slide1 l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Mark recapture lecture 2: Jolly-Seber Confidence intervals And a wee note on bias PowerPoint Presentation
Download Presentation
Mark recapture lecture 2: Jolly-Seber Confidence intervals And a wee note on bias

Loading in 2 Seconds...

play fullscreen
1 / 26

Mark recapture lecture 2: Jolly-Seber Confidence intervals And a wee note on bias - PowerPoint PPT Presentation


  • 217 Views
  • Uploaded on

Mark recapture lecture 2: Jolly-Seber Confidence intervals And a wee note on bias . Jolly-Seber For an OPEN population Repeatedly sampled Information on when an individual was last marked. LPB Colony size. Year. Open populations.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Mark recapture lecture 2: Jolly-Seber Confidence intervals And a wee note on bias' - brone


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Mark recapture lecture 2:

  • Jolly-Seber
  • Confidence intervals
  • And a wee note on bias
slide2

Jolly-Seber

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

LPB Colony size

Year

open populations
Open populations

Individuals enter or leave the population between surveys

Survey 2

Survey 1

slide4

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

Question:

What is formula for proportion marked?

slide5

Jolly-Seber

Remember Petersen (biased):

N= C M

R

slide6

Problem: We don’t 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 21+41+46=108, as some will have died or emigrated

slide7

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

slide8

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

slide9

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)

slide10

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)

slide11

Time 4

Time 5

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1

slide12

Time 4

Time 5

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1

slide13

Time 4

Time 5

Time 6

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1+1

slide14

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1+1

slide15

Marked animals alive but not found in sample 4

= Recaptures after sample 4 (Z4=1)

x

factor accounting for animals missed or lost from population

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1+1

slide16

Marked animals alive but not found in sample 4

= Recaptures after sample 4 (Z4=1)

x

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 (> 1)

=Total number of marked animals in population

6 marked at time 4 (S4), recaptured (R4)=1+1

slide17

Marked animals alive but not found in sample 4

= Z4 * S4 = 1* 6 = 3

R42

Marked animals in sample 4 (m4) = 3

+ Marked animals not in sample 4 (=3)

=Total number of marked animals in population

(M4 = 6)

slide19

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)

slide20

Jolly-Seber

Remember Petersen (biased):

N= C M

R

Rearrange to:

N = M

(R/C)

Number marked in population

Proportion marked

in sample

slide21

Jolly-Seber

Nt = Mt

(?)

Number marked in population (t)

Proportion marked

in sample t

slide22

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

slide23

Jolly-Seber

Nt = Mt

(?)

mt

nt

mt +1

nt + 1

? =

? (unbiased) =

Number marked in population

Proportion marked

in sample

slide24

Question:

m5 = 21

S5 = 9

R5 = 4

Z5 = 10

n5 = 43

What is N?

M5 = 21 + 10*(9+1) = 21+20 = 41

(4+1)

Proportion marked in sample

= (21+1) = 0.5

(43+1)

N5 = 41/0.5 = 82

slide25

Step 1: Make an educated guess as to the distribution (p 22 Krebs)

Y

Petersen

Is the ratio of

R/C > 0.10?

Binomial

Is the number of recaptures, R > 50?

Schnabel

Y

Normal

Schumacher-

Eschmeyer

Poisson

Jolly-Seber: complex lognormal assumed,

See Krebs p 47

slide26

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:

N=M/ 0.083 (upper bound)

N=M/ 0.177 (lower bound)