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 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
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
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
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
1. Background: State view MCQMC 2012 Sydney, Australia – p. 6/49
1. Background: Bay-Delta MCQMC 2012 Sydney, Australia – p. 7/49
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
1. Background: Catches by Year 4 Surveys sampling different life stages. Time Series of Average Catches for 4 Surveys Larvae Juveniles 14 40 12 10 30 8 20 6 4 10 2 0 0 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Year Year Sub−Adults Adults 8 4 7 6 3 5 2 4 3 1 2 0 1970 1980 1990 2000 2010 1970 1980 1990 2000 2010 Year Year MCQMC 2012 Sydney, Australia – p. 9/49
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 out of Delta during • January-March: protect mature and spawning adults • April-June: protect larvae and juveniles MCQMC 2012 Sydney, Australia – p. 10/49
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
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
2. Goals “If you don’t set goals, you can’t regret not reaching them.” Yogi Berra MCQMC 2012 Sydney, Australia – p. 13/49
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
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
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
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
3. Life History and Survey Data Example of Sample Coverage Sep-Dec MCQMC 2012 Sydney, Australia – p. 18/49
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
3. Life History and Survey Data Abiotic Data- per month & region • Water: temperature, salinity, clarity • Contaminants: NH 3 , Metals,Pesticides • “Gross” flows and Water Exports • “Detailed” flows: hydrology model output MCQMC 2012 Sydney, Australia – p. 20/49
4. Hierarchical Model: 4 Levels y t = smelt data n t = smelt abundance w t , X t = covariates γ, ω, η, n 0 = static parameters Level 1, Observations : f ( y t | n t , γ, w t ) Level 2, States : g ( n t | n t − 1 , θ t , ω ) Level 3, Random Effects † : h ( θ t | X t , η ) Level 4, Priors : π ( γ, ω, η, n 0 ) † - deferred. MCQMC 2012 Sydney, Australia – p. 21/49
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
4. Hierarchical Model: Resolution Cluster analysis to guide Spatial Resolution MCQMC 2012 Sydney, Australia – p. 23/49
4. Hierarchical Model: Resolution ⇒ Monthly × 4 Regions, n Month,Region SKT survey station locations, n= 47 38.6 38.4 719 Latitude 346 716 725 724 345 715 38.2 344 713 922 712 343 711 606 609 921 342 920 923 610 602 919 707 340 812 705 706 815 501 519 704 418 513 504 411 809 906 508 801 405 520 804 902 38.0 910 912 914 915 −122.6 −122.4 −122.2 −122.0 −121.8 −121.6 −121.4 −121.2 Longitude MCQMC 2012 Sydney, Australia – p. 24/49
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
4. Hierarchical Model: State Vectors n May,F W,A n May,W,A n Apr,F W,A n May,N,A n Apr,W,A n May,S,A n Mar,N n Apr,N,A n May,F W,ESC n Mar,S n Apr,S,A n May,W,ESC → → → . . . n Mar,W n Apr,F W,ESC n May,N,ESC n Mar,F W n Apr,W,ESC n May,S,ESC n Apr,N,ESC n May,F W,LSC n Apr,S,ESC n May,W,LSC n May,N,LSC n MCQMC 2012 Sydney, Australia – p. 26/49
4. Hierarchical Model: 3 Processes Survival, Birth, and Movement ≈ “Leslie”: ≈ M April B April S April n March n April ≈ M May B May S May n April n May ≈ M June S June n May n June ≈ M July S July n June n July MCQMC 2012 Sydney, Australia – p. 27/49
4. Hierarchical Model: Survival Quadratic function of Age: MCQMC 2012 Sydney, Australia – p. 28/49
4. Hierarchical Model: Survival Letting m = month, r = region, logit ( S m,r ) = β 0 + β 1 Age + β 2 Age 2 + β 3 Conductivity m,r + β 4 Clarity m,r n ′ m,r ∼ Binomial ( n m − 1 ,r , S m,r ) where n ′ m,r denotes abundance following mortality. MCQMC 2012 Sydney, Australia – p. 29/49
4. Hierarchical Model: Birth rate Quadratic function of Water Temperature: MCQMC 2012 Sydney, Australia – p. 30/49
4. Hierarchical Model: Birth rate ln ( λ m,r ) = γ 0 + γ 1 Temp m,r + γ 2 Temp 2 m,r n ′′ λ m,r n ′ � � m,r,Larvae ∼ Poisson m,r,Adults where n ′′ m,r,Larvae denote larval numbers in a time-region following reproduction. MCQMC 2012 Sydney, Australia – p. 31/49
4. Hierarchical Model: Movement “Guided” by Historical Evidence: %catch in Western Region. MCQMC 2012 Sydney, Australia – p. 32/49
4. Hierarchical Model: Movement ′′ Let n m, · denote total numbers of a given life stage summed over all regions prior to movement. n m,r ∼ ′′ � � Multinom n m, · , p m,FW , p m,W , p m,N (Spatial Reallocation) MCQMC 2012 Sydney, Australia – p. 33/49
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