"Kalman-filter reconstructions of temporal variation in productivity of Northeastern Pacific salmon"

Transcription

1 "Kalman-filter reconstructions of temporal variation in productivity of Northeastern Pacific salmon" Randall M. Peterman, Brigitte Dorner, Steven L. Haeseker 1, Brian J. Pyper 2, and Franz J. Mueter 3 School of Resource and Environmental Management (REM) Simon Fraser University Burnaby, British Columbia, Canada 2 S.P. Cramer & Associates, Inc., Gresham, Oregon 3 Sigma Plus Consulting, Fairbanks, Alaska 1 U.S. Fish & Wildlife Service, Vancouver, Washington PICES Symposium, Honolulu, April

2 Acknowledgments Other collaborators - Chris Wood - Mike Bradford - Dan Ware - Zhenming Su - Carrie Holt - Steve Haeseker Agencies - Washington Dept. of Fish and Wildlife - Canada Dept. of Fisheries and Oceans - Pacific Salmon Commission - Alaska Department of Fish and Game 2

3 Outline 1. Research objective: Understand variation in productivity of Pacific salmon 2. Past results - Spatial scale of positive covariation in -- Salmon productivity -- Environmental variables 3. New results - Do we get same conclusions when we account for observation error in salmon data using a Kalman filter? 3

4 1. Research objective What are the key environmental sources of variation in salmon productivity (~ recruits/spawner)? 4

5 1. Research objective What are the key environmental sources of variation in salmon productivity (~ recruits/spawner)? 1st step Identify spatial extent of positive correlation in productivity of salmon stocks Data on 120 salmon stocks 5

6 1. Research objective What are the key environmental sources of variation in salmon productivity (~ recruits/spawner)? 1st step Identify spatial extent of positive correlation in productivity of salmon stocks 2nd step: Screening Identify environmental variables with similar spatial scale to that of salmon productivity Data on 120 salmon stocks Data on environmental variables: coastal SST, coastal salinity, upwelling 6

7 2. Results of past research What is the spatial scale (extent) of positive correlation in productivity among salmon stocks? Abundance data (1950s to 2001) - Spawners (S), catch, adult recruits (R) 7

8 120 salmon stocks; averaging 31 years of S-R data 40 Pink salmon Alaska 43 stocks Yukon B.C Sockeye salmon Chum salmon Alaska stocks Yukon 16 B.C Alaska stocks Yukon B.C. 8

9 Removed within-stock density-dependent effect 2.5 Log e (recruits per spawner) Residual for brood year Spawners (thousands) 9

10 Residuals from fitted relation Residual for brood year Brood year 10

11 Pink salmon 2 Chignik Central Alaska Peninsula S.W. r = 0.62 Standardized residuals (mean=0, SD =1) Brood Year

12 Pairwise correlations in productivities among 43 pink salmon stocks 1.0 Correlation % confidence interval Distance between stocks (km) Mueter et al Fish. Oceanog. 12

13 Average correlations in productivities among 43 pink salmon stocks 1.0 Correlation Distance between stocks (km) Mueter et al Fish. Oceanog. 13

14 Regions of positive correlation in productivity of pink salmon stocks Norton Sound Cook Inlet Alaska Prince William Sound Yakutat Yukon Bristol Bay Alaska Peninsula Chignik Kodiak 500 km Northern B.C. Southeast Alaska B.C. Central B.C. Mainland B.C. Fraser River Washington WA Pyper et al. (2001) CJFAS 14

15 0.4 Pink Correlation Sockeye 50% correlation scales P S Distance between stocks (km) Mueter et al. (2002) Fish. Oceanog. 15

16 Correlation 0.4 Pink Chum Sockeye ~ 500 to 800 km P S C Distance between stocks (km) Mueter et al. (2002) Fish. Oceanog. 16

17 Correlation Also, correlation scale between pink-chum is ~ 500 km Pyper et al. (2005) TAFS 0.4 Pink Chum Sockeye ~ 500 to 800 km P S C Distance between stocks (km) Mueter et al. (2002) Fish. Oceanog. 17

