Estimating Population Size: Mark-Recapture


You've probably had the experience of turning on your kitchen light to grab a late night snack, only to spot several cockroaches as they scuttle out of sight. Although you personally may not want to know how many more cockroaches are living in your house, the size of a population of organisms is a fundamental piece of information in evolution and ecology. Population size has critical consequences for potential rates of evolution (gene flow, founder effects) and vulnerability to extinction, and the ability to measure population size strongly influences our efforts to assess the effects of various environmental components (abiotic or biotic, including human impacts).

Although the most accurate way to calculate the size of a population is to simply count every individual in the population, this is rarely practical or even possible (how would you do this for your cockroach population?). The United States spends tens of millions of dollars in an attempt to obtain exact counts for the U.S. human population, but few ecologists have access to the money and manpower of the U.S. government! Thus, ecologists have devised a variety of methods to estimate the size of populations through sampling. Today we will introduce a couple of basic methods of estimating the size of a population. Different methods require different assumptions, are applicable to different types of populations, and vary in their accuracy and ease of use. One of the tasks confronting an ecologist wanting to estimate the size of a particular population is to determine which method best suits the population, as well as the resources of the ecologist!

Proportional sampling

This method works only if you know the size of the range of the population (Rp), and assumes that individuals are uniformly distributed throughout the population's range. Range can be measured in terms of area (e.g., for plants and ground-dwelling animals) or volume (e.g., planktonic organisms). Sample a region of known size (Rs) within the population's range. The proportion of the population's range that you've sampled is then Rs/Rp. With a uniform distribution, the number of individuals in your sample (Ns) should be the same fraction of the total population as the sampled region to the population's total range. That is, Ns/Np = Rs/Rp. Therefore, Np = (Ns Rp)/Rs.

Once we have an estimate of population size (Np) then we become interested in knowing how accurate this value is. With the proportional sampling method, you cannot assess accuracy with only one sample because you have no way to measure the variability in your sampling procedures. Thus, it is better to take several smaller samples, for which you can calculate mean and variance statistics.

Proportional sampling is perhaps the simplest method of estimating population sizes, but its restrictions (i.e., known population range and uniform distribution throughout the range) are rarely appropriate for natural populations. Thus, this method is most applicable to those laboratory conditions where population range size (e.g. beaker volumes) can be precisely determined, and steps can be taken to ensure uniform distribution prior to sampling.

See an example of proportional sampling at the end of this lab writeup.

Petersen Index

Clearly cockroaches are not equally likely to be found anywhere in your house: you are most likely to see them in the kitchen and bathrooms (warm, moist, and/or food), but you might suspect that most of the population is living in areas that are inaccessible to you for sampling. This nonuniform distribution means that proportional sampling probably will not give you a good estimate of population size in this case. Mark-recapture methods (such as the Petersen Index) would be a better choice, because they do not require that you know the range size of the population nor do they require that individuals be uniformly distributed throughout that range. The essentials of the basic mark-recapture method are to 1) capture a subset of the population, 2) mark the captured individuals somehow, 3) release them, 4) capture a second subsequent sample, 5) count the number of marked and unmarked individuals in the second sample, and finally 6) plug the numbers into a simple equation. Thus the variables are:

Np: this is the population size we wish to estimate

M: size of the first sample = number of individuals that are marked

n: size of the second sample of organisms

R: number of marked animals in second sample


The Petersen Index uses these data to estimate the size of the population as follows:

Np = (M*n)/R

The assumptions of this method are:

1. closed population (no emigration or immigration)

2. no births or deaths

3. marked and unmarked individuals mix randomly after the first capture

4. all individuals have an equal probability of capture (no sampling bias to marking)

To evaluate the accuracy of mark-recapture estimates of population size, we can calculate the standard error (this statistic is related to standard deviation and variance).


The true value of Np lies within (+/-) 2 standard errors of the estimate. In other words, the larger the SE, the less confidence you have in your estimate.

See an example of the Petersen method at the end of this lab writeup.

Today's Lab

For today's lab, you will work in groups of two. Each group will receive a small container that represents a population of giant mealworm larvae (Tenebrio molitor).

Fig. 1 Larva of the Giant Mealworm

Classwork (i.e., hand this in before you leave)

  1. Estimate the size of your population first using the proportional sampling method, then using the mark-recapture method. Hand in your counts, calculations and measures of population size and standard deviation (or standard error) for both methods.
  2. Which technique was more accurate?
  3. Which technique was more precise?

Method 1. Estimate the size of your mealworm population using the proportional sampling method.

  1. Determine Rp for the entire population.
  2. Take a bedding sample of known volume (Rs).
  3. Count the number of larvae in your sample (Ns). When you have finished counting, return the sample (including the bedding) to the original population.
  4. Calculate Np.
  5. Repeat steps 2 and 3 five times.

Method 2. Estimate size of your mealworm population using the basic mark-recapture method.

  1. Collect an initial sample of around 20 individuals. The volume of bedding removed does not matter here as it does for method 1.
  2. Mark each mealworm with a SMALL dab of liquid correcting fluid. Put marked worms in a holding container for several minutes to allow the fluid to dry. Return the marked worms to the main population.
  3. Give the marked worms 30 minutes to mix in with the unmarked larvae. If they seem to be too inactive we may need to gently randomize the population ourselves!
  4. Remove a second sample of larvae from the general population. Count the numbers of marked and unmarked larvae in this second sample.
  5. Calculate Np and SE using the mark-recapture data. How does this estimate compare to that obtained by proportional sampling?

Proportional sampling example. Population range = Rp = 10,000 m2. Sample range = Rs = 100 m2.


Number of specimens collected = Ns

Estimated population = Np = Ns *Rp/Rs
















Mean estimated population size: 1120 +192.4. 95% confidence interval: 735.2 - 1504.7

Peterson index example.

  1. First sample M = 200, which were marked and returned.
  2. Second sample n= 100, of which 15 (=R) were marked.
  3. Estimated population size Np = (M * n) / R = 1333.3
  4. SE = SQRT{(M*n)(M-R)(n-R)/[R2(R+1)]} = 295.6

95% confidence interval: 742.1 - 1924.5

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