Spatial-temporal modelling of delta smelt in the San Francisco - - PowerPoint PPT Presentation

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Spatial-temporal modelling of delta smelt in the San Francisco - - PowerPoint PPT Presentation

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Spatial-temporal modelling of delta smelt in the San Francisco Estuary Ken Newman US Fish and Wildlife Service, California MCQMC 2012 Sydney, Australia p. 1/49 Modeling Team Members Wim Kimmerer, San Francisco State University

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SLIDE 1

Spatial-temporal modelling of delta smelt in the San Francisco Estuary

Ken Newman US Fish and Wildlife Service, California

MCQMC 2012 Sydney, Australia – p. 1/49

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SLIDE 2

Modeling Team Members

  • Wim Kimmerer, San Francisco State University

Ecologist

  • Pete Smith, US Geological Survey, ret.

Hydrologist

  • Randy Baxter, CA Dept. of Fish and Game

Fish Biologist

  • Emilio Laca, Univ. of CA at Davis

Scientist/Statistician

  • Bill Bennett, Univ. of CA at Davis

Biologist/Delta Smelt Expert

  • Wendy Meiring, Univ. of CA at Santa Barbara

Statistician

  • Fred Feyrer, US Bureau of Reclamation

Fish Biologist

MCQMC 2012 Sydney, Australia – p. 2/49

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SLIDE 3

Summary Points

  • High Socio-Political Motivation
  • Large, Complex Ecological Data Set
  • Ambitious Spatial-Temporal Model for a

Single Species

  • Challenging Estimation Problems—Only Toy

Solution Presented.

MCQMC 2012 Sydney, Australia – p. 3/49

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SLIDE 4

Outline

  • 1. Background
  • 2. Management and Modeling Goals
  • 3. Life History and Survey Data
  • 4. Hierarchical Model

(a) State Process Model (b) Observation Model

  • 5. PMCMC Results for Simulated Data
  • 6. Next Steps

MCQMC 2012 Sydney, Australia – p. 4/49

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SLIDE 5
  • 1. Background: Fish life stages

Delta smelt are a small estuarine fish, adults are 70-100mm in length, only found in the San Francisco Estuary

MCQMC 2012 Sydney, Australia – p. 5/49

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SLIDE 6
  • 1. Background: State view

MCQMC 2012 Sydney, Australia – p. 6/49

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SLIDE 7
  • 1. Background: Bay-Delta

MCQMC 2012 Sydney, Australia – p. 7/49

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SLIDE 8
  • 1. Background: Population Decline
  • Before 1981, Generally Abundant
  • Around 1981, a 1st Drastic Decline
  • 1993, made a “threatened” species under US

Endangered Species Act.

  • Around 2001/02, a 2nd Drastic Decline
  • 3 other species “collapsed”, striped bass, threadfin

shad, longfin smelt

  • POD- Pelagic Organism Decline

MCQMC 2012 Sydney, Australia – p. 8/49

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SLIDE 9
  • 1. Background: Catches by Year

4 Surveys sampling different life stages.

1970 1980 1990 2000 2010 2 4 6 8 10 12 14

Larvae

Year 1970 1980 1990 2000 2010 10 20 30 40

Juveniles

Year 1970 1980 1990 2000 2010 1 2 3 4

Sub−Adults

Year 1970 1980 1990 2000 2010 2 3 4 5 6 7 8

Adults

Year

Time Series of Average Catches for 4 Surveys

MCQMC 2012 Sydney, Australia – p. 9/49

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SLIDE 10
  • 1. Background: Management Actions

Subsequent management actions to help recover Delta Smelt, e.g., “Biological Opinions” 1995, 2004, 2008. For example, reduce amount of Water Exported

  • ut of Delta during
  • January-March: protect mature and spawning adults
  • April-June: protect larvae and juveniles

MCQMC 2012 Sydney, Australia – p. 10/49

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SLIDE 11
  • 1. Background: Consequences

Social, Economic, Legal, Political

  • Exported Water used for Agricultural and Municipal

purposes by 20+ million people.

  • Law suits filed by Environmental Groups for

“inadequate” protection.

  • Law suits filed by Water Contractors that actions

“inconsequential” for delta smelt.

MCQMC 2012 Sydney, Australia – p. 11/49

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SLIDE 12
  • 1. Background: Consequences

“faceless [] government bureaucrat took away [farmers’] lifeline, their water. . . . in order to protect a two inch fish. Now where I come from we call that bait.”, Sarah Palin. “Tiny fish threatens to turn California’s Central Valley into Dust Bowl”, News headline.

MCQMC 2012 Sydney, Australia – p. 12/49

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SLIDE 13
  • 2. Goals

“If you don’t set goals, you can’t regret not reaching them.” Yogi Berra

MCQMC 2012 Sydney, Australia – p. 13/49

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SLIDE 14
  • 2. Goals
  • 1. Management: To restore the delta smelt

population.

