions made about mobile populations are (refer to the introduction)?  What might happen in a real mobile population that would affect these assumptions, and thus your results?


Dandelion Population Map



= one Dandelion plant



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