Zoo 511 Pop Dy Lab
MARK - RECAPTURE POPULATION ESTIMATION
Purpose:
(1) To understand why population estimation in general and mark-recapture in particular are important for
fisheries ecology and management.
(2) To examine the precision and accuracy of the Petersen, Schnabel, and Jolly-Seber methods on laboratory
populations of known size.
Accurate estimates of population parameters for mobile animals can be obtained by mark-recapture methods.
These methods all make a series of assumptions about the population being sampled, and if these
assumptions are not correct the resulting estimates may be biased. In this exercise we will illustrate the use
of two of the common mark-recapture methods for artificial populations of known size in the laboratory. We
will also examine the effects of sample size and assumption violations on the resulting mark-recapture
estimates. We will apply the ideas illustrated using artificial populations (beans) to real world ecology and
management questions.
(1) Petersen Method:
You are a biologist working for the Wisconsin DNR. You are in charge of setting the walleye harvest
regulations on Crystal Lake. Management policies dictate that you must obtain a population estimate of
walleye and calculate the 95% confidence intervals. You will then take the lower 95% confidence interval,
and allocate 30% of that for harvest. You have limited resources to conduct this and other population
estimates, and you would be able to conduct more mark-recaptures on other lakes if you were able to use a
smaller sample size for your recapture sample. You are also interested in the effects of releasing walleyes
where they were caught and allowing them to mix throughout the population, vs. releasing them all in the
same location.
We will use mark-recapture techniques to estimate the number of walleye (beans) in Crystal Lake (a
container). At the end of this exercise, you will count the beans to obtain the actual population size in order
to answer the questions. For this experiment, get a container marked “Crystal Lake”, containing some
number of yellow beans. You will need to add 150 “marks” to this population (M) by adding 150 green
beans. You will sample this lake using two different sampling sizes (150 and 15), and with and without
random mixing.
Note that this is sampling without replacement. This means that you do not pick up a single bean, record if
it is marked or not, return it to the bucket before picking up another bean. If you had done this, it would be
called “sampling with replacement”. Instead, put the bean aside! With this sampling protocol, there is no
chance of recording the same individual bean multiple times. Then, at the end of the sample period put the
marked individuals back into the population for the next experiment.
(a)
Small sample size

Mix the beans thoroughly before you sample

Take a haphazard sample of 15 (C) beans from the bucket.

Count and record how many are marked (R).

Return all beans to container
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Zoo 511 Pop Dy Lab
(b)
Large sample size

Mix the beans thoroughly before you sample

Take a haphazard sample of 150 (C) beans from the bucket.

Count and record how many are marked (R).
(c) Unequal catchability – large sample

Return the unmarked beans from the previous sample first, then return the marked beans to the jar
last (i.e., put them on top), and don’t mix.

