Survival Estimation Using Estimated Daily Detection Probabilities Benjamin P. Sandford Fish Ecology...

Survival Estimation Using Survival Estimation Using Estimated Daily Detection Estimated Daily Detection

ProbabilitiesProbabilities

Benjamin P. SandfordBenjamin P. Sandford

Fish Ecology DivisionFish Ecology Division

NOAA FisheriesNOAA Fisheries

NOAA Fisheries

http://www.nmfs.noaa.gov/

• Steve Smith – statistical development and programming

• Steve Achord and PTAGIS – data

• COE and BPA - funding

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AcknowledgementsAcknowledgements


General ProblemGeneral Problem

CJS may not be the best survival estimation technique in certain circumstances:

1) Concurrent temporal changes in detection and survival probabilities;

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1) Concurrent temporally dynamic detection and survival probabilities;

2) Cohort has small sample size but additional data available to estimate detection probability; or

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1) Concurrent temporally dynamic detection and survival probabilities;

2) Cohort has small sample size but additional data available to estimate detection probability; or

3) Daily detection probabilities needed for non-survival estimation purposes, such as migration timing estimation.

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Specific ExampleSpecific Example

Study: PIT-tagging wild chinook salmon parr.

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Primary objective: Migration timing distribution passing Lower Granite Dam.

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0

50

100

150

200

250

300

350

400

450



Challenge: Small sample size.

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0

1

2

3



Challenge: Variable PIT-tag detection probability.

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



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Detection distribution inappropriate as index of passage distribution.

Daily detection probabilities needed to properly expand detection distribution into passage distribution.


ConceptConcept

Dam 1 detected distribution for Dam 2 detected day.

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Days at Dam 1

Detected N

Day at Dam 2

Detected N


ConceptConcept

Estimated Dam 1 undetected distribution for Dam 2 detected day

Assumption: same distribution.

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Day at Dam 2

Days at Dam 1

Estimated U

Detected U


ConceptConcept

Repeat and sum.

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Days at Dam 1 for first day at

Dam 2

Estimated U

Detected N

Days at Dam 1 for last day at

Dam 2

+…

+…

=

=Days at Dam 1


ConceptConcept

Estimated detection probability for day at Dam 1.

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Det. N

Day at Dam 1

Day at Dam 1

Est. UDet. N

Day at Dam 1

+ (1 – Tran. Prop.)


ConceptConcept

Estimated passage number for day at Dam 1.

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=Estimated detection probability for day at Dam 1

Detected N’

Day at Dam 1Estimated N’

Day at Dam 1


ConceptConcept

Estimated survival to Dam 1.

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Release Number

Estimated N’

All Days at Dam 1

Sum( )


Schaefer MethodSchaefer Method

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t

j j

ijjm

muiu

1 ..ˆ

Estimated undetected at LGR on day i.



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t

j j

ijjm

muiu

1 ..ˆ



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)1(ˆˆ

1..

.

iii

ii

Tum

mP

Estimated detection probability at LGR on day i.



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i

ii

P

nN

ˆˆ

Estimated passage number at LGR on day i.



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R

N

S

s

i

i 1

ˆ

ˆ

Estimated survival to LGR.



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Adjustments in the passage distribution tails:

- No “detected at LGR” fish: Use LGR to LGO travel time.

- Estimates of 0 or 1: Use spill regression.

- Minor effect on overall estimates.


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Variance and 95% confidence intervals: Use Bootstrap.

Standard Error estimate: Standard Error of bootstrapped estimates.

95% confidence intervals: 25th and 975th values of the ordered bootstrap estimates.

Wild Chinook Parr Example - OverallWild Chinook Parr Example - Overall

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YearReleaseNumber

EstimatedPassageNumber

EstimatedSurvival

StandardError

95%Lower

Conf. Int.

95%Upper

Conf. Int.

1993 14478 2283 15.8% 0.7% 15.3% 18.2%

1994 12747 2401 18.8% 0.8% 17.6% 20.6%

1995 24417 3289 13.5% 0.3% 12.9% 14.3%

1996 6835 1411 20.6% 1.2% 19.1% 24.0%

1997 5634 1173 20.8% 1.8% 18.6% 25.8%

1998 6225 1516 24.4% 1.0% 23.0% 26.8%

1999 12922 2575 19.9% 0.8% 18.5% 21.7%

2000 13390 2374 17.7% 0.7% 16.7% 19.6%

2001 6526 1276 19.5% 0.6% 18.5% 20.7%

2002 14399 2066 14.3% 0.8% 13.3% 16.4%

Total 117573 20363 17.3%

Average 18.5% 0.9% 17.4% 20.8%

Wild Chinook Parr Example - 1999Wild Chinook Parr Example - 1999

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StreamRelease

Number

EstimatedPassageNumber

"Daily"Estimated

Survival

CJSEstimated

Survival Difference

Bear Valley Creek 820 131 16% 20% -4%

Big Creek 960 156 16% 14% 2%

Cape Horn Creek 270 56 21% 23% -2%

Elk Creek 700 162 23% 23% 0%

Herd Creek 959 210 22% 19% 3%

Lake Creek 545 79 14% 20% -5%

Lower Big Creek 467 218 47% 38% 9%

Loon Creek 1029 286 28% 33% -5%

Marsh Creek 769 218 28% 23% 5%

Salmon River South Fork 998 143 14% 12% 2%

Secesh River 936 136 15% 14% 0%

Sulfur Creek 443 72 16% 15% 2%

Valley Creek 1001 174 17% 19% -1%

Total 9897 2041 21% 20% 1%

Lower Big Creek - 1999Lower Big Creek - 1999

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10%

20%

30%

40%

Dete

cti

on

Prob

ab

ilit

y

CJS = 33% “Daily” = 28%

Det

ecti

on P

rob

abili

ty

Survival Estimation Using Estimated Daily Detection Probabilities Benjamin P. Sandford Fish Ecology...

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