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 = ?