Spatial issues in WCPO stock assessments

(bigeye and yellowfin tuna)

Simon HoyleSPC

Introduction

• Overview of WCPO fisheries and stock assessments

• Summary of spatial issues• Deeper examination of several issues

WCPO

Complex fisheries

• Fishing methods – longline, purse seine, pole and line, other

• Fleets– JP DW LL, JP offshore LL, Korea, China, US, …

• Species– Skipjack, bigeye, yellowfin, albacore, swordfish, …

• Spatial– Oceanography, thermocline depth, seasonal changes,

convergence zones, seamounts, migrations, age effects, EEZs,

Spatial stratification

– bigeyetuna

– yellowfintuna

30

S1

0S

10

N3

0N

120E 150E 180 150W 120W

R1 R2

R3 R4

R5 R6

LPS Z

Max=39395Max=39395Max=39395Max=39395

Legend

30

S1

0S

10

N3

0N

120E 150E 180 150W 120W

R1 R2

R3 R4

R5 R6

LP

S ZMax=348801Max=348801Max=348801Max=348801

Legend

Model structure• 6 regions. Qtrly age classes (e.g. 40 bigeye).• Input data

– Catch, CPUE, size frequency, tag recapture• Population dynamics

– Recruitment: overall regional proportion, temporal trend, regional deviates, B-H SRR.

– Growth (estimated).– Age-specific natural mortality (fixed).– Movement dynamics (estimated).

• Fitting to data– LL CPUE index – shared catchability and selectivity among

regions.– Size frequency, given selectivity by fishery– Tagging data

Selected spatial issues

• Regionalization of model– Choosing the right regions

• Regional scaling of CPUE• Estimating movement among regions• Spatial effects not included in the model

Criteria for defining regions• Simplicity (“less is more”)• Homogeneous abundance trend (CPUE) in

region*• Homogeneous size data in a region*• Biogeography• Enough data from region to reliably index

abundance and size• Specific management issues (e.g. ID)• Consistency between assessments – fishery

interactions

Spatial heterogeneity – YFT CPUE trendsJP LL standardised CPUE.

GLMs include 5*5 lat/long, HPB, bet_cpue, and no_hooks.

Consistent local variation accounted for by lat-long GLM effects

Different trends require separate regions

Spatial CPUE variation

• Yellowfin in region 3, one band of latitude per plot.

• Less pronounced decline north of 10N

• Steep decline in far west (of 120E), arguably deserves separate region

17.5

7.5 2.5

-2.5 -7.5

12.5

Spatial heterogeneity - Size• Most size data 10 lat * 20 long blocks.• Compare trends in median length/weight

between 10*20 blocks.• Minimal size data from far west (of 120E)

120 140 160 180 200 220

-40

-20

020

1950

120 140 160 180 200 220-4

0-2

00

20

1960

120 140 160 180 200 220

-40

-20

020

1970

120 140 160 180 200 220

-40

-20

020

1980

120 140 160 180 200 220

-40

-20

020

1990

120 140 160 180 200 220

-40

-20

020

1950

120 140 160 180 200 220

-40

-20

020

1960

120 140 160 180 200 220

-40

-20

020

1970

120 140 160 180 200 220

-40

-20

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1980

120 140 160 180 200 220

-40

-20

020

1990

Decadal trends in median yellowfin size by 10*20 lat/long cell.

Red fish smallYellow fish large

JP LL size data.

Consistent local effects may require separate fisheries

Different trends may require separate regions

weight length

LL 3 fishery subdivision – different sizes

30

S1

0S

10

N3

0N

120E 150E 180

R1 R2

R3 R4

R5 R6

00N 120E 00N 140E

10N 120E 10N 140E

10S 120E 10S 140E

LL ALL 3 fishery (yft) changed to exclude area approx. PNG waters.

New fishery with different selectivity, catchability. High catch in the 1950-60s.

Trends arguably different for 10S, 0N, and 10N (as for CPUE, but trends imply different things)

Region and fishery definitions

• Rule of thumb– If population trajectories differ, separate regions– If fish sizes differ, separate fisheries

• Pragmatic choice– Does it affect the results?

• May need more (smaller) regions where fish & effort are concentrated

• More data makes smaller regions possible

Scaling up size data

• Catch at size varies with – Time (cohorts moving through fishery)– Fishing method (even to vessel level)– Set (fish school by size)– Space (consistent local effects)

• Assume constant selectivity for fishery• But effort moves around region through time,

which affects size– Sampling is ad hoc, may not be representative of catch

Scaled size data

Size data

Catch

0 50 100 150

0.0

00

.02

0.0

4

WCPO scheme for scaling up size data

• Catch data (numbers of fish) from a region are aggregated at the same spatial resolution as the size data (usually 20° longitude, 10° latitude cells).

• Check size data are available from all cells that cumulatively account for 70% of the total quarterly catch from the region. If not, reject the size data from that quarter.

• Check there are at least 20 fish sampled from each of the main cells fished and at least a total of 50 fish sampled per quarter. If not, reject the size data from that quarter.

• Combine the sample data from each cell weighted by the catch in each cell (number of fish).

• Scale the overall weighted sample to the total number of fish measured in the quarter.

‘Representative’ size data• Size data changes may drive population biomass estimates• Model ‘assumes’ size changes within fishery reflect changes in

population + sampling error• Should size data reflect the catch or the population? • Length frequency data can strongly affect population trend (e.g. sth

Pacific albacore assessment)• Standard approach is to reflect catch, but this may be problematic if

there is significant size variation in space• If this occurs,

– Downweight size data sample size to reflect heterogeneity– Define more fisheries

• ‘Standardize’ size data?– Also an issue for other effects on selectivity, such as LL set depth and gear type

Regional CPUE scaling

30S

20S

10S

010

N20

N30

N

120E 140E 160E 180 160W 140W 120W 100W 80W

1 2 7

3 4 8

5 6

0

20

40

60

80

100

120

1 4 7 10 13 16 19 22 25 28 31 34 37Time

CP

UE

Region specific CPUE index

= relative abundance between regions i.e. region scaling factors.

