Chapter 17 . Classification of Fish Stock-Recruitment Relationships 347
parameters (a" <1" b, and b). Figure 17.5b) illustrates the performance of the
Fuzzy-SR model and the estimated parameters as weH as the summary statistics
are summarized in Table 17.2. The Fuzzy-SR model produced the best fit to the
original recruitment time series based on the estimated root-mean-square-error
(RMSE), AIC and the correlation coefficient (r). The Crisp-SR model performed
better than the Ricker-SR model.
17.4.2.3
Bootstrap Re-samp/ing Analysis
The residual diagnostics do not show any violation for the assumption of
independence and homogeneity. Then the bootstrap residuals procedure in
Section (17.3.2) is carried out for N = 1000 times to generate the bootstrap
samples for the Fuzzy-SR parameters (al' a z • b I and b z ). These bootstrap samples
can be readily used to obtain the uncertainty estimate, such as confidence intervals
and standard errors (Table 17.2 and Table 17.3). In addition, these samples can be
used to test the significance of environmental impact (SST) on this stock (the first
row in Fig. 17.6). It can be concluded that the SST has highly significant impact
on this stock and the productivity parameter increased from 0.52 in "Cool" regime
to 1.72 in "Warm" regime.
Furthermore, the associated management policy parameters SMSY and ~SY can
be readily calculated from equation (17.4) based on the bootstrap samples (Table
17.3). The resultant sampling distributions are illustrated in Fig. 17.6 (last two
rows). It is also apparent that the distributions for these parameters are not exactly
normal.
17.5
Summary and Discussion
The Fuzzy-SR model developed in this paper for SR analysis was based on
extensions of the traditional Ricker model (Ricker-SR) and the Ricker model with
crisp classification for the selected environmental variable (Crisp-SR). This
approach can be naturaHy extended to any other form of SR models, such as the
Beverton-Holt; Cushing; Deriso-Schnute and Shepherd listed in Quinn and Deriso
(1999). Although the Fuzzy-SR model in this paper was illustrated by only one
environmental variable (i.e. SST), it can be easily adapted to classify more
environmental factors (such as salinity) and any fishery intervention factors.
Unlike traditional SR models, Fuzzy-SR adapts the fuzzy logic decision algorithm,
wh ich helps to classify underlying empirical relationships. This enables more
reasonable parameter estimates and consequently better advice for fisheries
management. To address the lack of suitable uncertainty estimation in the fuzzy
logic machine-learning method, a bootstrap re-sampling approach was proposed to
make statistical inference for the SR parameters, to develop distribution plots for
the SR parameters productivity and capacity (i.e. a and b), and further to make
inferences for fishery policy parameters. It was found that the resampling
parameters (a" <1" b, and b). Figure 17.5b) illustrates the performance of the
Fuzzy-SR model and the estimated parameters as weH as the summary statistics
are summarized in Table 17.2. The Fuzzy-SR model produced the best fit to the
original recruitment time series based on the estimated root-mean-square-error
(RMSE), AIC and the correlation coefficient (r). The Crisp-SR model performed
better than the Ricker-SR model.
17.4.2.3
Bootstrap Re-samp/ing Analysis
The residual diagnostics do not show any violation for the assumption of
independence and homogeneity. Then the bootstrap residuals procedure in
Section (17.3.2) is carried out for N = 1000 times to generate the bootstrap
samples for the Fuzzy-SR parameters (al' a z • b I and b z ). These bootstrap samples
can be readily used to obtain the uncertainty estimate, such as confidence intervals
and standard errors (Table 17.2 and Table 17.3). In addition, these samples can be
used to test the significance of environmental impact (SST) on this stock (the first
row in Fig. 17.6). It can be concluded that the SST has highly significant impact
on this stock and the productivity parameter increased from 0.52 in "Cool" regime
to 1.72 in "Warm" regime.
Furthermore, the associated management policy parameters SMSY and ~SY can
be readily calculated from equation (17.4) based on the bootstrap samples (Table
17.3). The resultant sampling distributions are illustrated in Fig. 17.6 (last two
rows). It is also apparent that the distributions for these parameters are not exactly
normal.
17.5
Summary and Discussion
The Fuzzy-SR model developed in this paper for SR analysis was based on
extensions of the traditional Ricker model (Ricker-SR) and the Ricker model with
crisp classification for the selected environmental variable (Crisp-SR). This
approach can be naturaHy extended to any other form of SR models, such as the
Beverton-Holt; Cushing; Deriso-Schnute and Shepherd listed in Quinn and Deriso
(1999). Although the Fuzzy-SR model in this paper was illustrated by only one
environmental variable (i.e. SST), it can be easily adapted to classify more
environmental factors (such as salinity) and any fishery intervention factors.
Unlike traditional SR models, Fuzzy-SR adapts the fuzzy logic decision algorithm,
wh ich helps to classify underlying empirical relationships. This enables more
reasonable parameter estimates and consequently better advice for fisheries
management. To address the lack of suitable uncertainty estimation in the fuzzy
logic machine-learning method, a bootstrap re-sampling approach was proposed to
make statistical inference for the SR parameters, to develop distribution plots for
the SR parameters productivity and capacity (i.e. a and b), and further to make
inferences for fishery policy parameters. It was found that the resampling