December 2013 Your Babysitting Committee Coral Kincaid Mardi Rawding Mary Trott.
Directed Acyclic Graphs: A tool to incorporate uncertainty in steelhead redd-based escapement...
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![Page 1: Directed Acyclic Graphs: A tool to incorporate uncertainty in steelhead redd-based escapement estimates Danny Warren Dan Rawding March 14 th, 2012.](https://reader035.fdocuments.in/reader035/viewer/2022070409/56649e735503460f94b72c42/html5/thumbnails/1.jpg)
Directed Acyclic Graphs: A tool to incorporate uncertainty in steelhead redd-based escapement estimates
Danny WarrenDan Rawding
March 14th, 2012
![Page 2: Directed Acyclic Graphs: A tool to incorporate uncertainty in steelhead redd-based escapement estimates Danny Warren Dan Rawding March 14 th, 2012.](https://reader035.fdocuments.in/reader035/viewer/2022070409/56649e735503460f94b72c42/html5/thumbnails/2.jpg)
Outline
• Coordinated Data Assessments Project• What’s a DAG?• Mill, Abernathy, Germany monitoring history
Redd Estimates
Escapement EstimatesUsing DAGs
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Coordinated Data Assessments• Broad effort across numerous Columbia Basin entities• Goal to improve data timeliness, reliability, and transparency• Focused on 3 high-level indicators:
o Natural Spawner Abundanceo Smolt to Adult Ratioo Recruits per Spawner
Needs identified:
Improved data infrastructure Better documentation Standardized analytical methods
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SIMPLE DAG HEREA
pred_pF
So what’s a DAG?• Graphical representation
of a statistical model
• Explicitly depicts the data, equations, and statistical distributions
• Easy to translate into code or statistical nomenclature
• Accounts for all uncertainty in indicator estimates
a_LB a_UB b_LB b_UB
a b
adults[i]
females[i]
pF[i]
For(i IN 1 : sex_obs)
DAG for % Female
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AgeYear 3 4 5 6 7 U2005 5 78 46 3 0 342006 10 158 50 6 0 772007 8 65 34 0 0 462008 2009 12 35 14 0 0 282010 2011
Bayesian Approach for Redd Estimates
• Posterior Probability ~ Likelihood * Prior Distribution• Does not rely on normal distribution• Yeilds similar results to maximum likelihood as long as
priors are vague.• Hierarchical modeling allows sparse or missing data
borrow strength from other data
Age data from Toutle River Fish Collection Facility
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• Define Sampling Frame or Universe (potential spawning dist.)
• Representative sampling design (SRS,GRTS,SYS,etc)
• Estimate the redd denisty
• Use goodness of fit (GOF) tests to check if the observed density fits the model
• Total Redds = Obs redds + (redd density * unsurveyed distance)
• Adults = Total redds
• NOS = (1-pHOS) * Adults
• Adults[age] = Adults * % by age
Redd-Based Escapement Estimate
Females per redd% Female
*
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Redd Survey Design 2005-2011
• Census on mainstems and some tributaries
• One reach with landowner conflict
• Several supplemental reaches near peak
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Redd Survey Design 1994-2004
• Systematic approach to establish index reaches surveyed throughout season
• Supplemental reaches surveyed near peak
• Redd density expanded to unsurveyed reaches
• No surveys or estimates in Mill Creek
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• Redd locations are clumpy!
• Some reaches have few redds.
• Others have many, especially below the hatchery.
Steelhead Redd Locations
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
5
10
152005 Mill-Abernathy-Germany Redd Density
Redds per mile
Coun
t
Negative Binomial Poisson Log Normal
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Goodness of Fit
p-Value for Distribution
Negative Binomial Poisson Truncated
Normal
Mean 0.47 0.02 0.16Min 0.41 0.00 0.09
Max 0.52 0.26 0.40
p of 0.50 = Best fit
p of 0 or 1 = Poor fit
Bayesian p-value tests how well model fits observed data
Summary of years 1994-2011
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DAG used for analysis
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WinBUGS Output
Also a text file with:
• Mean and median
• Standard deviation
• 95% CI
• Sample iterations
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Total Redds
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 20120
150
300
450
Total Redds with 95% CI
Year
Coun
t
No error for complete census surveys!
Implementation of census surveys
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Total Escapement
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 20120
200
400
600Total Escapement
Year
Coun
t
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 20120
200
400
600Total Natural Origin Spawners
Year
Coun
t
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• Redd data in this basin follows a negative binomial distribution (not normal) in part due to hatchery effects.
Patterns and Variability
CV
Pre-2005 2005-11
Total Redds 14-33% 0-6%
Total Escapement 18-45% 16-20%
NOS 18-45% 23-27%
NOAA has proposed CV < 15% of escapement
Greatest sources of variability: Females per Redd estimate CV = 13.5%Sampling design CV = 14-33%
Increasinguncertainty
pNOS CV >25%
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Discussion
• There is a need for greater transparency and documentation of redd-based abundance estimates
• Census survey design is ideal, but stratified sampling of high and low density areas would also lead to precise estimates
• Hierarchical modeling is an effective tool for time-series data with gaps or limited data
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Questions?Photo : Steve VanderPloeg