mast – a multistock age structured tag-integrated assessment model for atlantic bluefin tuna...
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MAST – A Multistock Age Structured Tag-Integrated
Assessment Model for Atlantic Bluefin Tuna
Nathan Taylor, Murdoch McAllister, Barbara Block and Gareth Lawson
Outline
• Background– The mixing problem in a spatially structured
assessment of Atlantic bluefin tuna
• Existing approaches and their problems• Justification for a new approach• The data• Basic MAST model structure• The likelihoods• Some results• Key Issues
Background – This is story of several mixed stock fisheries
Mixing
• The basic stock assessment problem is that there are at least three ‘stocks’ mixing– A resident med stock– A migratory med stock– A migratory GOM stock– Others?
• Movement is seasonal and large scale.
Mixing con’t
• The most recent controversy about this issue arose in the mid 1990’s starting with– Rooker’s otolith microchemistry work 1990
and now 2008– Archival and conventional tags (Block et al.
Lutcavage et al.)
• As usual a read through the literature show that mixing in the med is an old, old controversy
Existing Stock Assessment Approaches
• VPA
• 2 Stock VPA
• Surplus production
• Other SS type models
• Kurota’s sequential bayesian approach
Motivations for MAST• Kurota et al. method
– estimates F and movement from tagging data– ignores stock mixing, reference points and N – doesn’t do projections
• VPA assessments – Have predicted in 1998, 2000, 2002 stock rebuilding yet none has occurred– Have limited ability to account for stock-mixing– Can’t evaluate spatial/ seasonal management options
• Methods that utilize 3 types of tagging data to estimate stock mixing and seasonal movements could provide ‘better’ assessments
– Advocated in 2001 ICCAT mixing workshop– Can account for movement probabilities by stock of origin rather than by area marked (with
supplementary genetic info)– Flexible number of stock areas, and definitions of such areas– Parameterized with Fmsy leading (Martell et al. 2008)– Reference points, N, rebuilding etc.– Exploration of smaller scale spatial closures etc.– Fit to supplementary data
• Otolith micro-chemistry (as multinomial samples of each stock of origin)• Maturity samples
The Data
• Catch Data
• CPUE indices
• Conventional Mark-recapture data
• PSAT and Archival Tags
• Otolith microchemistry (although current very coarse scale)
Catch Data
Conventional Tags (~69 000 depending which ICCAT database
year)
Data Archival Tags
Archival and PSAT tag tracks
MAST the detailed introduction
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Multi-stock Spatial Model
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•Currently we’ve define these areas as ICCAT areas•Catch and effort data won’t contain much information about movement transitions – hence the need for the tag data
Stock 1 Stock 2
ICCAT (2002) BFT Management Areas
Catch At Age Model - Multi-stock, Area
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• N=numbers• i,j=areas• a=age• t=time• M=Natural mortality• f=fleet• v=selectivity• F=fishing mortality• s=stock
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Movement modeling
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Use tag data to get at p’s and f
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Movement Transitions
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Parameters get out of hand in a hurry
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Nages
Quarters
Years (or year grouping)
With 3 age groups, six areas, quarterly time steps this may include up to 432 estimated parameters per time block – a lot!!
Basic MAST model structure
• Four areas• Four fleets (long line, purse seine, bait boat and
other)• Last column of movement matrices given as the
compliment of the other three• No mixing in spawning areas• Start time 1950• Force movement probabilities in the spawning
quarters to come from the (currently fixed) maturity ogives.
Movement Transitions
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Basic MAST Model Structure con’t
1. Divide catches by fleet into 4 areas (GOM, MED, Eastern Atlantic and Western Atlantic).
2. Initialize3. For all subsequent time steps, move the fish according the movement
transition matrices by age group4. Add up the total number of fish in each area (sum of fish that stayed there
(diagonals) and fish that moved there).5. Compute total vulnerable biomass (sum of both stocks in each area)
1. Use this to predict CPUE and fit CPUE data6. Compute stock ratio in each area, quarter
• This gives the predicted ratio (for fitting stock comp data)• Also returns the probability that you’ve marked a fish of stock i (more on this
later)7. Calculate U (Catch/VulBiomass) or F by internal integration of the catch
equation.8. remove caught fish9. Compute predicted precaptures
Likelihoods
CPUE likelihoods
• Log normal• In a typical case, you predict CPUE given some
predicted vulnerable stock biomass (or numbers as applicable).
