340
D.G. Chen
Step 1: Construct the Fuzzy-SR model from Seetion (17.2.2) from the original
SR data (S" R" SST" t=1 to n) and obtain the parameter estimates (i.e. a J , a 2 , bJ' b 2 ,
a and ß) from the hybrid optimal learning algorithm in Section (17.3.1);
Step 2: Calculate the residuals, c t = Y t - Y t • Perform the residual diagnostics
for independence and homogeneity. If the residuals are identically independently
distributed (i. i. d.) with a zero mean and a constant variance of cl, then go to Step
3. Otherwise, go back to Step 1 with a proper transformation for the SR data;
Step 3: Randomly draw an i. i. d. sampie { -*t t t=1 with replacement from the
residuals c t = Y t - Y t and construct the matrix X and y* = [Y*l'''''Y*n] in
equation (17.12)with Y*t =-t+-*t,t=I,,,.,n;
Step 4: Using the procedure from (17.14) to get a new set ofparameter vector
B=(a J , a 2 , b J , b 2 ) with the resampled data;
Step 5: Repeat Step 3 to Step 4 a large number of times, say, N, (with 1000 as a
suggested number of repeats).
The above steps will yield a sampie for the Fuzzy-SR parameter vector as B J ,
A, B N • This sampie can be used to construct a sampling distribution for the SR
parameters: a J , a 2 , b J and b 2 . The sampling distributions can then be obtained for
the fishery management policy parameters, such as MSY spawner, SMSY and MSY
exploitation rate, u MSY from equation (17.4).
17.4
Two Real Oata Analyses
17.4.1
West Coast Vancouver Island Herring Stock
17.4.1.1
Data Prescription and Pre/iminary Analyses
It was found from a long-term research program of the west coast of Vancouver
Island (WCVI), British Columbia herring stock that the SST (in year t-3) has
profound impact on the biomass of 3-year old herring recruits (in year t) along
with the biomass of spawners (i.e. parents) in the year in wh ich the recruits were
born (Ware 1991; Ware and McFarlane 1995; ehen and Ware 1999).
Temperature is believed to be a proxy "signal" which reflects inter-annual
variability in the relative biom ass of larval and juvenile herring predators, and
possibly some important components ofthe herring food supply. In general, cooler
(warmer) temperatures tend to produce larger (smaller) recruitments 3-years later.
D.G. Chen
Step 1: Construct the Fuzzy-SR model from Seetion (17.2.2) from the original
SR data (S" R" SST" t=1 to n) and obtain the parameter estimates (i.e. a J , a 2 , bJ' b 2 ,
a and ß) from the hybrid optimal learning algorithm in Section (17.3.1);
Step 2: Calculate the residuals, c t = Y t - Y t • Perform the residual diagnostics
for independence and homogeneity. If the residuals are identically independently
distributed (i. i. d.) with a zero mean and a constant variance of cl, then go to Step
3. Otherwise, go back to Step 1 with a proper transformation for the SR data;
Step 3: Randomly draw an i. i. d. sampie { -*t t t=1 with replacement from the
residuals c t = Y t - Y t and construct the matrix X and y* = [Y*l'''''Y*n] in
equation (17.12)with Y*t =-t+-*t,t=I,,,.,n;
Step 4: Using the procedure from (17.14) to get a new set ofparameter vector
B=(a J , a 2 , b J , b 2 ) with the resampled data;
Step 5: Repeat Step 3 to Step 4 a large number of times, say, N, (with 1000 as a
suggested number of repeats).
The above steps will yield a sampie for the Fuzzy-SR parameter vector as B J ,
A, B N • This sampie can be used to construct a sampling distribution for the SR
parameters: a J , a 2 , b J and b 2 . The sampling distributions can then be obtained for
the fishery management policy parameters, such as MSY spawner, SMSY and MSY
exploitation rate, u MSY from equation (17.4).
17.4
Two Real Oata Analyses
17.4.1
West Coast Vancouver Island Herring Stock
17.4.1.1
Data Prescription and Pre/iminary Analyses
It was found from a long-term research program of the west coast of Vancouver
Island (WCVI), British Columbia herring stock that the SST (in year t-3) has
profound impact on the biomass of 3-year old herring recruits (in year t) along
with the biomass of spawners (i.e. parents) in the year in wh ich the recruits were
born (Ware 1991; Ware and McFarlane 1995; ehen and Ware 1999).
Temperature is believed to be a proxy "signal" which reflects inter-annual
variability in the relative biom ass of larval and juvenile herring predators, and
possibly some important components ofthe herring food supply. In general, cooler
(warmer) temperatures tend to produce larger (smaller) recruitments 3-years later.