Sampling Strategies for Chinook-Salmon Spawning Populations

1. Sampling Strategies for Chinook-SalmonSpawning Populations • What sampling strategies should be used for estimating the number of chinook redds on a river network*? Status estimation – number of spring-chinook redds in Middle Fork Salmon River one year Jean-Yves Pip Courbois, Steve Katz, Chris Jordan, Michelle Rub, and Ashley Steel – NOAA Fisheries, NWFSC – Russel F. Thurow and Daniel J. Isaak – U.S. Forest Service, Rocky Mountain Research Station 1 *a lot like the Middle Fork Salmon R.

2. Chinook redds • At the conclusion of the annual spawning migration, adult female chinook prepare a spawning bed, a redd Disturbed gravels (light-colored area) indicate a Chinook redd Total number of redds is an indicator of population health, now and future 2

3. 0 10 20 40 Kilometers The Middle Fork Salmon River • National Wild and Scenic River in the Frank Church River of No Return Wilderness – roadless area • Drains about 7,330 km2 of central Idaho • Two level 4 HUCs and 126 level 6 HUCs • Home to 15 native fishes including 7 salmonid taxa • Spring chinook salmon – ESA listed • 655 km of chinook spawning reaches • Index reaches N 3

4. Number of redds – “the Truth” • Since 1995 we have counted the number of redds in the entire watershed via helicopter • Where necessary sampled by foot • This study uses six years of data: • These data will be considered the truth 4

5. Examples: Small and large runs 1995 2002 5

6. Objectives • Criteria • Design-based standard error of estimator • coverage probability (how many times 95% confidence interval actually contains the number of redds) • cost • Sampling and measurement unit: 200-meter reaches (N=3,274) • Keep things fair by sampling the same total length of stream, sampling fraction =.1 and .05 (n=327 and 164) • Although some standard errors can be calculated analytically the coverage needs to be addressed via simulation. 6

7. Methods • Use simulation by resampling the population over and over . . . 7

8. Costs & crew-trips • Each sampling unit in the MF is assigned to an access point • There are two types of access points: air fields and trailheads, same price • Cost for access sites = maximum distance from access site to sampling reaches in each “direction” along network • Total cost = sum of costs for 15 access sites 4 “directions” = 4 round trips required 8

9. Distances distances in 5km intervals. Maximum distance is 33 km. Many areas require over 20 km hike 9

10. The sampling strategies • Index – Sample the index reaches or SRS within index only. • Simple random sampling – • Cluster sampling – simple random sampling of 1 km. length units. • Systematic sampling – Sort tributaries in random order systematically sample along resulting line. • Stratify by Index – Sample independently within and outside the index regions. • Adaptive cluster sampling – Choose segments with a simple random sample. If sampled sites have redds sample adjacent segments. • Spatially balanced design – GRiTS, select segments as sampling units rather than points. 10

11. Index sampling • When the sample size is smaller than the overall size of the index region a simple random sample of the segments within the index is collected. • Two possibilities to estimate the number of redds from the index sample: • Assume there are no redds outside of the index – estimates will be too small (all) • Assume that the average number of redds per segment outside the index is the same inside and simply inflate the index estimator – estimates will be too large (rep) 11

12. Systematic sampling • Order the tributaries in random order along a line • Choose sampling interval, k, so that final sample size is approximately n • Select a random number, r, between 1 and k • Sample reaches r, r+k, r+2k, …, r+(n-1)k • Systematic sampling is cluster sampling where clusters are made up of units far apart in space and one cluster is sampled k r r+k r+2k r+3k r+4k 12

13. Stratify by Index • Stratify by index and oversample index reaches • Simple random sample in each stratum • Allocation: • Equal allocation: Usually does not perform well • Proportional allocation: Does not oversample index sites so will probably not have good precision • Optimal allocation: need to know the standard deviation 13