• In this case we predicted total vulnerable biomass as the sum of vulnerable biomass of both stocks in each area.
• 31 indices constructed for ABFT• Switches for stock-specific indices (where
sampling has shown all the fish to be of one stock or the other)
PSAT and Archival Tagging Data
• Convert tag track data into discreet block observations
• 1 2 1 1 1 2 - -1 2 3 1 2 2 2 1• There were some issues with this
technique, like fish that crossed box boundaries within a quarterly time step
• Rare, but when they occurred we assigned the fish’s location state to the area it spent the greatest proportion of a quarter in
Estimating movement with discreet state-space likelihood DeValpine and
Hastings (2002)
)|()()( 11 tttt YyPYPYP
P(all the data up until time t) posterior
P(all the data up until time t-1) prior
P(observation|data to t-1) ‘likelihood’
Yt=data up until time tyt=observation at time tst=state at time t (alive, dead in area a)
DeValpine con’t
),|()|()|( 111 tttts
ttt YsyPYsPYyPt
Capture probabilities (P(observation given the state)
‘prior’ probabilities of state s
Devalpine (con’t)
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tstttt
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YsPsypYsP
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1
1
If the state is defined as alive in area 1, this can be thought of as the probability of a geolocation in area1, or in a conventional mark-recapture sense as the capture probability
Probabilities of the state are given by the model
DeValpine ExampleData 1 1 0 0 0
Data 2 0 0 1 0
P(yt) 0.2 0.2 0.2 0.2
p(yt|st)
Alive 1 - 0.8 0 0.8
Alive 2 - 0.8 0.2 0.8
dead 1 0 1
P(st|Yt-1)
Alive 1 1 0.86 0.75
Alive 2 0 0.09 0.16
dead 0 0.03 0.09
P(st|Yt)=p(yt|st)P(st|Yt-1)/Σ P(st|Yt-1)
Alive 1 1 0.69 0
Alive 2 0 0.07 1
dead 0 0.035 0
P(yt|Yt-1)= Σ P(yt|st)P(st|Yt-1) - 0.87 0.03
P(Yt-1)P(yt|Yt-1). 1 0.87 0.026
P(alive1)Mv11+P(alive2)Mv21+P(dead)Mvd1
Definition of tag states in MAST
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Tag on fish in areas 1-3
Tag on deck of fishing boat in areas 1-3
Tag is shed
Tag is on dead fish
Poisson Likelihoods for conventional data
• Divide fish up into marked cohort
• Predict numbers alive by area at subsequent time steps
• Poisson likelihood of observed recaptures by area given predicted recaptures
• Predicted recaptures=[Number alive][reporting rate][Fishing mortality]
But you usually don’t know which stock the fish you marked belonged to
With unknown stock of origin much more complex
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Tag on deck of fishing boatStock 1Stock 2
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Tag is on dead fish1Stock 1Stock 2
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1. Initial probability given by ratio of stock s vulnerable biomass to total
Data
• 31 CPUE indices
• 69000 conventional mark-recapture releases (depending on which copy of the ICCAT database you have)
• PSAT
• Archival tag data
• I extracted Oct 2nd Science paper data using Otolith microchemistry
Microchemistry
• I extracted the coarse data from Rooker et al. Science 2008 and fit the observed proportions for each age group as binomial
• But… I ignored the apparent stock mixing they report in the Med (~ 5 % GOM in the med).– No profound intellectual reason behind this,
MAST doesn’t currently permit mixing in the spawning areas
Sample Results
• I’ve simplified greatly but this model is a monster• Still occasionally have convergence/parameter
boundary problems• Computationally burdensome!