  • 2. Modeling: To develop a Decision support tool

for Assessment & Prediction of Effects of Mgmt Actions

MCQMC 2012 Sydney, Australia – p. 14/49

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SLIDE 15
  • 3. Life History and Survey Data

Delta smelt are a mostly annual species.

  • Mature Adult Females spawn ≈ 2000 eggs: April-May
  • Larval/Post-Larval stage, 6-25mm: April- June
  • Juvenile/Sub-Adults stage, 25-50mm: June-November
  • Adults/Mature stage, 50-80mm: November-April

MCQMC 2012 Sydney, Australia – p. 15/49

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SLIDE 16
  • 3. Life History and Survey Data

Spatial Movements

  • Spawning: “Upstream” in Less Saline Waters
  • Larvae: “Downstream”, water dynamics
  • Juveniles + Sub-Adults: "low salinity zones"
  • Adults: Back “Upstream”

MCQMC 2012 Sydney, Australia – p. 16/49

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SLIDE 17
  • 3. Life History and Survey Data

Delta Smelt Data

  • Larvae (20mm):

Apr-Jun, 1995-2010, 40 sites ⇒ n=1920+

  • Juveniles (Townet):

Jun-Aug, 1962-2010, 32 sites ⇒ n=4416+

  • Sub-Adults (Midwater Trawl):

Sep-Dec, 1967-2010, 100 sites ⇒ n=17,600+

  • Adults (Kodiak Trawl):

Jan-Apr, 2002-2010, 40 sites ⇒ n=180+

and more ...

MCQMC 2012 Sydney, Australia – p. 17/49

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SLIDE 18
  • 3. Life History and Survey Data

Example of Sample Coverage Sep-Dec

MCQMC 2012 Sydney, Australia – p. 18/49

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SLIDE 19
  • 3. Life History and Survey Data

Other Biotic Data- per month & region

  • Zooplankton Survey, 1972-2010, 20 sites: Prey
  • Phytoplankton Survey, 1975-2010, 20+ sites: Lowest

Trophic Level

  • Benthics Survey, 1975-2010, 10 sites: Effects on Prey

MCQMC 2012 Sydney, Australia – p. 19/49

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SLIDE 20
  • 3. Life History and Survey Data

Abiotic Data- per month & region

  • Water: temperature, salinity, clarity
  • Contaminants: NH3, Metals,Pesticides
  • “Gross” flows and Water Exports
  • “Detailed” flows: hydrology model output

MCQMC 2012 Sydney, Australia – p. 20/49

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SLIDE 21
  • 4. Hierarchical Model: 4 Levels

yt = smelt data nt = smelt abundance wt, Xt = covariates γ, ω, η, n0 = static parameters Level 1, Observations : f(yt|nt, γ, wt) Level 2, States : g(nt|nt−1, θt, ω) Level 3, Random Effects† : h(θt|Xt, η) Level 4, Priors : π(γ, ω, η, n0) †- deferred.

MCQMC 2012 Sydney, Australia – p. 21/49

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SLIDE 22
  • 4. Hierarchical Model: State Model

Spatial-temporal resolution: Time: distinguish life stages Space: distinguish region-specific mgmt actions

MCQMC 2012 Sydney, Australia – p. 22/49

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SLIDE 23
  • 4. Hierarchical Model: Resolution

Cluster analysis to guide Spatial Resolution

MCQMC 2012 Sydney, Australia – p. 23/49

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SLIDE 24
  • 4. Hierarchical Model: Resolution

⇒ Monthly × 4 Regions, nMonth,Region

−122.6 −122.4 −122.2 −122.0 −121.8 −121.6 −121.4 −121.2 38.0 38.2 38.4 38.6

SKT survey station locations, n= 47

Longitude Latitude

340 342 343 344 345 346 405 411 418 501 504 508 513 519 520 602 606 609 610 704 705 706 707 711 712 713 715 716 719 724 725 801 804 809 812 815 902 906 910 912 914 915 919 920 921 922 923

MCQMC 2012 Sydney, Australia – p. 24/49

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SLIDE 25
  • 4. Hierarchical Model

State Vector Components: Distinguish time and cohorts

  • August-March: “Adults” by Region (4)
  • April-July: “Early" Larval Subcohort (4)
  • May-July: “Late” Larval Subcohorts (4)

MCQMC 2012 Sydney, Australia – p. 25/49

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  • 4. Hierarchical Model: State Vectors

       nMar,N nMar,S nMar,W nMar,F W        →                   nApr,F W,A nApr,W,A nApr,N,A nApr,S,A nApr,F W,ESC nApr,W,ESC nApr,N,ESC nApr,S,ESC                   →                               nMay,F W,A nMay,W,A nMay,N,A nMay,S,A nMay,F W,ESC nMay,W,ESC nMay,N,ESC nMay,S,ESC nMay,F W,LSC nMay,W,LSC nMay,N,LSC n                               → . . .

