Estimating Population Abundance: Mark-Recapture
Biol 301L
Ecologists are often interested in understanding population dynamics. That is,
how populations change over time in terms of genetic make up and number of
individuals. The size of any population is dependent on many things. Population size
and genetic make-up (gene pool) may change due to immigration/emigration, drift, and
factors influencing births and deaths. How do ecologists estimate the size of any
population of interest? This can be a perplexing issue, especially if the population is
quite large or cryptic. It would be inefficient in terms of time and effort to count each
and every individual, so ecologists estimate population size using several methods. The
methods used vary depending mainly on the organism of interest. Plants are sessile,
whereas most animals are mobile organisms. A line-transect estimate may be useful for
enumeration of sessile organisms, but not so for mobile organisms, or ones that are
difficult to observe. Mark-recapture is a useful method for determining the abundance
of many animal populations. There are several types of mark-recapture estimates
available. We will utilize the Petersen method of mark-recapture to estimate the
population abundance of Drosophila over time.
In general mark-recapture studies are done with or without replacement.
Individuals counted in a recapture sample may or may not be released back into the
population. In this lab we will introduce recaptured individuals back into the population.
Therefore, we will use a population estimator that assumes sampling with replacement.
The Petersen Method
The Petersen method is a simple technique, in that it is very intuitive. The size of a
population is estimated based on a proportion of marked individuals in a recapture
experiment. The formula for estimating population abundance based on the Petersen
method is:
N C

M R
therefore:
 CM
N
R
Where N = size of the population at time of sampling
M = # marked in the initial sample
C = total captured in second sample
R = number marked in second sample

N = estimate of population size at time of marking
Unfortunately, this estimate tends to bias the results by overestimating population size. It
may also be extremely biased with a small sample size. An unbiased estimator based on
the Petersen method was developed by Bailey (1952), where:

M (C  1)
N =
( R  1)
This estimator assumes sampling with replacement, and is nearly unbiased when the
number of recaptures (R) > 7.
Example:
If you mark 50 individuals (M) and catch at the second sampling a total of 100
(C), of which 15 are already marked (R), then the unbiased estimate of population size is:

5(101)
50(100  1)
N =
=
= 315.625 or 316 total individuals.
16
(15  1)
How accurate is this estimate? After all, this calculated value is not the true population
abundance.
As with most statistics, the biggest concern is the reliability of the estimator.
Confidence intervals can provide insight to this question. A confidence interval (or limit)
is a range of values that is expected to include the true population size a given percentage
of the time. Typically, a 95% confidence interval will be calculated, but you can
construct confidence intervals for any percentage. A 95% confidence interval will tell
you that 95% of the time, the true population size will fall within the calculated range.
The calculation is first scaled by the ratio of marked-recaptured individuals (R) to total
number captured in the second sample (C) The values obtained are then used in the
original Petersen estimator to calculate confidence limits for the estimated population
size.
The formula for calculating confidence limits for the estimated population size is:
1
 R  1  R
 
 C  C
R
 z
C  1
C




M 
Calculate the bottom portion of the equation first (use absolute values for any negative
numbers):
R
± z
C
 R  1  R
 
 C  C
(C  1)




Where: R = number marked in second sample
C = total captured in second sample
z= standard normal deviate for (1-) level of confidence. (This value is fixed
based on the level of confidence. For a 95% confidence level z= 1.96
In the previous example, C = 100, and R = 15.
15
± 1.96
100
 15  1  15


 100  100
(100  1)




= 0.15 ± 1.96
0.150.14 
99 
= 0.15 ± 0.0285
The ± symbol indicates two values should be obtained. That is 0.15 + 0.0285, and 0.15 –
0.0285. The scaled limits in this example are 0.178 and 0.122. To obtain a 95%
confidence interval for this estimated population, we use these limits in the original
Petersen estimator:

CM
N =
R
R
C
, and the Petersen estimate uses ,
C
R
you must take the inverse of the scaled limits. Therefore:
Because these values represent the scaled limits of
 1 
Lower 95% confidence interval = 
50  = 281
 0.178 
 1 
Upper 95% confidence interval = 
50 = 410
 0.122 
Remember, our estimate of population size was 316 individuals based on the data
presented above. Thus, you can say with 95% confidence that the true population size is
somewhere between 281 and 410 individuals. This is quite a large range, and therefore
our estimate is not very reliable. Is there anything we can do to increase our
accuracy?
Assumptions of the Petersen Method

If N is to be an accurate estimate of population size the following must hold true:
1. The population is closed, so that N is constant. (that is, the population should
not change between marking and recapturing.)
2. All animals have the same chance of getting caught in the first sample.
3. Marking individuals does not affect their catchability
4. Animals do not lose marks between the two sampling periods.
5. All marks are reported upon discovery in the second sample.
Drosophila Mark-Recapture calculations:
In the space provided below, indicate the values for the Petersen estimate based on
your mark-recapture data from your Drosophila population. Then calculate the
estimated population size using the unbiased estimator, as well as 95% confidence
limits for the estimated population size. Show your work.
Petersen parameters:
M=
C=
R=
Unbiased population estimate:
95% confidence limits for the estimated population size:
Is your estimate accurate? Why, or why not? Explain.