Without mixing before you sample, take a haphazard sample of 150 beans

Then count how many are marked (R). Write this down.
d) Repeat (c) with a sample size of 15.
Using the Excel spreadsheet (Q1), enter the number of marked fish (M – always 150 in this case), the
number of fish sampled and examined for marks (C- your sample size), and the number of recaptures (Rhow many of your sample were marked). This spreadsheet contains equations in the highlighted cells - DO
NOT CHANGE THESE EQUATIONS! They will automatically calculate the estimated population size,
variance, the 95% confidence limits, and recapture rates (R/C) for each of your samples.
Once you have completed the above equations, count the number of yellow beans in your container. Your
true population size is the number of yellow beans plus the number you marked (150).
Answer the following questions:
What was the effect of sample size on your population estimates? On the confidence intervals?
Given the protocol for setting walleye harvest levels, would you recommend using the small or large sample
size and why? List one advantage of using the sample size that you DID NOT choose.
What happened when you sampled without mixing the “population”? What was the effect of sample size in
this case? What happened to your recapture rate?
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Zoo 511 Pop Dy Lab
What are some biological reasons that a situation of non-mixing might occur with a mark-recapture study?
Choose the population estimate in which you have the most confidence. Calculate 30% of the lower 95%
confidence interval. This is the portion of the population you will allocate for harvest. How confident do
you feel in this management decision? What would you do differently to feel more confident?
(2) Petersen method – segregated by length
This is a technique that can be used when you are interested in different segments of a population
(segregated by sex, length, etc), or when you have reason to believe that catchability might vary among
these segments.
You are a graduate student researching a newly created marine protected area (MPA) in the Philippines.
Your task is to develop a baseline population estimate for groupers inside the reserve, for comparison
with future samples of populations in and out of the reserve. You are particularly interested in small
groupers, because you believe that groupers are not reproducing successfully, but are concerned that
small fish are somewhat less vulnerable to your sampling gear than mid-sized or large groupers.
Therefore, you will segregate your population estimates into three size classes, and obtain population
estimates for each segment (as well as the population as a whole).
For this experiment, use a container labelled “MPA”, containing 3 sizes of groupers (beans). Remove
100 beans. Mark all fish (beans) using an elastomer tag (sharpie). Record in your Excel spreadsheet
(Q2) the number marked (M) from each size group. Be sure the marks are clearly visible!
Return the marked fish to the reserve. Allow them to redistribute and intermingle with non-marked fish
(shake up the beans). Capture 200 fish. Record the number collected from each size category (C), and
how many were marked (R). The spreadsheet will automatically calculate population parameters for
each length class, the total when all length classes are summed, and the total if the length classes are not
segregated.
Count your beans, noting the number from each size class.
Answer the following questions:
What are the population estimates for each size group? Does one group appear to be less precisely estimated
than others?
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Zoo 511 Pop Dy Lab
Compare your population estimate of the population as a whole (without length segregation) to your
combined estimate of the separate length classes. Are they different? Which one is more accurate? Which
is more precise?
What are some biological reasons that catch rates might differ among size classes? What about among
sexes?
(3) Jolly-Seber Method:
This technique is applicable to open populations which are sampled many times over a long time period.
This is a much more complicated method of mark-recapture than the previous two. You will need to be very
careful about entering your data correctly into the appropriate Excel worksheet.
You are an ecologist working with Trout Unlimited. You believe that brook trout are being harvested from
several nearby trout streams before they can reproduce, thus resulting in population declines. You are able to
close one stream to fishing, while a nearby, similar stream remains open. You want to estimate population
size, survival rates, and new recruits in each of 5 months for each population. For the sake of learning, we
will know exactly the recruitment and survival rates for these populations, and evaluate our ability to
estimate them. Of course, in a real situation you would not know the true values of these parameters!
Join up with one other group. Pick one group to sample the harvested population, and one group to
sample the unharvested population. Each group will sample one population, and then you will share
results. Both groups will also need a supply of unmarked beans, and an area to hold “mortality” beans (see
below). The unharvested population is increasing in size, while the harvested population is declining. The
unharvested population starts at a population of 20, and the harvested population starts at a population of
200. In each case, the sequence of operations is as follows:
MIX — SAMPLE RANDOMLY — COUNT MARKED AND UNMARKED AND RECORD WHEN
LAST MARKED — MARK ALL BEANS UNIQUELY FOR THAT TIME PERIOD (INCLUDING
THOSE THAT ARE ALREADY MARKED) — RETURN ALL BEANS — MIX WELL—- REMOVE
RANDOMLY (=mortality) — ADD UNMARKED BEANS (=births) -- REPEAT.
The 'remove randomly' represent emigration and mortality from harvest, predation, disease, etc. and these
beans are set aside because in the real world you would never see these animals. The 'add unmarked'
represents births and immigration.
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Zoo 511 Pop Dy Lab
In each experiment the population size, survival rate and new recruits are known for each sample time. You
can thus compare the estimated population parameters from the Jolly-Seber model with their known values.
Note that the sequence above will be repeated 7 times for each population, representing seven different
months of sampling.
Each group will do one of the following two experiments:
Exp
Starting Population
Size
Harvest
200
Time
Size
Sample Remove
(Deaths)
Add Unmarked
(Births)
1
50
44
0
2
50
35
0
3
40
40
0
4
30
32
0
5
20
18
0
---------------------------------------------------------------------------------------------------------------------Exp
Starting Population
Size
No harvest
20
Time
Size
Sample Remove
(Deaths)
Add Unmarked
(Births)
1
8
2
18
2
18
3
34
3
27
7
60
4
45
11
105
5
50
18
198
Record your data as you proceed in the table appropriate to your population for Question 3 (harvest or no
harvest), filling in one column of the table for each of the seven samples. For each sampling period, you will
record the number of fish marked in each of the previous time periods and the total number of fish sampled.
For your first sample, there will be no marked animals, and in each time period you will mark every fish you
catch. Be sure to use a unique mark for each sampling period, so when you catch a marked fish, you
know when it was last marked! If you catch a marked fish, record when it was LAST marked, and then
mark it again with the mark appropriate to that time period. Once you fill in the matrix of marked fish and
the total number of fish caught, the parameters in the highlighted cells will fill in automatically.
Exchange your data with that of the group who did the other experiments. Answer the following questions:
How do your estimated survival rates compare to the mortality you know you inflicted? Do your mortality
estimates vary over the sampled months?
How does the population that is harvested compare to that which is unharvested? Which parameters are
different? Which are the same?
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Zoo 511 Pop Dy Lab
Why can’t you estimate survival in the first and last years? Look at (but don’t change) the equations in the
cells where survival is estimated to help you answer this.
What do you conclude about the effects of fishing on these populations?
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