MCQMC 2012 Sydney, Australia – p. 26/49

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SLIDE 27
  • 4. Hierarchical Model: 3 Processes

Survival, Birth, and Movement ≈ “Leslie”:

nApril ≈ MApril BApril SApril nMarch nMay ≈ MMay BMay SMay nApril nJune ≈ MJune SJune nMay nJuly ≈ MJuly SJuly nJune

MCQMC 2012 Sydney, Australia – p. 27/49

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SLIDE 28
  • 4. Hierarchical Model: Survival

Quadratic function of Age:

MCQMC 2012 Sydney, Australia – p. 28/49

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SLIDE 29
  • 4. Hierarchical Model: Survival

Letting m = month, r = region, logit(Sm,r) = β0 + β1Age + β2Age2 +β3Conductivitym,r +β4Claritym,r n′

m,r ∼ Binomial (nm−1,r, Sm,r)

where n′m,r denotes abundance following mortality.

MCQMC 2012 Sydney, Australia – p. 29/49

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SLIDE 30
  • 4. Hierarchical Model: Birth rate

Quadratic function of Water Temperature:

MCQMC 2012 Sydney, Australia – p. 30/49

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SLIDE 31
  • 4. Hierarchical Model: Birth rate

ln (λm,r) = γ0 + γ1Tempm,r + γ2Temp2

m,r

n′′

m,r,Larvae ∼ Poisson

  • λm,rn′

m,r,Adults

  • where n′′m,r,Larvae denote larval numbers in a

time-region following reproduction.

MCQMC 2012 Sydney, Australia – p. 31/49

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SLIDE 32
  • 4. Hierarchical Model: Movement

“Guided” by Historical Evidence: %catch in Western Region.

MCQMC 2012 Sydney, Australia – p. 32/49

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SLIDE 33
  • 4. Hierarchical Model: Movement

Let n

′′

m,· denote total numbers of a given life stage

summed over all regions prior to movement. nm,r ∼ Multinom

  • n

′′

m,·, pm,FW, pm,W, pm,N

  • (Spatial Reallocation)

MCQMC 2012 Sydney, Australia – p. 33/49

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SLIDE 34
  • 4. Hierarchical Model: Obs’n Model

Data from 4 fish surveys:

Adults, Jan-May, Kodiak Trawl ySKT,m,r ∼ Lognormal

  • µSKT,m,r, σ2

SKT

  • µSKT,m,r = log(λSKTnAdults,m,r − σ2

SKT/2)

σ2

SKT = log

  • CV 2

SKT + 1

  • where m = Jan, Feb, . . ., May

MCQMC 2012 Sydney, Australia – p. 34/49

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SLIDE 35
  • 4. Hierarchical Model: Obs’n Model

Larvae, Apr-June, 20mm Net y20mm,m,r ∼ Lognormal

  • µ20mm,m,r, σ2

20mm

  • Juveniles, June-July, Townet

yST N,m,r ∼ Lognormal

  • µST N,m,r, σ2

ST N

  • Sub-Adults, Sep-Nov, Midwater Trawl

yFMWT,m,r ∼ Lognormal

  • µFMWT,m,r, σ2

FMWT

  • MCQMC 2012 Sydney, Australia – p. 35/49
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SLIDE 36
  • 4. Hierarchical Model: Obs’n Model

Caveats

  • y’s = sample (catch/volume) × Total Volume
  • Gear efficiency values “arbitrary”: λSKT

“high”, λ20mm, from Kimmerer (2008), λSTN “professional” judgment, λFMWT from Newman (2008)

  • CVSKT, CV20mm, CVSTN, CVFMWT “guided” by

results for midwater trawl (Newman 2008)

MCQMC 2012 Sydney, Australia – p. 36/49

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SLIDE 37
  • 5. PMCMC Estimation and Results

Particle Marginal Metropolis-Hastings, Andrieu, et al. 2010 (JRSS-B). Time Period: January 2002 through December 2010 ⇒ 108 Abundance Vectors. Much simplified SSM for “initial” fitting.

