Sampling Strategies for Chinook-Salmon Spawning Populations

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Sampling Strategies for Chinook-SalmonSpawning
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

a lot like the Middle Fork Salmon R.
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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
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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

N
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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

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Examples Small and large runs
1995
2002
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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
  (N3,274)
• Keep things fair by sampling the same total
  length of stream, sampling fraction .1 and .05
  (n327 and 164)
• Although some standard errors can be calculated
  analytically the coverage needs to be addressed
  via simulation.

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Methods

• Use simulation by resampling the population over
  and over

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

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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)

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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, rk, r2k, , 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
rk
r2k
r4k
r3k
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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

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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
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Results Normalized standard error of estimators

Run size
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Standard error estimation for systematic strategy
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Results Empirical coverage probability

• Empirical coverage probability

Run size
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Costs
kilometers traveled
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Relative precision per cost
Precision per cost
Units 1/km traveled
10 sampling fraction
run size
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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

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Six years
1997
1998
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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?

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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.
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Six years
1995
1996
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Six years
2001
2002
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Stratify by 6th field HUC
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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

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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
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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
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Access to MFSR

• Roadless area
• Airplane access possible

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air vs. car access
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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)

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Stratify by Index

• Oversample index sites where most redds are
  located
• Simple random sample in each stratum
• Equal allocation
• Proportional allocation

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Stratify by index

• Optimal allocation
• Using

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Stratify by index

• Using

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To do

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