12th IMR\PINRO Symposium
Applying the Bayesian approach in assessment of red king crab (Paralithodes camtschaticus)
and northern shrimp (Pandalus borealis) stocks in the Barents Sea
by
Sergey Bakanev and Boris Berenboim PINRO, Murmansk, Russia
Introduction
Bayesian’s theorem has been applied in fishery biology since 1990s. At present these models are widely used to describe the status of stocks and in forecasting.
The estimates of the stock status made by this method have been supported by CCAMLR, FAO, NAFO, NEAFC, ICES.
Goal
to review the possibility of using this method for assessing the
population dynamics and TAC of northern shrimp and red king crab in the Barents Sea
The Bayesian approach was used to construct a posterior model parameters distributions
)
|
( data
p
)
| ( data
p
) ( p
is the posterior probability distributions ? of parameters?,
is the likelihood function of difference between s urvey indices and absolute biomass,
is the estimated or assumed prior probability distribution of unobservable parameters (catchability coefficients, MSY, carrying capacity, etc.).
) (
)
| (
)
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( data p data p
p
Methods
State equations
1
1
1
m t t
t t
t
t
K
B K
MSY B V
C B
B
Production model for red king crab and shrimp stocks
a m
R PR t
t
PR molt G e e
R
1 * *
,*
*
b m
y t
m P
PR t
t t
t
P R PR molt G e C e e
P
1 (( * *
,) *
*
( 1)*) *
1, 11
1
, )
1 ( , ,
, 1
, 1
,
1 [ ( ) ] *
l
l l tl
nl t
l M y t l M
t l t
l l
l t
l P N O e C e m e R
N t t
ol t
l M
y t l M
t l t
l t
l
N O e C e m e
O
1, 1 [(
1,
1,)
t
1, ( 1) t]( 1
1,) *
Cohort model Catch Survey Analysis (CSA) for red king crab
Cohort model Length-Based Analysis (LBA) for red king crab
Methods
Shrimp input data
Russian trawl survey data, Norwegian trawl survey data,
Ecosystem trawl survey data Area-swept method
(observed abundance by year)
Fishery data
Russian and Norwegian CPUE, total catch
Consumption by cod (AFWG)
Crab input data
Trawl survey data
Area-swept method (observed abundance by
length, sex, shell condition, year)
Fishery data
Catch in numbers
(by length, shell condition, year)
Tagging data
(length increment per moult, moulting probability)
Results for shrimp
Comparison of observed and model estimated values:
CPUE and survey stock biomass indices
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1982 1986 1990 1994 1998 2002 2006
0 0.5 1 1.5 2 2.5
R-CPUE N-CPUE N-Surv Eco-Surv B(est)
Bt/Bmsy
CPUE and Survey Indecies
Results for shrimp
Dynamics of northern shrimp stock in the Barents Sea by management zone applying the precautionary approach for
1982-2005
(dark area – safe zone)
1994 2006
2000
1995 1990
1982
0 0.5 1 1.5 2 2.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
BMSY
Zlim Blim
Relative mortality(Zt/Zmsy)
Relative biomass (Bt/Bmsy)
Results for shrimp
0 0.25 0.5 0.75 1
0 200 400 600 800 1000 1200
Removal by fishery and cod ('000 t)
Risk of exceeding MSY
The cumulative probability of exceeding MSY
Results for red king crab
Fitted (lines) and observed survey index (circles) of legal stock using production, CSA, LBA models in REZ of the Barents Sea
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
1994 1996 1998 2000 2002 2004 2006
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Production CSA LBA Survey index
Abandunce of legal stock, '000 spec. Index of legal stock, '000 spec.
Results for red king crab
6 7 8 9 10 11
2007 2008 2009 Abandunce of legal stock, '000 000 spec.
А
6 7 8 9 10 11
2007 2008 2009
B
Forcasted legal stock with annual catch
of 2 million (А), 3 million (B) and 4 million (C) in 2007-2009 according to production (1), CSA (2) and LBA (3) models
6 7 8 9 10 11
2007 2008 2009
1 2 3
C
Conclusions
The Bayesian approach can be used for estimating the population dynamics of northern shrimp and red king crab in the Barents Sea and Spitsbergen area.
The dynamics of the Barents Sea red king crab population parameters is extremely unstable. But the presence of strong year-classes make it possible to forecast the stock dynamics and develop appropriate management strategies.