18 Conclusion on spatial scale Regional-scale (~ 500 to 800 km) - Positive correlation in productivity among stocks -- pinks, chum, sockeye 18

19 Mechanisms, part 1 At which life stage does most covariation arise? Late freshwater or early ocean life stages Sockeye salmon (Peterman et al. 1998) Pink salmon (Pyper et al. 2001) Chum salmon (Pyper et al. 2002) 19

20 Mechanisms, part 2 What is driving spatial covariation in productivities? Which environmental variable(s) have a similar (i.e. regional) spatial scale to that of salmon productivities (~ 500 to 800 km)? - Upwelling? - Coastal sea-surface temperature (SST)? - Coastal sea-surface salinity? 20

21 Result: Summer sea-surface temperature spatial scale ~ 500 km, same as salmon productivity Added summer SST as explanatory variable to models of salmon productivity - Regional SST was specific to each stock's location of ocean entry 16 models that included summer SST fit much better than 8 models without SST Mueter et al. (2002a,b) Fish. Oceanog. and CJFAS, and Su et al CJFAS 21

22 Repeated analyses with PDO (large-scale index) - PDO was less important than regional SST Therefore, environmental processes at the regional scale are the most important - Larger, ocean-basin scale processes reflected by PDO, AOI, etc. may drive large-scale forcing, but there are different responses in different regions. Mueter et al. (2002) CJFAS 22

23 Largescale processes (thousands of km) PDO, ALPI, NPI, AOI,... 23

24 Largescale processes (thousands of km) PDO, ALPI, NPI, AOI,... SST 2 SST... SST SST 3 k 1 24

25 Largescale processes (thousands of km) PDO, ALPI, NPI, AOI,... SST 2 SST 3... SST k SST 1 Regionalscale processes (< 800 km) Prod. stock 1 Prod. stock 2 Prod. stock 3 Prod. stock 4 Prod. stock 5... Prod. stock m 25

26 3. New results that account for observation errors Errors in estimation of abundance of spawners and recruits (observation error = "noise") Residuals in salmon productivity 0 Year Interested in process variation (="signal"), not in "noise" Used Kalman filter method - From engineering - Helps detect "signal" amid "noise" 26

27 Standard method Productivity estimates Signal + Noise Data 27

28 Standard method Productivity estimates Signal + Noise Data Productivity estimates Kalman filter method Signal Noise Peterman et al CJFAS

29 Brian Pyper's (in prep.) comparisons of Kalman filter versions of Ricker stock-recruitment model Found time-varying Ricker 'a' model was best for most salmon populations Do we draw same conclusions as before when we use Kalman filter estimates of productivity? 29

30 Standard method (least squares) Ln(R t / S t ) = a - bs t + u t Constant a and b parameters R = adult recruits S = spawners 30

31 Standard method (least squares) Ln(R t / S t ) = a - bs t + u t Constant a and b parameters R = adult recruits S = spawners Kalman filter method Observation equation Ln(R t / S t ) = a t - bs t + v t Note: time-varying Ricker a parameter System equation a t = a t-1 + w t random walk Estimates a t each year Peterman et al. (2000) CJFAS 31

32 Independent testing of methods is rarely done We tested via simulations: - Standard method - Kalman filter method Specified hypothetical "true" change in Ricker a t parameter, then: - Generated population dynamics stochastically 2. Estimated underlying parameters from simulated data 3. Compared estimates with "true" values 32

33 Scenarios for "true" Ricker a ("signal") Ricker a parameter Sine Ricker a parameter Year Step Autoregressive lag Year Year Peterman et al. (2000) CJFAS 33

34 Index of Productivity (Ricker 'a' parameter) "True" Standard method Kalman Filter Simulation test Year 34

35 3.0 "True" Standard method Kalman Filter Simulation test Index of Productivity (Ricker 'a' parameter) Year Year Peterman et al. (2000) CJFAS 35

36 Mean squared error in Ricker a parameter estimates compared to the "true" Ricker a parameter Kalman filter method Standard method (least squares) "True" Therefore, used a Kalman filter to reconstruct historical time series of productivity Sine wave in a Step in a Autoregressive a Constant a Peterman et al. (2000) CJFAS 36

