mast – a multistock age structured tag-integrated assessment model for atlantic bluefin tuna...

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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Stock 1 Stock 2

ICCAT (2002) BFT Management Areas

Catch At Age Model - Multi-stock, Area

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Use tag data to get at p’s and f

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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)

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P(all the data up until time t-1) prior

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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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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

mast – a multistock age structured tag-integrated assessment model for atlantic bluefin tuna...

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