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

Steve Smith – statistical development and programming Steve Achord and PTAGIS – data COE and BPA - funding NOAA Fisheries Acknowledgements

General Problem CJS may not be the best survival estimation technique in certain circumstances: 1)Concurrent temporal changes in detection and survival probabilities; NOAA Fisheries

General Problem CJS may not be the best survival estimation technique in certain circumstances: 1)Concurrent temporally dynamic detection and survival probabilities; 2)Cohort has small sample size but additional data available to estimate detection probability; or NOAA Fisheries

General Problem CJS may not be the best survival estimation technique in certain circumstances: 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. NOAA Fisheries

Specific Example Study: PIT-tagging wild chinook salmon parr. NOAA Fisheries

Specific Example Primary objective: Migration timing distribution passing Lower Granite Dam. NOAA Fisheries

Specific Example Challenge: Small sample size. NOAA Fisheries

Specific Example Challenge: Variable PIT-tag detection probability. NOAA Fisheries

Specific Example NOAA Fisheries Detection distribution inappropriate as index of passage distribution. Daily detection probabilities needed to properly expand detection distribution into passage distribution.

Concept Dam 1 detected distribution for Dam 2 detected day. NOAA Fisheries Days at Dam 1 Detected N Day at Dam 2 Detected N

Concept Estimated Dam 1 undetected distribution for Dam 2 detected day Assumption: same distribution. NOAA Fisheries Day at Dam 2 Days at Dam 1 Estimated U Detected U

Concept Repeat and sum. NOAA Fisheries 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

Concept Estimated detection probability for day at Dam 1. NOAA Fisheries Det. N Day at Dam 1 Est. U Det. N Day at Dam 1 + ( 1 – Tran. Prop. )

Concept Estimated passage number for day at Dam 1. NOAA Fisheries = Estimated detection probability for day at Dam 1 Detected N’ Day at Dam 1 Estimated N’ Day at Dam 1

Concept Estimated survival to Dam 1. NOAA Fisheries Release Number Estimated N’ All Days at Dam 1 Sum ()

Schaefer Method NOAA Fisheries Estimated undetected at LGR on day i.

Schaefer Method NOAA Fisheries Estimated undetected at LGR on day i.

Schaefer Method NOAA Fisheries Estimated undetected at LGR on day i.

Schaefer Method NOAA Fisheries Estimated undetected at LGR on day i.

Schaefer Method NOAA Fisheries Estimated detection probability at LGR on day i.

Schaefer Method NOAA Fisheries Estimated detection probability at LGR on day i.

Schaefer Method NOAA Fisheries Estimated passage number at LGR on day i.

Schaefer Method NOAA Fisheries Estimated passage number at LGR on day i.

Schaefer Method NOAA Fisheries Estimated survival to LGR.

Schaefer Method NOAA Fisheries Estimated survival to LGR.

Schaefer Method NOAA Fisheries 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.

Schaefer Method NOAA Fisheries Variance and 95% confidence intervals: Use Bootstrap. Standard Error estimate: Standard Error of bootstrapped estimates. 95% confidence intervals: 25 th and 975 th values of the ordered bootstrap estimates.

Wild Chinook Parr Example - Overall NOAA Fisheries Year Release Number Estimated Passage Number Estimated Survival Standard Error 95% Lower Conf. Int. 95% Upper Conf. Int %0.7%15.3%18.2% %0.8%17.6%20.6% %0.3%12.9%14.3% %1.2%19.1%24.0% %1.8%18.6%25.8% %1.0%23.0%26.8% %0.8%18.5%21.7% %0.7%16.7%19.6% %0.6%18.5%20.7% %0.8%13.3%16.4% Total % Average18.5%0.9%17.4%20.8%

Wild Chinook Parr Example NOAA Fisheries Stream Release Number Estimated Passage Number "Daily" Estimated Survival CJS Estimated SurvivalDifference Bear Valley Creek %20%-4% Big Creek %14%2% Cape Horn Creek %23%-2% Elk Creek % 0% Herd Creek %19%3% Lake Creek %20%-5% Lower Big Creek %38%9% Loon Creek %33%-5% Marsh Creek %23%5% Salmon River South Fork %12%2% Secesh River %14%0% Sulfur Creek %15%2% Valley Creek %19%-1% Total %20%1%

Lower Big Creek NOAA Fisheries CJS = 33%“Daily” = 28% Detection Probability