“FORGOTTEN SIGNALS IN FISHERIES MANAGEMENT”

Supervisors

​

Emer Rogan

(Department of ZEPS, University College Cork, Ireland)

​

Ciaran Kelly

(Fisheries Science Services, Marine Institute, Ireland)

​

Edward Codling

(Lecturer in Mathematical Biology, University of Essex, UK)

By, Deepak George Pazhayamadom

​

Department of Zoology, Ecology and Plant Science (ZEPS)

University College Cork (UCC), Cork, Ireland

​

Systems – Indicators - Signals

This guy happy or not?

Hey dude,

How are you?

Not good at all

No

a) Not good

b) Not so good

c) Not so bad

d) Ok

e) Good

f) Very good

g) Great

a) Relationship

b) Environment

c) Physical health

Ok

a) Response

b) Expressions

c) Movement

d) Interactions

1.Not Good� (Hit)

2. Good� (False Alarm)�3. No answer� (Miss)

OC

Probability

Distribution

a) Variability

b) Environment

c) Interactions

Response

Indicators

1. OC� (Hit)

2. IC� (False Alarm)�3. No signal� (Miss)

Fisheries

In-control�or�Out-control

SYSTEM

SIGNAL

PROBABILITY

NOISE

SIGNAL

+

NOISE

SIGNAL

DETECTION

DECISION

OBSERVATION ERROR

Fisheries Management

(Traditional approach)

​

Fishery Dependent Data:

Catch (BIAS, NOISE)

Fishery Independent Data:

Survey (BIAS, NOISE)

Fisheries Management

(Alternative approach)

​

SSB, F

[Estimated Indicators]

(Stock abundance and Exploitation)

Population models with assumptions

Monitor with Reference Limits

(Acceptable, Precautionary, Limit)

Regulate with output controls

​

HCR (Eg: TAC)

Other measures (Eg: Effort)

Next Year

Limit 1000 1.5

Precautionary 1500 0.8

Acceptable 2000 0.5

F

SSB

Statistical Process Control�[Signal Detection Method]

Statistical Signals

[Stock Indicators]

Maximize Yield

Stabilize Yield

SPC

(Statistical Process Control)

• Data and process analysis
• Making inferences about process behaviour
• Decision making

Data for time = n

Monitor Parameter

In Control ?

YES

NO

Corrective Action

Product

START

(For days = 30)

Monitor pH

8.1>pH>8.4 ?

YES

NO

Correct Cause

END

(Fish lives)

MARINE AQUARIUM

​

Parameters:

1. pH (8.1 – 8.4), µ = 8.25

2. Temperature (72 – 78^oF), µ = 75^oF

3. Nitrate (< 1.0 ppm), µ = Zero

​

For pH:

​

Upper Control Limit (UCL) = 8.4

Mean = 8.25

Lower Control Limit (LCL) = 8.1

​

Whether pH is 8.4 > x > 8.1 ? OR

​

If not, What to do ?

​

YES

Fish dies

NO

d = d+1

If

d = 30

d = 0

YES

NO

If

d = 30

END

(Fish lives)

YES

NO

SPC is a statistical technique concerned with stabilizing processes to fixed targets

Fisheries Management

Parameters:

1. Indicator 1

2. Indicator 2

3. Indicator 3

​

For Indicator 1:

​

Upper Control Limit (UCL) =

Mean =

Lower Control Limit (LCL) =

​

​

Whether Indicator 1 is UCL> x > LCL ?

​

If not, What to do ?

Control Charts

Pictorial representation of SPC

​

1. Shewhart Control Chart (Detect transient changes)

µ = Reference Mean (Target)

h = Reference Limit

2. CUSUM : Cumulative Sum Control Chart (Detect persistent changes)

​

[z_t=(D-µ)/σ] D = Indicator(Time Series)

​

µ = Reference Mean (Target)

σ = Standard Deviation (Permissible)� k = Allowance Parameter� h = Reference Limit

​

Lower CUSUM : Ф^-_n = min (0, Ф ^-_n-1 + z_n + k), Ф^-₀ = 0

Upper CUSUM : Ф⁺_n = max (0, Ф ⁺_n-1 + z_n - k), Ф⁺₀ = 0�

Monitor a process using indicator/s and stabilize the system using corrective action if the control chart signals an “Out of Control” situation.

UPPER CONTROL LIMIT (UCL)

CONTROL MEAN (Cµ)

LOWER CONTROL LIMIT (LCL)

First OC

UPPER CONTROL LIMIT (UCL)

Allowance Parameter (‘K’)

First OC

UCL

LCL

Cµ

K

Fisheries Management

σ

CUSUM parameters

Objective: Whether performance of CUSUM is consistent with the current traffic light approach� of traditional stock management ?

Precautionary SSB limit (B_pa) was used to define the shift of detection

​

Fisheries used : Irish Sea cod� Celtic Sea & Bay of Biscay Megrim� North East Atlantic Mackerel

​

Reference Period : All years for which SSB was above B_pa

​

Allowance Parameter (k) : ½ [ ( µ– B_pa ) / σ ]

​

Decision limit (h) : Tuned using R-scripts provided by FISBOAT project � (Mesnil and Petitgas, 2009)

​

Indicators : Age-based catch numbers, catch weights and their proportions�� Indicators highly correlated with SSB were considered good

CN6

r= 0.09310228

CN11

r= 0.90395651

Indicator Correlation

Greenland Halibut in Subareas I and II (1964-2006)

Irish Sea Cod

(Division VIIa)

Irish Sea Cod

(Division VIIa)

Celtic Sea and Bay of Biscay Megrim�(Sub-area VII and Divisions VIIIa,b,d,e)

Celtic Sea and Bay of Biscay Megrim�(Sub-area VII and Divisions VIIIa,b,d,e)

North East Atlantic Mackerel�(Southern, Western and North Sea)

North East Atlantic Mackerel�(Southern, Western and North Sea)

Discussion

• CUSUM for real time qualitative assessments

​

• Performance of CUSUM was found consistent with traditional traffic light approach

​

• Delayed signals might happen when recruitment to the fishery occur before maturity

​

• Performance of CUSUM with species having different life histories

​

• Role of CUSUM in a fisheries management framework with Harvest Control Rules (HCRs)

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Irish Sea Cod

(Division VIIa)