– Big 64 bit computer that I now love– Hours to fit– MCMC’s sometimes
• Reporting rate is the thing• Data aren’t final – genotyping all the electronic
samples in progress
Estimated F, All CPUE indices, All tag data, using reported catches
0.0
0.5
1.0
1.5
x
Area 1LLPSBBOth
0.0
0.5
1.0
1.5
2.0
x
Area 2
1950 1960 1970 1980 1990 2000 2010
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
x
Area 3
1950 1960 1970 1980 1990 2000 2010
0.0
0.2
0.4
0.6
0.8
x
Area 4
Year
F
1950 1970 1990 2010
0.6
0.8
1.0
1.2
1.4
b$years
b.ra
tio[i,
]
Area 1
1950 1970 1990 2010
0.4
0.5
0.6
0.7
0.8
0.9
b$years
b.ra
tio[i,
]
Area 2
1950 1970 1990 2010
0.1
0.2
0.3
0.4
0.5
b$years
b.ra
tio[i,
]
Area 3
1950 1970 1990 2010
-1.0
-0.5
0.0
0.5
1.0
b$years
b.ra
tio[i,
]
Area 4
Proportion of GOM stock by area
If we fix conventional reporting rates at 0.5
Conventional reporting Rates fixed at 0.2
Recruitment Anomalies
Catches - maybe0
1000
020
000
3000
040
000
X
Y
Area 1LLPSBBOth
X
Y
Area 2
1950 1960 1970 1980 1990 2000 2010
010
000
2000
030
000
4000
0
X
Y
Area 3
1950 1960 1970 1980 1990 2000 2010
X
Y
Area 4
Year
Cat
ches
Catches - doubled0
10000
20000
30000
40000
50000
X
Y
Area 1LLPSBBOth
X
Y
Area 2
1950 1960 1970 1980 1990 2000 2010
010000
20000
30000
40000
50000
X
Y
Area 3
1950 1960 1970 1980 1990 2000 2010
X
Y
Area 4
Year
Catc
hes
Double catch scenario – reporting rates by area free
01
02
03
04
05
06
07
0
x
We
st
Area 1
Area 2
Area 3
Area 4
1950 1960 1970 1980 1990 2000 2010
02
00
40
06
00
x
Ea
st
Year
SS
B (
kt)
Results con’t
• Current biomass is very sensitive to assumptions/estimates of reporting rates particularly in the Western stock
• Regardless the model predicts– most of Western stock depletion occurred before the start of
current assessment year(s).• Having been affected by Japanese long lining GOM and also, US
long lining in the 60-70s.• Also the mixing scenarios will predict that large Norwegian long ling
catches in the 60’s would have affected the GOM stock– The GOM stock has been at a low level since 1970 but the
current catch rate declines in the eastern US are likely due to large removals of Eastern fish.
– No matter what the parameterization the model shows that the Med stock has been steadily depleted since 1950
Biomass By Area
1020
3040
5060
70
GOM
b$years
2040
6080
100
120
140
West Atlantic
b$years
1950 1960 1970 1980 1990 2000 2010
050
100
150
200
250
300
East Atlantic
b$years
1950 1960 1970 1980 1990 2000 2010
100
200
300
400
500
600
Med
b$years
Year
Tot
al B
iom
ass
(kt)
Vast Majority of CPUE Indices Correspond to small proportion of time-series
Otolith microchemistry data
• Data as presented are highly aggregated over years (not a problem).