( , ) ( ) ( )ln( ) other parametersu v u vCATCH aYRQTR bLATLONG

Area weighted GLM index

CPUE indices comparable between regions and reflect relative biomass in each region.

1. GLM model for each region.Data aggregated 5*5 lat/long, HBF, month. YR/qtr index.

2. Region scalar.

Sum coefficients within region (at HBF=5).YR/QTR index multiplied by region scalar.

( , , , ) , , ,ln LL HBF y qtr LATLONG R HBF R y R qtrCPUE a b c d

30S

20S

10S

010

N20

N30

N

120E 140E 160E 180 160W 140W 120W 100W 80W

Legend0 3.5

Relative YFT CPUE – from WCPO GLM.

Region scaling factors.

0

0.2

0.4

0.6

0.8

1

1.2

1 2 3 4 5 6

Region

Sc

alin

g f

acto

r

YFT area weighted CPUE indices - WCPO

0

0.5

1

1.5

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2.5

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4

1952 1955 1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003

Re

lati

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e

Region 6

Region 5

Region 4

Region 3

Region 2

Region 1

Spatial variation in biology

• Reproduction– Maturity– Sex ratio– Fecundity at length

• Growth

Reproductive parameters may vary in space (e.g. bigeye maturity)

• Model assumes same reproductive output at age for all females. – Affects ‘spawning biomass’ reference points– Affects other ref pts when steepness < 1

L50= 102.4 cm

L50=135 cm

L50=105 cm

Yellowfin growth (within WCPO)

0 5 10 15 20 25

050

100

150

200

Age class

Leng

th (

FL)

cm

2006 MFCLRegion 3 MFCLLehodey & Leroy 1999Yamanaka 1990

0 5 10 15 20 25

050

100

150

200

Age class

Leng

th (

FL)

cm

2006 MFCLRegion 3 MFCLID/PH tagsPNG tagsother tags

Region 3 growth estimated by using only region 3 data

Slower initial growth within region 3 (western equatorial) compared to overall growth estimated by MFCL WCPO model.

WCPO growth estimates strongly influenced by Region 1 size data.

Change growth; change fixed M-at-age (length-based).

Spatial variation in yft growth0

5010

015

020

0

1 5 10 15 20 25

Age (quarters)

Leng

th (

cm)

Base case2006 SARegion 3 growthInitial values

Improved fit to the length frequency data from region 3 small fish fisheries when apply region 3 growth to WCPO model.

Model pars/outputs – biomass (yellowfin)

Total and adult biomass.

R3 and R4 account for most of the biomass.

010

2030

4050

6070

Region 1

050

100

200

300 Region 2

050

100

150

200

Region 3

010

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0

Region 4

010

2030

Region 5

010

2030

40

1950 1960 1970 1980 1990 2000

Region 6

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060

080

0

1950 1960 1970 1980 1990 2000

WCPO

To

tal b

iom

ass

(1

00

0s

mt)

TotalAdult

Model pars/outputs

(bigeye) – recruitment

R3 and R4 account for most of the recruitment.

Increase in R3 recruitment from early 1990s.

Most recent recruitment approximates long-term average.

0.0

0.5

1.0

1.5

Region 1

02

46

810

12

Region 2

05

1015

Region 3

02

46

810

12

Region 4

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0.4

0.6

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Region 5

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1950 1960 1970 1980 1990 2000

Region 6

010

2030

4050

1950 1960 1970 1980 1990 2000

WCPO

Re

cru

itme

nt (

mill

ion

s o

f fis

h)

Model pars/outputs

(bigeye) – fishery impact

020

4060

8010

0

Region 1

050

100

200

300 Region 2

010

030

050

070

0 Region 3

010

020

030

040

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Region 4

05

1015

2025

3035

Region 5

010

2030

1950 1960 1970 1980 1990 2000

Region 6

020

060

010

00

1950 1960 1970 1980 1990 2000

WCPO

Fished biomass

Unfished biomass

To

tal b

iom

ass

(1

00

0s

mt)

Estimating movement

• Biological issues– Food, oceanography, spawning

• Effects and consequences– Fishing pressure variation– Biomass trends

• Data– Tagging data directly inform movement– Length frequency and CPUE data also affect

estimates

Movement model

• Instantaneous movement at start of quarter• Between regions that share common

boundary• Parameter indicates prop. in A that move to B• Usually 4 seasonal movements each way

across each boundary pair• Other time effects not modelled• Age effects usually not estimable

Bigeye movement – tagging data(> 1000 n. miles)

Model pars/outputs – movement (bigeye)R1 R2

R3 R4

R5 R6

Quarter 1

R1 R2

R3 R4

R5 R6

Quarter 2

R1 R2

R3 R4

R5 R6

Quarter 3

R1 R2

R3 R4

R5 R6

Quarter 4

Max. 4% per quarter

Reg 1 Reg 2 Reg 3 Reg 4 Reg 5 Reg 6

0.0

0.2

0.4

0.6

0.8

1.0

Pro

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f bio

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ss b

y so

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eg

ion

Movement issues

• Movements are difficult to estimate and data are not very informative– Implausible estimates seen – e.g. albacore

assessment– Model uses movement and recruitment to account

for lack of fit in age-based selectivity estimates. • May be better to use biologically reasonable

diffusion rates as prior distributions– Would also permit age-based movement estimates– Oceanography needs to be included

Conclusions

• Multiple spatial issues • Work in progress…