Chapter 17 . Classification of Fish Stock-Recruitment Relationships 343
parameters (a. and ß) are learned from the procedures described in Section 17.3. In
the optima learning process, the initial value for the centre-parameter a. is chosen
to be the long-term time series average and initial slope parameter ß is chosen to
be 200 to reflect the crisp classification. Figure 17.3b) illustrates the performance
of the Fuzzy-SR model. The estimated parameters as weIl as the summary
statistics are summarized in Table 17.2. For comparison, a Ricker SR model was
also fit to the data.
A comparison of the results produced by the three different models is
summarized in Table 17.2. The model comparison is based on three criteria. The
first is the estimated root-mean-square-error (RMSE) in which the smaller the
RMSE, the better the model fit. The second criterion is the well-known Akaike
information criterion (AIC) (Sakamoto et. al. 1986) to penalize MSE from the
number of the model parameters. When using AIC criterion to compare the model
fit, the smaller the AIC, the better the fit. The third criterion is the correlation
coefficient (r). From all these three criteria, the Fuzzy-SR model produced the
best fit to the original recruitment time series. The Crisp-SR model performed
better than the Ricker-SR model, which is consistent with the results obtained by
Ware (1996).
Table 17.3. Summary statJstJcs of the bootstrap re-sampling distributions
corresponding to two different environmental regimes: "Cool" and "Warm". The
column "Model" represents the estimate from the Fuzzy-SR model, "Mean" is the
mean for the 1000 bootstrap sampies and "CI" is the 95% sample confidence
interval obtained from 2.5% and 97.5% sampie quantiles.
WCVI Herring
SEAK Pink
Model
Mean
CI
Model
Mean
CI
a,
1.47
1.46
(0.98,1.92)
0.52
0.61
(0.103, 1.3)
b,
3.16E-02 3.13E-02 (2.28E-2,4.07E-2) 1.23E-04 l.55E-04 (6.12E-6,3.98E-4)
Cool
SMSY
NA
NA
NA
1960
1808
(484,3770)
J,!MSY
NA
NA
NA
0.24
0.27
(0.05,0.53)
a2
0.54
0.59
(0.64,1.17)
1.72
1.84
(1.36, 2.49)
b2 5.46E-02 5.6IE-02 (3.38E-2,7.6IE-2) 6.82E-05 1.03E-04 (5.27E-6,2.91E-4)
Warm
SMSY
NA
NA
NA
9573
8589
(2670, 24600)
'"MSY
NA
NA
NA
0.65
0.68
(0.55,0.81)
parameters (a. and ß) are learned from the procedures described in Section 17.3. In
the optima learning process, the initial value for the centre-parameter a. is chosen
to be the long-term time series average and initial slope parameter ß is chosen to
be 200 to reflect the crisp classification. Figure 17.3b) illustrates the performance
of the Fuzzy-SR model. The estimated parameters as weIl as the summary
statistics are summarized in Table 17.2. For comparison, a Ricker SR model was
also fit to the data.
A comparison of the results produced by the three different models is
summarized in Table 17.2. The model comparison is based on three criteria. The
first is the estimated root-mean-square-error (RMSE) in which the smaller the
RMSE, the better the model fit. The second criterion is the well-known Akaike
information criterion (AIC) (Sakamoto et. al. 1986) to penalize MSE from the
number of the model parameters. When using AIC criterion to compare the model
fit, the smaller the AIC, the better the fit. The third criterion is the correlation
coefficient (r). From all these three criteria, the Fuzzy-SR model produced the
best fit to the original recruitment time series. The Crisp-SR model performed
better than the Ricker-SR model, which is consistent with the results obtained by
Ware (1996).
Table 17.3. Summary statJstJcs of the bootstrap re-sampling distributions
corresponding to two different environmental regimes: "Cool" and "Warm". The
column "Model" represents the estimate from the Fuzzy-SR model, "Mean" is the
mean for the 1000 bootstrap sampies and "CI" is the 95% sample confidence
interval obtained from 2.5% and 97.5% sampie quantiles.
WCVI Herring
SEAK Pink
Model
Mean
CI
Model
Mean
CI
a,
1.47
1.46
(0.98,1.92)
0.52
0.61
(0.103, 1.3)
b,
3.16E-02 3.13E-02 (2.28E-2,4.07E-2) 1.23E-04 l.55E-04 (6.12E-6,3.98E-4)
Cool
SMSY
NA
NA
NA
1960
1808
(484,3770)
J,!MSY
NA
NA
NA
0.24
0.27
(0.05,0.53)
a2
0.54
0.59
(0.64,1.17)
1.72
1.84
(1.36, 2.49)
b2 5.46E-02 5.6IE-02 (3.38E-2,7.6IE-2) 6.82E-05 1.03E-04 (5.27E-6,2.91E-4)
Warm
SMSY
NA
NA
NA
9573
8589
(2670, 24600)
'"MSY
NA
NA
NA
0.65
0.68
(0.55,0.81)