Mark Recapture lecture 1
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Transcript of Mark Recapture lecture 1
Mark Recapture lecture 1An example from Sockeye salmon….
Mark recapture lectures
• Petersen method
• Schnabel method
• Schumacher-Eschmeyer
• Jolly Seber
Closed population
Open population
Overview of methods to help your reading of Krebs Chp 2
Closed populations
No individuals enter or leave the population between surveys
Survey 1 Survey 2
Open populations
Individuals enter or leave the population between surveys
Survey 1 Survey 2
What makes a population closed?
• Dispersal barriers• Philopatry• Large surveyed area
• Slow reproductive/death rate• Short time between surveys
What type of population are snow geese?
La Pérouse Bay
Snow Goose
Recording which birds are marked, and marking new birds
Year
LP
B C
olo
ny
size
Petersen method: Closed population
Catch several animals
Survey 1:
Mark all M animals
Return animals to population
Catch C animals
Survey 2:
Count recaptures (R)
Return animals to population
Survey 1:
M = 12
Survey 2:
C = 15R = 4
C = 15R = 4
What is the total population size (N)?
Note that the proportion marked in the populationequals the proportion marked in the 2nd sample
N = M C R
M = RN C
M = 12
C = 15R = 4
What is the total population size (N)?
Note that the proportion marked in the populationequals the proportion marked in the 2nd sample
N = (M+1) (C+1) (R+1)
M = 12
-1N = 13 * 16 5
-1
When would Petersen give you a bad estimate?
• Population not closed
• Marked animals likely to be re-trapped
• Marked animals likely to die
• Marks fall off
Schnabel method: closed population
Survey 2 Survey 3 Survey 4 Survey 5Survey 1
Essentially, Petersen estimates on multiple surveys
Schnabel method: closed population
Catch Ct animals
Survey t:
Mark Ut unmarked animals
Return animals to population
Record Rt recaptures
Schnabel method: closed population
Catch Ct animals
Survey t:
Mark Ut unmarked animals
Return animals to population
Record Rt recapturesWhat’s the relationship between Ct, Rt, and Ut ?
Ct = Rt + Ut
Schnabel method: example
Time (t) Ct Rt Ut
1 20
2 20 5
3 20 13
4 20 10
How many individuals marked by beginning of time 5?
Schnabel method: example
Time (t) Ct Rt Ut
1 20 0 20
2 20 5 15
3 20 7 13
4 20 10 10
How many individuals marked by beginning of time 5?
Schnabel method: example
Time (t) Ct Rt Ut
1 20 0 20
2 20 5 15
3 20 7 13
4 20 10 10
Σ = 58
Schnabel method: example
Time (t) Ct Rt Ut
1 20 0 20
2 20 5 15
3 20 7 13
4 20 10 10
Σ = 58
In general: Mt = U1 + U2..Ut-1
Schnabel formulas:
N = Σ (Ct Mt)
Σ Rt
( just weighted average of Petersen estimates!)
N = Σ (Ct Mt)
Σ Rt+1
Marked > 10% of population
Marked < 10% of population
Schnabel method: example
Time (t)
Ct Rt Ut Mt CtMt
1 20 0 20
2 20 5 15 20
3 20 7 13 35
4 20 10 10
0
48
Schnabel method: example
Time (t)
Ct Rt Ut Mt CtMt
1 20 0 20 0
2 20 5 15 20 400
3 20 7 13 35 700
4 20 10 10 960
Σ = 2060
0
48
Σ = 22
Schnabel method: example
Time (t)
Ct Rt Ut Mt CtMt
1 20 0 20 0
2 20 5 15 20 400
3 20 7 13 35 700
4 20 10 10 960
0
48
Σ = 2060Σ = 22
N = Σ (Ct Mt) = 2060 = 94
Σ Rt 22
Schnabel method: example
Time (t)
Ct Rt Ut Mt CtMt
1 20 0 20 0
2 20 5 15 20 400
3 20 7 13 35 700
4 20 10 10 960
0
48
Σ = 2060Σ = 22
What proportion of total population marked by end?
Scumacher-Eschmeyer method (for Schnabel experiment)
N = C M
R
R = 1 * M
C N
y = mx + b
Scumacher-Eschmeyer method (for Schnabel experiment)
N = C M
R
R = 1 * M
C N
RC
M
Slope = ?