Deepak George Pazhayamadoma, Emer Rogana, Ciaran Kellyb and Edward Codlingc
aSchool
of Biological, Earth and Environmental Sciences (BEES), University College Cork, Ireland; bFisheries Science Services, Marine Institute, Ireland;
cDepartment of Mathematical Sciences, University of Essex, United Kingdom
Can we manage a fishery if no previous data are available?
Historical data
No
Yes
Quantitative stock
assessments
Self Starting
Cumulative Sum
SS-CUSUM
100
Qualitative risk
assessments
2
-4
20
-2
0
SS-CUSUM
60
40
Large Fish Indicator (LFI)
80
2.0e+07
1.0e+07
0
0.0e+00
Spawning Stock Biomass
4
Control Limit
Upper SS-CUSUM (Positive deviations)
Lower SS-CUSUM (Negative deviations)
Out of Control
5
10
Years
15
20
5
10
Years
15
20
5
10
15
20
Years
No historical data at 0th year
1
Self starting CUSUM (Hawkins, 1998)
SS-CUSUM
• SS-CUSUM is an indicator monitoring tool.
Running mean
• SS-CUSUM do not need a reference point.
(Calibrated using real time data)
• SS-CUSUM calculate the cumulative deviations of indicator from running mean
Three parameters
Parameters
1. Allowance (k)
• Allowance (k) accommodate the inherent variability in observations
2. Control limit (h)
3. Winsorizing constant (w)
• Control limit (h) produce signal if the indicator is in an out-of-control (OC) situation
• Winsorizing constant (w) make self starting CUSUM robust to outliers
EVALUATION
OF
SS-CUSUM USING A STOCHASTIC
SIMULATION TEST
Indicator observations corresponding to outof-control situations are omitted while
calibrating the running mean
• A stable fish stock was overfished and indicators were monitored using SS-CUSUM
97
• Signals obtained from SS-CUSUM were used to calculate sensitivity and specificity
•Receiver Operator Characteristic (ROC) curves
95
94
93
MEASURES USED
92
PERFORMANCE
LFI running mean
• Specificity is the probability of getting a true signal when there was no overfishing
96
• Sensitivity is the probability of getting a true signal when overfishing was applied
5
10
15
20
Years
2
RESULTS (ROC CURVES)
• SS-CUSUM was successful in detecting the fishing impact.
• An indicator is best when the apex of ROC curve is closer to upper left corner.
0.6
Sensitivity
0.4
0.8
0.6
0.4
Sensitivity
BEST
GOOD
0.8
1.0
1.0
•The method performed best with Large Fish Indicators (LF catch numbers, LF catch weight and LF CPUE).
WORST
CONCLUSION
0.0
0.2
0.4
0.6
0.8
1.0
0.2
Recruitment
Landings
CPUE
Large Fish CPUE
Young Fish CPUE
0.0
0.0
0.2
Large Fish Catch Numbers
Large Fish Catch Weight
Mean Age
Mean Length
Mean Weight
0.0
0.2
1-Specificity
0.4
0.6
0.8
1.0
1-Specificity
All stock indicators in the study were useful in detecting fishing impact and hence
SS-CUSUM can be potentially used for monitoring data poor fisheries
REFERENCE:
Hawkins, D.,Olwell, D., 1998. Cumulative sum charts and charting for quality improvement: Springer Verlag, pp:162-168.
3