Linking  Temporal  and  Spa1al  Data  Sets  for  Hierarchical  Bayesian  

Network  Analysis  and  Predic1on  of  Delta  Smelt  

Popula1ons    BJ  Miller  

Bob  Oliver    

The  first  of  two  presenta7ons  

Our  Purpose  

•  A  different  predic7ve  model,  Bayesian  Network  Analysis,  for  delta  smelt  (and  similar  problems)  

•  Recommenda7ons  to  improve  sampling  &  rou7ne  monitoring  

•  Preliminary  results  ranking  factors  important  to  larval-­‐juvenile  delta  smelt  

The  Delta  Smelt  Problem  

•  Abundance  declined  by  2  orders  of  magnitude  this  century  

•  On  St/Fed  Endangered  Species  lists  •  Persistent  record  low  levels  •  Many  regression-­‐based  analyses  •  No  predic7on  models  to  inform  management  

The  Fish  &  Wildlife  Manager  and  the  Bank  President  

Fish  &  Wildlife  Manager  

•  Numbers  of  Delta  Smelt  

•  Mul7ple  factors  

•  Factors  act  hierarchically  

•  Iden7fy  important  factors  

Bank  President  

•  Probability  of  loan  default  

•  Mul7ple  factors  

•  Factors  act  hierarchically  

•  Iden7fy  important  factors  

The  Fish  &  Wildlife  Manager  and  the  Bank  President  

Fish  &  Wildlife  Manager  

•  Numbers  of  Delta  Smelt  

•  Mul7ple  factors  

•  Factors  act  hierarchically  

•  Iden7fy  important  factors  

•  No  solu1on—fix  everything  

that  can  be  fixed  

Bank  President  

•  Probability  of  loan  default  

•  Mul7ple  factors  

•  Factors  act  hierarchically  

•  Iden7fy  important  factors  

•  Solved  using  Bayesian  

methods—credit  ra1ng  

Method  

•  Ini7al  focus  on  20  mm  survey  (1995-­‐2014)  – Samples  for  important  early  life  stages  – Concurrent  samples  for  zooplankton  prey  – Samples  biweekly  

•  Iden7fied  possibly  important  factors  •  Considered  hierarchical  influences  •  Divided  habitat  into  zones  •  Allowed  for  7me  variance  in  rela7onships  

How  Does  the  Method  Work?  

•  Experts  collabora7vely  draw  the  influence  diagram:  BUGSAT  

•  Organize  data  •  Analyze  influence  diagram  with  data  •  Modify  the  influence  diagram  based  on  expert  opinion  or  analysis  results  

•  Repeat  un7l  sa7sfied  

length  of  

spaw

ning  

perio

d  

starva7o

n  

pred

a7on

 

air  tem

perature  

phyto-­‐

plankton

 

N/P  con

c.  

Asian  clam

 

turbidity

 

N  &  P  input  

Delta  inflow  

Simplified  hierarchy  delta  smelt  abundance  

Delta

 inflo

w  

aqua7c  vegeta7

on  

dam  con

struc7on

 

SWP-­‐CV

P  en

trainm

ent  

turbidity

 near  

pumps  (adu

lts)  

Old-­‐M

iddle  

River  fl

ow  

X2  (juven

iles)  

expo

rts  

San  

Joaquin  

River  fl

ow  

expo

rts  

Delta

 inflo

w  

lethal  water  

tempe

rature  

air  

tempe

rature  

water  te

mpe

rature  

prey  

density

 

turbidity

 

sedimen

t  washo

ut  

turbidity

 

pred

ator  

abun

dance  

contam

inant  

effects  

contam

inant  

loading  

Delta

 inflo

w  

power  plant  

entrainm

ent  

diversion  

%  sm

elt  n

ear  p

lants  

water  te

mpe

rature  

air  tem

perature  

Resid

ence  7me  

Delta  inflow  

Conceptual  Model  Delta  Smelt  

Delta Smelt Resiliency Strategy

3 July 2016

Chart  from  “Delta  Smelt  Resiliency  Strategy”  

Influence Diagram

The  Data  Problem  

Data  Issues  

•  Missing  data  •  Sample  dates  and  loca7ons  vary  from  survey  to  survey  

•  Sampling  does  not  cover  all  important  loca7ons  

•  Important  factors  not  sampled  well    

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Conclusions  

•  Analyze  with  method  that  is  appropriate  for  – Hierarchical  influences  –  Varying  rela7onships  over  years  –  Varying  rela7onships  by  zones  

•  Lamina7on  is  necessary,  but  not  ideal  •  Obvious  requirements  for  rou7ne  monitoring  –  Extend  historical  records  –  Sample  where  Delta  Smelt  are  –  Sample  simultaneously  for  all  poten7ally  important  factors    

Conclusion  

Bayesian  Network  Analysis  –  Is  collabora7ve  –  Has  been  extensively  used  to  solve  important  

problems  –  Requires  sophis7cated,  well-­‐developed  analy7cal  

methods  –  Offers  the  possibility  of  conver7ng  the  hopelessly  

complex  problem  to  Delta  Smelt  into  a  simpler  problem