14. include neighbor Meets criteria and do not meet criteria 1 2 1 3 2 5 6 4 4 6 4 6 1 3 3 2 in original sample Adaptive cluster sampling • Original sample is simple random sample • If sampled site meets criteria also sample sites in neighborhood • Criteria: presence of redds • Neighborhood: segments directly upstream and downstream • Continue until sites do not meet criteria • Both legs of confluences • Two sample sizes: • ADAPT-EN – equate expected final sample size • ADAPT-N – equate original SRS sample size Meets criteria Final sample includes: 14

15. Results: Normalized standard error of estimators Run size 15

16. Standard error estimation for systematic strategy 16

17. Results: Empirical coverage probability • Empirical coverage probability Run size 17

18. Costs kilometers traveled 18

19. Relative precision per cost Precision per cost Units = 1/km traveled 10% sampling fraction 19 run size

20. Conclusions Precision • Medium to large runs: Systematic strategies (systematic and GRTS) • Standard error difficult to estimate for systematic strategy • Small runs: Stratified by index • Requires optimal allocation which is difficult to determine Cost and precision • Small runs – cheap strategies best, either index or SRS-1km • Medium runs – intermediately priced designs, stratify by index • Large runs – precise strategies best, either systematic strategies or stratified by index 20

21. Six years 1997 1998 21

22. Discussion • Adaptive cluster strategy is not as precise as other designs. • It is optimal for rare clustered populations • during small years the redds are not clustered enough • during large years they are not rare enough • only during the medium years does it compete with other designs • Many of the designs require extra information • Stratified • Adaptive • These results suggest more complex designs such as combining stratified with systematic or adaptive • Real vs. simulated data? 22

23. Acknowledgements • Tony Olsen (US-EPA), Damon Holzer, George Pess, (NOAA-Fisheries) • Funding for this research has been provided by NOAA-Fisheries Northwest Fisheries Sciences Center Cumulative Risk Initiative and partially by the US EPA cooperative agreement CR29096 to Oregon State University and its its subagreement E0101B-A to the University of Washington. • This research has not been formally reviewed by NOAA-Fisheries or the EPA. The views expressed in this document are solely those of the authors; NOAA-Fisheries and the EPA do not endorse any products or commercial services mentioned herein. Lucas Boone Courbois, born August 4, 2004 Seattle WA. 23

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25. Six years 1995 1996 25

26. Six years 2001 2002 26

27. Stratify by 6th field HUC 27

28. Points vs. Lines • Pick points -- points are picked along stream continuum and the measurement unit is constructed around the point • advantages: • different size measurement units are easily implemented • disadvantages: • difficulty with overlapping units • inadvertent variable probability design because of confluences and headwaters • Analysis may be complicated • Pick Segments – Universe is segmented before sampling and segments are picked from population of segments • advantages: • simple to implement • simple estimators • disadvantages: • Difficult frame construction before sampling • Cannot accommodate varying lengths of sampling unit 28

29. Methods • Sampling strategies include sampling design and estimator • Sampling and measurement unit: 3,274 200-meter segments • Measurement design assumes no measurement error Estimator for the total . . . sample design and confidence interval 29

30. Adaptive Cluster Sampling • Use the draw-by-draw probability estimator: • Let wi be the average number of redds in the network of which segment i belongs, then • with variance Thompson 1992 30

31. Access to MFSR • Roadless area • Airplane access possible 31

32. air vs. car access 32

33. Index sample • Not sure how to build estimates for total number of redds in Middle fork. • expand current estimator (assume same density outside of index) • use current estimate (assume 0 redds outside of index) 33

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35. Stratify by Index • Oversample index sites where most redds are located • Simple random sample in each stratum • Equal allocation: • Proportional allocation: 35

36. Stratify by index • Optimal allocation • Using 36

37. Stratify by index • Using 37

38. To do • stratified by 6th field HUC • Better estimators for Adaptive designs. • Cost function • including road/airplane travel • crew trips/day units 38