1. Sampling Strategies for Chinook-Salmon Spawning Populations
4/15/2017
Sampling Strategies for Chinook-Salmon Spawning Populations
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
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
Our objectives here are simple, to determine which sampling strategy should be used to estimate chinook spawning status. 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. The Middle Fork Salmon River
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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
Km2 = square kilometers.
Index reaches – delineated in the 1950’s, change periodically, these are those used since approx 1995, “good salmon habitat” N 10 20 40
Kilometers 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
year
1995
1996
1997
1998
2001
2002
Total redds 20 83
424
661
1789
1730 4

5. Examples: Small and large runs
1995
2002 5

6. 4/15/2017
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.
65.4 and 32.8 km. sampled 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 in 5km intervals. Many areas require over 20 km hike
Maximum distance is 33 km.
Many areas require over 20 km hike 9

10. The sampling strategies
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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.
Generalized random tessellated design from EPA’s EMAP designs and now from these two projects represented here. 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
year
1995
1996
1997
1998
2001
2002
proportion in index
0.76
0.54
0.48
0.42
0.46 13

14. 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
include
neighbor 6 5 6 4 3
Meets criteria 4
and
do not meet
criteria 1 3 2
Two sample sizes:
ADAPT-EN – equate expected final sample size
ADAPT-N – equate original SRS sample size
in original
sample 2 1
Meets criteria
Final sample includes: 2 1 3 4 6 14

15. Results: Normalized standard error of estimators
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Results: Normalized standard error of estimators
Run size 20 83
424
661
1789
1730
GRTS
75.6
35.1
16.6
13.7
11.0
10.9
SYS
68.4
38.4
17.0
14.0
10.2
10.8
STRS-index
(optimal)
59.6
31.5
17.4
14.3
13.3
12.3
ADAPT-N
76.4
35.8
18.2
14.8
12.1
11.8
SRS
36.3
19.5
16.1
13.8
ADAPT-EN
76.6
35.9
21.3
18.5
19.2
18.1
Cluster
93.2
44.5
29.6
24.9
24.4
23.6
This is the CV of t-hat. Now we can compare these over the run size.
Index - all
34.4
29.6
32.5
32.7
34.6
31.1
Index – rep.
247
158
132
129
122
134 15

16. Standard error estimation for systematic strategy
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Standard error estimation for systematic strategy
This problem is not evident in the GRTS design. 16

17. Results: Empirical coverage probability
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Results: Empirical coverage probability
Empirical coverage probability
Run size 20 83
424
661
1789
1730
GRTS
81.1
90.7
93.0
92.0
93.4
93.8
SYS
88.7
92.6
91.2
96.0
94.1
STRS-index
(optimal)
77.3
91.3
92.8
94.6
93.2
ADAPT-N
83.3
93.6
94.4
94.2
SRS
82.4
89.8
92.7
94.0
93.9
ADAPT-EN
82.5
92.3
Cluster
75.1
86.7
89.9
91.8
92.2
This is the CV of t-hat. Now we can compare these over the run size.
Index - all
98.7
99.8
92.9
77.6
32.7
55.9
Index – rep.
89.4
2.0
0.2 17

18. 4/15/2017
Costs
kilometers traveled 18

19. Relative precision per cost
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Relative precision per cost
Precision per cost
Units = 1/km traveled
10% sampling
fraction
There are several possibilities for combining the precision and cost:
Two simple approaches are to hold one fixed and find the minimum of the other
Otherwise
Here is the precision per mean cost in 1/km traveled.
One could also plot the precision per std. Dev. Of cost.
Or use something such as CI width per km. Traveled.
In either case the y-axis is difficult to interpret
The standard errors are standardized by the size of the run then multiplied by the cost in kilometer traveled by foot. So the precision is unit free and the denominator is in KMs.
So small runs: either stratified by index or SRS-1km are best bang for our buck
medium runs: stratified by index
Large runs: Systematic. 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. Lucas Boone Courbois, born August 4, 2004
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

24. 24

25. Six years
1995
1996 25

26. Six years
2001
2002 26

27. Stratify by 6th field HUC27

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, 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)
year
1995
1996
1997
1998
2001
2002
Number counted in Index 19 62
290
448
1178
1199
Total number of redds 20 83
424
661
1789
1730 33

34. 34

35. Stratify by Index Oversample index sites where most redds are located
Simple random sample in each stratum
Equal allocation:
Proportional allocation:
year
1995
1996
1997
1998
2001
2002
5.33
12.68
36.61
47.34
121.43
106.98
coverage
90.4
94.6
94.2
94.8
92.9
93.4
year
1995
1996
1997
1998
2001
2002
7.77
15.26
41.08
52.37
124.90
115.56
coverage
88.0
94.7
95.0
94.9
94.4
93.6 35

36. Stratify by index Optimal allocation Using year 1995 1996 1997 1998
2001
2002
proportion in index
0.76
0.54
0.48
0.42
0.46
n index
746
530
475
464
407
445
n other
230
446
501
512
569
531
year
1995
1996
1997
1998
2001
2002
5.49
12.76
36.60
47.26
120.50
106.58
coverage
92.0
95.0
94.3
95.5
92.9
93.5 36

37. Stratify by index Using year 1995 1996 1997 1998 2001 2002 n index 746
530
475
464
407
445
n other
230
446
501
512
569
531 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