MCQMC 2012 Sydney, Australia – p. 37/49

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SLIDE 38
  • 5. PMCMC Estimation and Results

(1) Simulated Observation Data: nFeb,2002 ≈ MoveFeb,2002 × SurvivalFeb,2002 × nJan,2002 yFeb,2002 ≈ λSKT,Feb,2002nFeb,2002 nMar,2002 ≈ MoveMar,2002 × SurvivalMar,2002 × nFeb,2002 . . . using real Covariates for modeling survival and birth processes

MCQMC 2012 Sydney, Australia – p. 38/49

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SLIDE 39
  • 5. PMCMC Estimation and Results

(2) Only 3 of 44 parameters estimated:

  • Survival β3 ( Conductivity)
  • Survival β4 ( Clarity)
  • Birth γ1 (Linear, Temperature)

MCQMC 2012 Sydney, Australia – p. 39/49

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SLIDE 40
  • 5. PMCMC Estimation and Results

(3) Sequential MC step to generate proposal state vector time series (100+ months):

  • Small number of Particles (50 adequate here)
  • Importance sampler = state pdf: “plug & play”

necessary (Ionides)

MCQMC 2012 Sydney, Australia – p. 40/49

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SLIDE 41
  • 5. PMCMC Estimation and Results

SMC Evaluation of p(yt|nt, θ)

  • Adult data: 10 years × 5 months = 50 vectors
  • Larvae data: 10 years × 3 months = 30 vectors
  • Juvenile data: 10 years × 2 months = 20 vectors
  • Sub-adult data: 10 years × 3 months = 30 vectors

Thus 130 vector pdf evaluations per particle.

MCQMC 2012 Sydney, Australia – p. 41/49

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SLIDE 42
  • 5. PMCMC Estimation and Results

(4) MCMC step: RW proposals, normally distributed around previous value, tuned to get acceptance rates in the range of 20-40% (5) Priors for 3 parameters–all Normal dist’ns

MCQMC 2012 Sydney, Australia – p. 42/49

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SLIDE 43
  • 5. PMCMC Estimation and Results

Posterior distributions for survival and birth parameters.

S.conduct.b3

Density −1.2 −1.0 −0.8 1 2 3 4 5

S.conduct.b3

Iteration 2000 6000 −1.3 −1.2 −1.1 −1.0 −0.9 −0.8

S.secchi.b4

Density −0.5 −0.3 −0.1 1 2 3 4 5

S.secchi.b4

Iteration 2000 6000 −1.0 −0.8 −0.6 −0.4 −0.2

B.temperature.b1

Density −4 −3 −2 −1 1 0.00 0.10 0.20 0.30

B.temperature.b1

Iteration 2000 6000 −4 −3 −2 −1

MCQMC 2012 Sydney, Australia – p. 43/49

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SLIDE 44
  • 5. PMCMC Estimation and Results

Interpretation of Coefficients—relevance to Mgmt Actions

5000 15000 25000 0.3 0.4 0.5 0.6 0.7

Survival vs Conductivity|age 12 months

Conductivity 20 40 60 80 100 140 0.60 0.65 0.70

Survival vs Water Clarity|age 12 months

Secchi 5.0 5.5 6.0 6.5 7.0

Birth Rate vs Water Temperature

MCQMC 2012 Sydney, Australia – p. 44/49

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SLIDE 45
  • 5. PMCMC Estimation and Results

Contribution to Marginal Likelihood from Different Surveys

all.log.wts SKT.DS Twentymm.DS STN.DS FMWT.DS −600 −400 −200 200

Sample Weights

Data Sets MCQMC 2012 Sydney, Australia – p. 45/49

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  • 6. Next Steps: ∆’s in Data
  • New sub-region water volumes (US Geological Survey)
  • Particle Tracking Model output for historical period,

1962-2010

MCQMC 2012 Sydney, Australia – p. 46/49

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SLIDE 47
  • 6. Next Steps: ∆’s in State Model
  • Alternative Spatial configurations
  • Movement guided by PTM output
  • Random effects “option”

logit(Smth,region) ∼ Normal

  • β0 + β1Age + . . . , σ2

S

  • Additional Xm,r: Prey, Water “Exports”

MCQMC 2012 Sydney, Australia – p. 47/49

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SLIDE 48
  • 6. Next Steps: ∆’s in Obs’n Model
  • ZiLN, Zero-Inflated LogNormal.
  • Gear efficiency models, logistic vs dome shaped

(Millar).

  • Data-based, survey specific coefficients of variation.
  • More“y’s”: mortality at water pumps, Beach Seine

catch, . . .

MCQMC 2012 Sydney, Australia – p. 48/49

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SLIDE 49
  • 6. Next Steps: ∆’s Model Fitting
  • Initial n0 by “inverting” y0 (then discard)
  • Adaptive MCMC proposals for starting PMCMC

process

  • Improved Sequential Monte Carlo step:
  • Auxiliary particle filter (Pitt & Shepherd, 1999);
  • Residual resampling (Liu & Chen, 1998)
  • More efficient language
  • Bayes Factors or RJ-PMCMC?

MCQMC 2012 Sydney, Australia – p. 49/49