GENERAL ECOLOGY
BIO 340
MARK-RECAPTURE
SAMPLING A MOBILE POPULATION:
THE MARK-RECAPTURE METHOD
INTRODUCTION
Thus far, we have used sampling methods designed to measure the density and
dispersion of sessile organisms (plants and galls). Obviously a different methodology
is necessary to measure the abundance of organisms that can move around. A large
number of techniques exist for sampling and estimating populations of mobile
organisms. This exercise examines one method, the mark-recapture method,
which is particularly well suited to the study of larger invertebrates and vertebrates.
In this exercise, you will perform a simulation that will allow you to examine the
effects of sampling effort on the final population estimate. You will also get the
opportunity to estimate the population size of CMU students using a benign markrecapture technique.
OBJECTIVES
In today's lab you will
•
estimate the population size of an unknown population.
•
learn the four assumptions underlying the mark-recapture technique.
•
calculate the likely error of your population estimate.
•
use the mark-recapture technique to estimate the size of the student body at
CMU.
KEY WORDS
Be able to define the following terms.
marking period
census population
marked cohort
natality
immigration
mortality
emigration
marking effort
sampling effort
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GENERAL ECOLOGY
BIO 340
MARK-RECAPTURE
BACKGROUND
Unlike plants, animals are often secretive and usually mobile. Consequently, simple
counts or plot sampling techniques are useless for determining population size.
Therefore, methods that involve marking individuals have been developed. The most
common of these methods is the Lincoln-Peterson Method. Individuals are captured
during a marking period and a mark is applied to their bodies. The marked
individuals are then released. After a certain period of time (long enough to allow the
animals to redistribute themselves randomly), individuals in the mobile population are
again captured and counted. This second cohort of individuals is called the census
population. Within this census population a certain number of individuals will carry
the mark which was applied earlier (marked cohort) and others will be unmarked. It
is important that you keep track of the number of marked and unmarked individuals in
the census population.
There are four very important assumptions that must be met in order for this
technique to accurately estimate population size.
1. All individuals in the population must have an equal chance of being caught (no
differences for age, sex, size, etc.).
2. There must be no input of new individuals to the population during the intervening
time interval. Changes in the population due to natality (births) and immigration
(outside animals entering the population) will dilute the marking effort
3. Marking must not alter an individual's behavior, make them more likely to
emigrate or be preyed upon, or influence their likelihood of being recaptured.
4. Emigration (individuals leaving the population) and mortality (deaths) must be
equal for marked and unmarked individuals.
The ability to meet these assumptions requires a great deal of knowledge about the
natural history of the species being studied. It is necessary to know such things as
the reproductive history of the population, mortality patterns, seasonal patterns of
activity and movement, biases in the capture of the animals, etc. It may turn out that
the species in question violates some or all of the assumptions. If this happens,
there are methods of estimating population size that take into account various factors
that might be altering the numbers in the population. While we will not study these
here it is important to know that they are available.
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GENERAL ECOLOGY
BIO 340
MARK-RECAPTURE
A large number of methods exist for sampling mobile populations. Birds may be
sampled with mist nets, fish with trap nets, mice with Sherman live traps, and caribou
by helicopter with a tranquilizer gun (Can you see Marlin Perkins now?). Regardless
of the sampling method, the calculation for estimating population size is the same.
One simply equates the proportion of marked individuals in the census population
(m/p) to the proportion of marked individuals in the unknown population (M/P). Thus,
our calculation formula is the following:
M m
=
(eqn. 1)
P p
where:
M = number of marked individuals
P = unknown population size
m =†
number of marked individuals recaptured (marked cohort)
p = number of recaptured individuals, both marked and unmarked
(census population)
The size of M represents the marking effort and the size of p represents the
sampling effort. The unknown population size (P) may be estimated by rearranged
the above formula such that P = (Mp)/m.
A BETTER ESTIMATOR
The Schnabel method simply extends the Petersen method to more than 1 resample.
The theory is exactly the same – N0 is estimated by the ratio of the number of marked
animals released into the population to the estimated proportion of marks in the
population. In fact, the Schnabel estimate of N0 is simply a weighted average of s
individual Petersen estimates, namely
N =
0
 (C M
ÂR
t
t
t
†
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)
(eqn 2)
GENERAL ECOLOGY
BIO 340
MARK-RECAPTURE
where Mt is the number of marked animals in the population just before the sample at
time t is taken, Ct is the number of animals in the sample at time t, and Rt is the
number of animals in the sample at time t that had a mark. The averaging over time
periods provides a more precise estimate of the population size and allows you to
evaluate if the assumptions have been violated. Not surprisingly, the assumptions for
the Schnabel estimate are the same as those for the Petersen method.
Example
The following data are from sunfish marked and released in an Indiana lake.
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Totals (S)
Ct
10
27
17
7
1
5
6
15
9
18
16
5
7
19
162
Rt
0
0
0
0
0
0
2
1
5
5
4
2
2
3
24
Newly marked
10
27
17
7
1
5
4
14
4
13
10
3
4
na
119
Mt
0
10
37
54
61
62
67
71
85
89
102
112
115
119
984
CtMt
0
270
629
378
61
310
402
1065
765
1602
1632
560
805
2261
10740
Note that the cells in the Mt column are the sum of the "new marked fish" from all
previous time periods. Thus, with equation 2, the estimated N0 is equal to 10740/24
= 447.5
DIRECTIONS
CMU STUDENTS
Each laboratory section will participate in a population census of CMU students. We
will use a modification of the mark-recapture technique. This modification (called the
Schnabel Method) employs multiple marking periods and a marked cohort that is
ever-increasing in size. The Tuesday morning section will begin marking students
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BIO 340
MARK-RECAPTURE
during class change time. Tuesday afternoon and Thursday sections will mark and
census students. The Friday morning section will only census students.
Groups of 3-4 students should position themselves at “strategic” points around
campus. Each group should approach traveling students and ask if they would be
willing to participate in the four-day study. Interested students should be marked by
attaching red flagging tape to their book bags or coats. Mark as many students as
possible and record the number marked. Also, record the number of intercepted
students already wearing a piece of red flagging tape.
The results from this mark-recapture exercise will be tabulated and returned to each
section the following week. You will be expected to discuss the population estimate
and the degree to which the four assumptions were met.
DISCUSSION QUESTIONS
1. Why are emigration and mortality acceptable in a sample population as long as
the rate is the same for marked and unmarked individuals?
2. How different are the mean populations estimates and standard deviations for the
various sampling and marking efforts? Explain.
3. Which sampling/marking effort gave you the most accurate results (i.e., smallest
%Error)? Why?
4. What are some of the practical constraints when using a high sampling effort in an
actual field study?
5. How would a biologist determine how many organisms to mark in order to
generate a reliable estimate of P?
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GENERAL ECOLOGY
BIO 340
MARK-RECAPTURE
CMU STUDENT CENSUS
Lab section:_________________
newly marked
(M)
number
unmarked
Campus location:____________________
number
recaptured (r)
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