Mark recapture lecture 2:

1

• Mark recapture lecture 2
• Jolly-Seber
• Confidence intervals

2

• Jolly-Seber
• For an OPEN population
• Repeatedly sampled
• Information on when an individual was last marked

LPB Colony size
Year
3
Open populations

• Individuals enter or leave the population between
  surveys

Survey 2
Survey 1
4
Catch nt animals Check if each animal is
marked Total unmarked (ut) Total marked
(mt) Mark all with code for this time
period Release St (equals nt if no handling
mortality)
NO
YES
5
Jolly-Seber Remember Petersen (biased) N C M
R
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Problem We dont know how many marked in
population (M) Sample 1 mark 21
animals Sample 2 mark 41 animals Sample 3
mark 46 animals How many marked at
beginning of sample 4?
Not 214146108, as some will have died or
emigrated
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Time 1
Time 2
Time 3
Mark 3, but 1 of these emigrates
Mark 2 more, no loss of marked animals
Mark 3 more, but 1 marked animal dies
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Time 4
How many marked animals are alive and present in
the population at time 4?
Marked animals in sample 4 (m4) 3
Marked animals not in sample 4 Total number
of marked animals in population
9
Time 4
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 Total number
of marked animals in population
6 marked at end of time 4 (S4)
10
Time 4
Time 5
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 Total number
of marked animals in population
6 marked at end of time 4 (S4)
11
Time 4
Time 5
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 (gt 1) Total
number of marked animals in population
6 marked at time 4 (S4), recaptured (R4)1
12
Time 4
Time 5
Time 6
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 (gt 1) Total
number of marked animals in population
6 marked at time 4 (S4), recaptured (R4)11
13
Marked animals alive but not found in sample 4
Recaptures after sample 4 (Z41) factor
accounting for animals missed or lost from
population (S4 / R4) 6/2 3
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 (gt 1) Total
number of marked animals in population
6 marked at time 4 (S4), recaptured (R4)11
14
Marked animals alive but not found in sample 4
Z4 S4 1 6 3 R4
2
Marked animals in sample 4 (m4) 3

Marked animals not in sample 4 (3) Total
number of marked animals in population (M4
6)
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Biased formula for number of marked animals in
population
Mt mt Zt St Rt
Unbiased formula for number of marked animals in
population
Mt mt Zt (St 1)
(Rt 1)
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Jolly-Seber Remember Petersen (biased) N C M
R Rearrange to N M (R/C)
Number marked in population
Proportion marked in sample
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Catch nt animals Check if each animal is
marked Total unmarked (ut) Total marked
(mt) Mark all with code for this time
period Release St (equals nt if no handling
mortality)
NO
YES
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Jolly-Seber Nt Mt (?)
mt nt
mt 1 nt 1
?
? (unbiased)
Number marked in population
Proportion marked in sample
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Confidence intervals

• A range around the estimate of a parameter which
• if repeated
• would include the true value of the parameter a
  certain percentage of the time

( )
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95 Confidence interval 19/20 of these
confidence intervals contain the true value
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Example of 95 confidence intervals 1500
Canadians polled March, 2004 Liberals 24 (21.5
to 26.5) Conservatives 16 (13.5 to 18.5) NDP
10 (7.5 to 12.5) Bloc Quebecois 8 (5.5 to
12.5) Other/dont know 28 (25.5 to 30.5)
Source Globe and Mail Sunday March 28th, 2004
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Difference between confidence interval and
variance Variance know distribution of data
points around estimate (mean) Eg. We measured
height of 500 British Columbians (1.4 m 0.2
m) Confidence interval only have parameter
estimate, have to guess what the distribution of
repeated measurements might look like Eg. We
obtained percentage of Canadians who said they
may change political parties, and estimated CI
(53 2.5)
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Step 1 Make an educated guess as to the
distribution (p 22 Krebs)
Is the ratio of R/C gt 0.10?
Petersen
Binomial
Is the number of recaptures, R gt 50?
Schnabel
Normal
Schumacher- Eschmeyer
Poisson
Jolly-Seber complex lognormal assumed, See Krebs
p 47
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Step 2 Calculate CI for either R or R/C (as
appropriate)
-see formulae in Krebs
Step 3 Insert upper and lower bound for R or R/C
into the formula for estimating population size
to obtain CI
For example, if CI for R/C is (0.083, 0.177), to
calculate CI for N by Petersen NM/ 0.083
(lower bound) NM/ 0.177 (upper bound)