LINCOLN-PETERSEN ESTIMATES FOR CLOSED POPULATIONS
AND JOLLY-SEBER ESTIMATES FOR OPEN POPULATIONS
1. Lincoln-Petersen estimates of population size are based on a simple ratio and
depend on the assumption that the population is closed to emigration,
immigration, births or mortality during the sampling period.
If we capture and mark a sample of individuals, then release them and after they
mix with the entire population we can estimate the size of the entire population
using the following equation:

N C
 ,
M m

where N is our estimate of population size at the time of the original sample,
M is the number of individuals released on the first occasion, C is the size of the
second sample we capture and m is the number of marked animals in the second
sample. This formula is intuitive; the ratio of total population size to the number
of marked individuals in the original sample should be the same as the ratio of the
size of the second sample to the number of marked individuals in the second
sample.
a. Remove 40 beans from your jar and mark each of the beans you remove with
a black mark. Replace the beans and thoroughly mix them. Remove a second
sample of 40 and record the number of marked beans in your second sample.
Estimate the size of your population using the above equation.

M  1C  1  1 . Calculate this
The unbiased estimate of N is: Nˆ 
m  1
m
estimate. One estimate for the confidence intervals for the ratio
C

(proportional to N ), is given by
 
 
m
m
m   1  f  C 1  C
  z
C  
C 1
 

1 
.
 2C 


Where f is the ratio m/M, i.e., the proportion of the population sampled in the
second sample. z is 1.96 for p = 0.05. Calculate the confidence interval for

your estimate of N .
b. Replace the beans you used in experiment a. Draw a sample of 80 beans and
mark them with a red mark. Replace these beans and draw a second sample of
80. Repeat the calculations form part a. How does the estimate and its
precision compare with those of part a?
2. We’re going to perform a simple capture-recapture experiment using the JollySeber method for open populations. We’ll simulate mortality by removing beans
between samples. We will base our estimates on five samples of 30 each.
Because the Jolly-Seber approach requires more detailed information about the
pattern of captures it is necessary to individually mark beans. So, place a unique
marker on each bean in each sample before you place it back into the
“population”. Once a bean is uniquely marked it doesn’t need to be marked
again.
a. Remove a sample of 30 beans and mark each one with a unique number.
Replace these beans, mix thoroughly and remove 10 beans to simulate
mortality. Draw a second sample of 30, record the beans that were
previously marked and mark each of the new beans with a unique number.
Return the sample to the population, mix and remove the 10 “mortalities”.
Repeat this process three more times for a total of five samples.
We’re going to want to produce an M array like the one we saw in class.
Time of last capture
1
1
2
3
4
5
6
7
8
9
10
Total marked (mt)
Total unmarked (ut)
Total caught (nt)
Total relaeased (st)
2
15
3
1
15
4
0
0
37
Time of Capture
5
6
7
0
0
0
1
0
0
2
0
0
61
4
1
75
3
77
m6
8
0
0
0
1
2
4
69
9
0
0
0
0
0
0
0
8
10
0
0
0
0
0
0
0
1
14
76
15
91
90
8
11
19
19
15
12
27
26
R6
0
22
22
21
15
26
41
41
16
32
48
46
37
45
82
82
64
25
89
88
79 81
22 26
101 107
99 106
11
0
0
0
0
0
0
0
0
0
19
19
3
22
22
We need to produce a capture history for each individual we capture. These will look
like the following:
Z6
Individual
1
2
3
4
5
…
40
41
History
10111
11011
10000
11001
10011
…
00011
00010
We can use the pattern of captures to calculate the values in the m array. For example of
the individuals captured on occasion one, two were recaptured on occasion two, one was
recaptured first on occasion three, and one was first recaptured on occasion four. Two
individuals were released on occasion two, etc. Use your capture histories to produce an
m-array and use the formulas below to calculate number of marked individuals:
s  1Z t  m .
Mˆ  t
t
Rt  1
Estimate population size as:
population that is marked.

 M
N 


, where  is the estimate of the proportion of the