• Data are aggregated within years which is a problem
A note on Rooker et al
Integrating across time not such a great idea – and doesn’t tell us much about the state of the stock
Future Work
• Simulation testing to do• Age at maturity hotly contested in reality
– Has big effects on SR relationship/reference points– Has big effects on movement dynamics in this
parameterization
• Growth rates/morphs currently fixed between each stock and assignments of marked fish into age groups is done outside the model
• Time/area/fleet varying reporting rates• Time/area/fleet gear selectivites
Some final thoughts• Movement parameter estimates affected by CPUE data, how much CPUE
downweighting I do has big effects on movement parameters and also on current stock size
– Is there is a defensible way of doing this?• Tag data are relatively good but spatial catch/effort data can be incomplete
with respect to space/time/fleets– Spatial catches in any give year don’t add up to total catches for example
• The most important information (current F) in the assessment year is also the most uncertain
• Delays in reporting tag recoveries• Reporting rates and lags• Catch and CPUE time series sometimes not available in years immediately preceding
the assessment.• Tries to account for CPUE data using movement
• A more detailed stock assessment won’t help is there is no governance• In 2006 for the Med.
– Japanese Imports=2*quota– Quota=2*recommended quota
Focus Questions
Spatial structuring of fisheries in assessment models• What is the best approach to define fisheries and/or populations in stock assessment models? Spatial population dynamics models• When should sub-populations be modeled?• When can interactions between sub-populations be ignored?• Is it reasonable to assume catchability and selectivity is the same among areas?
– In Atlantic bluefin tuna case, probably no. When the fleet is targeting spawning aggregations in spawning areas, difference in age/size structure in these areas, hyperstability due to spawning aggregations.
Information about movement among sub-populations• Should age- or length-frequency data provide information about movement?• Do genetics (or other data e.g. otolith micro-chemistry, morthometics, isotopes....) provide useful
information on movement.– If there sampling were done well we could fit binomial/multinomial likelihoods to the data – in particular if
there were time series stock proportions by area – but there currently aren’t– For ABF, if sampling of heads could be done for stock structure and also used for aging it would be hugely
useful.• What characteristics should a tagging program have to provide adequate information to
parameterize a spatial stock assessment model?– Need to representatively sample areas and time of year. In the Atlantic case, the huge majority of fish were
marked a few discreet coastal areas on the US coast.– If we could devise a tag that automatically broadcast its identy and location as soon as the fish was brought
ot the surface then we could find out way around some of the reporting rate issues.– Other promising techniques might be to use hollow hooks to get individual DNA samples, then sample the
market for those fish
Acknowledgements
• For money– Lenfest
• For wise council– Carl Walters– Rob Ahrens– Steve Martell - Jon Schnute (PBS mapping)- All collaborators
1980 1985 1990 1995 2000 2005
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Can GLS
SSB All CPUE Indices, All tag data, Reported catches
02
04
06
0
x
We
st
Area 1Area 2Area 3Area 4
1950 1960 1970 1980 1990 2000 2010
01
00
30
05
00
x
Ea
st
Year
SS
B (
kt)
Double catch scenario0
10
20
30
40
50
60
70
x
We
st
Area 1
Area 2
Area 3
Area 4
1950 1960 1970 1980 1990 2000 2010
02
00
40
06
00
x
Ea
st
Year
SS
B (
kt)
A good sampling program?
A really long time ago…
• Aristotle 325 BC
• Cetti 1777
Discussion - CPUEs
• If the catch data are lies, then so too are the CPUE data– In addition we’ve been fitting the standardized indices rather
than breaking them out into finer (quarterly) time steps
• Noisy! Don’t contain much information about depletions• Not long enough• Don’t consider spatial hyperdepletion or hyperstability
effects (fishing on spawning aggregations for example)• Several cases where catches are going up and CPUE
also going up
Mark-recapture data themselves have their issues
• The number of reported releases in the ICCAT database has varied in database from 1995-present
• Sampling is very limited and unrepresentative I can’t stress this point enough the overwhelming majority of releases of all tag types come from the Eastern seaboard of the United States
Fishery data and modeling much more troublesome than tag data
• Spatial resolution has varied over time
• Spatial catch reporting by fleet/country has not been consistent over time
• Some obvious gross simplifications of ICCAT data
• Gross under-reporting of eastern catches
• Targeting behaviour, q, gear selectivity has changed considerably over this period
The Road Ahead - Testing