37 Standardized time series i.e., Transformed each reconstructed data series: mean = 0 and SD = Made different time series data sets comparable 37

38 Productivity of 8 Bristol Bay, Alaska sockeye stocks 2 Standardized residuals from Ricker model mean r = Year of spawning Peterman et al CJFAS

39 Productivity of 8 Bristol Bay, Alaska sockeye stocks 2 Standardized residuals from Ricker model mean r = Standardized productivity (Ricker 'a' parameter) from Kalman filter Year of spawning mean r = 0.60 Peterman et al CJFAS

40 Productivity of 8 Bristol Bay, Alaska sockeye stocks 2 Standardized residuals from Ricker model mean r = Standardized productivity (Ricker 'a' parameter) from Kalman filter Note mean r = Year of spawning Peterman et al CJFAS

41 Kalman filtering reduces "noise" and increases correlation 0.6 Mean pairwise correlation 0.4 in productivity among stocks 0.2 Residuals Kalman filter 'a' values 0 Sockeye in Bristol Bay, Alaska 41

42 Cook Inlet & Kodiak chum salmon Standardized productivity (Ricker 'a' parameter) from Kalman filter mean r = 0.62 Brood year (year of spawning) CI.outer CI.southern CI.Kamishak CI.UpperCook Kodiak 42

43 Inside Washington chum salmon 2 mean r = 0.61 Skagit River Standardized productivity (Ricker 'a' parameter) from Kalman filter Brood year (year of spawning) Nooksack and Samish rivers Sillaguamish and Snohomish rivers Hood Canal South Sound, fall South Sound, summer South Sound, winter 43

44 Mean correlation in productivity among stocks Kalman filtering reduces "noise" and increases correlation Residuals Kalman filter 'a' values 0 Sockeye in Bristol Bay, Alaska Chum (five regions) 44

45 Yakutat, Prince Wm. Sound, Lower Cook pink salmon Standardized productivity (Ricker 'a' parameter) from Kalman filter Brood year (year of spawning) Situk.R Humpy.Ck Eastern Montague Southeast South.District Outer.District Kamishak 45

46 Chignik, Alaska Peninsula pink salmon Standardized productivity (Ricker 'a' parameter) from Kalman filter Brood year (year of spawning) Chigni.Bay Central Eastern Western Perryville NW.District SE.Scentral SW.Unimak 46

47 Average correlation between Bristol Bay sockeye and sockeye in other regions 0.6 Average correlation among stocks in productivity (Ricker 'a' parameter from Kalman filter) Bristol Kodiak Copper Fraser Bay Cook BC Chignik Inlet Central 47

48 Average correlation between Washington pinks and pinks in other regions 1.0 Average correlation among stocks in productivity (Ricker 'a' parameter from Kalman filter) Wash. BC SEAK AK Norton S. CentralKodiak Chignik Pen. AK

49 Conclusions from Kalman filter results 1. Kalman filter estimates show clearer "signal" (variation in historical biological processes) 2. Clearer evidence that salmon productivity is highly positively correlated among stocks within regions 3. Still have smaller or negative correlations between regions 49

50 Kalman filter code and worked examples in Excel and S-Plus: Available from Simon Fraser University: 50

51 Relevant publications ( Kalman filter models: - Peterman et al. (2003) CJFAS 60: Peterman et al. (2000) CJFAS 57: 181 Salmon productivity: - Pyper et al. (2005) Trans. Amer. Fish. Soc. 134: 86 - Mueter et al. (2002) CJFAS 59:456, plus 60: Pyper et al. (2002) Tr. Am. Fish. Soc. 131: 343 chums - Pyper et al. (2001) CJFAS 58: 1501 pinks - Peterman et al. (1998) CJFAS 55: 2503 sockeye Oceanographic variables: - Mueter et al. (2005) Trans. Amer. Fish. Soc. 134: Mueter et al. (2002) Fisheries Oceanography 11: