Growth Issues in Tuna RFMO Stock Assessment:

A Cabinet of Curiosities

Dale Kolody, Paige Eveson, Rich Hillary

CSIRO Oceans & Atmosphere Flagship

Koeller 2003: Tractatus Logicus assessmenticus

Outline

• Tuna RFMOs context

• Data Issues• Have we sorted out the basics?

• Model Issues• Favourite functions and error models• Space/time variability• Size selectivity

• Assessment Model Integration Issues• Keeping it in perspective• How not to understate the uncertainty?

Controversy

CynicismScepticism

The 5 Tuna Regional Fisheries Management OrganizationsTuna and Tuna-like species

Rese

arch

$$$

/ fis

h

CCSBT

IOTC

FAO Global Tuna Catch Estimates (excluding neritics)

2012 Landed value US$ 12+Billion

5% of global capture fisheries

1950 1970 1990 20100.0

1.0

2.0

3.0

4.0

5.0

Catc

h (M

illio

n to

nnes

)

1950-2014 (tonnes)

4.5 Million tonnes of tuna >2 Tokyo Domes

Example assessment: WCPFC Yellowfin

• 1 stock• 9 regions• 33 fisheries• Quarterly• Data quality range

Fit to:• CPUE (effort)• Catch• Size frequencies• Tags

Key Estimates: Recruitment (R0 and devs), catchability, selectivity, length-at-age, movement

Most tuna and billfish assessments are spatially aggregated

Processes governing Size-at-Age:

Time

Leng

th

Above average

Below average

•Spatial and Temporal variability:

• Regional Environmental Variability

• Density dependent effects

• Evolutionary changes

•Genetics (e.g. Sex dimorphism)•Seasonal foraging success, migration and spawning costs•Local environment

Size dependent natural and fishing mortality

Different spawningtiming

e.g. Risky foraging behaviour causes high predation risk

e.g. Starvation and disease

Population level:

Individual level:

Size and Age Data – Observations

Time

Leng

th

Length error

Size selective fishing gear

Observations may be integrated over a time window

Age Error

Size selective catch sampling

Growth Models in most tRFMO assessments

Age

Leng

th Mean length-at-ageVariability in length-at-age

…some exceptions

• Infer Catch-at-age • Biomass Calculations• Age tag releases

A bit of history from the last millenium:Catch-at-Length vs: cohort-sliced catch-at-age

• Catch-at-age from a catch-at-length matrix•VPA assessments, e.g. ICCAT Northern Bluefin Tuna•Some parallel Statistical Catch-at-Age assessments in

IOTC

Southern bluefin otolith ages and “cohort-slicing”

Age

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cm)

0 5 10 15 20 25 30

050

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Age

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cm)

0 5 10 15 20 25 30

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(Knife-edge partitioning)

Age 0

Age 20+

Age 2

Age 7Age 13

SBT “cohort-slicing” age estimation error simulations

0 5 10 15 20

-40

020

40 M =0. 1, F=0

25 00 0 15 16 3 91 97 55 78 33 83

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-40

020

40 M =0. 1, F=0. 1

45 31 7 16 67 1 61 33 22 56 83 0

0 5 10 15 20

-40

020

40 M =0. 1, F=0. 2

86 39 4 19 27 7 43 01 96 0 21 4

0 5 10 15 20

-40

020

40 M =0. 1, F=0. 3

12 36 30 16 73 1 22 64 30 6 41

Perc

ent

Erro

r

Age

0 5 10 15 20

-40

020

40 1970

37 75 53 18 62 39 40 52 24 57

0 5 10 15 20

-40

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40 1980

14 19 1 38 51 29 29 116 4 37 8

0 5 10 15 20

-40

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1990

20 6 21 25 92 9 20 6 30

0 5 10 15 20

-40

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1997

0 82 75 911 95 36

Perc

ent

Erro

rAge

Constant M(age), F(age) Estimated M(age), F(age)

From Eveson and Polacheck 2001

Not bad to age 10 Large errors, but strong negative correlation with adjacent cohorts for ages <10

Historical legacy

•Probably not as bad as most people think•But its probably time to move on

Part I: Data Challenges

• Catch Length Frequency Distributions

• Age estimates from hard parts (otoliths, scales,fin spines,vertebrae)

• Tag growth increment data

Catch Length Frequency Data

Length

Freq

uenc

y

Fournier et al 1989

Catch-at-Length Data Issues• (size selective fishery discussed as a model issue)• Size selective sampling of catch likely, e.g.

• poorly stratified in space and time – artisanal fisheries• Purse Seine grab samples vs: spill samples• Poling live farm tuna (Southern Bluefin ?)• Xu’s Albacore example – samplers like big fish• Selection of small fish for ageing (Maunder’s comment)

• Maldives SKJ bimodal Pole and Line catch sampling?

+-

Direct ageing of Hardparts

• Otoliths, fin spines or vertebrae circulus counts

Direct Age estimation Issues:

Dortel et al. 2014

Indian Ocean Yellowfin

Da Silva et al. 2014

Linfinity ?

Poor annual rings for most tropical tunasDaily counts to ~ 4 years max

Eastern Pacific Bigeye

Linfinity ?

Direct Age estimates

South Pacific Albacore otoliths

Williams et al. 2012

Annual counts for temperate tunas and billfish

De Martini et al. 2007

North Pacific Swordfish fin spines

Growth Rate variability among populations

• E.g. Swordfish

Young and Drake 2004

How much growth variability is actually due to age estimation variability?

• E.g. Pacific Swordfish

• Difference between NMFS and CSIRO curves largely attributable to lab variability

• No independent age validation (Fukushima?)

0 2 4 6 8 10 120

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Swordfish Fin Spine Age Estimate Comparison

(jittered)

NMFS

CSIR

O

From Young et al. 2008

Age Validation of tuna otoliths

• OTC or SrCl injections at tag release

• Count rings at recapture and compare with time at liberty

Indian Ocean tuna otoliths – validation of daily increments

• For YFT and BET, daily counts appear validated, but not perfect• For SKJ, daily counts are not supported (in Indian Ocean).

Yellowfin Bigeye Skipjack

Daily age validation OK(Bigeye and Yellowfin)

• So what about annual?

• Not very consistent(problems at the origin?)

Sardenne et al. 2014

Issues with direct aging (hardparts) data

• Validation not easy (usually done as part of a tag-recapture experiment via chemical marking of hardparts at tagging)

• Validating deposition rates of increments and validating reader counts are separate but generally confounded issues

• Within and between reader counts can vary greatly in precision and accuracy

What’s the assessment modeller to do with conflicting age estimates (and other discontinuous model specification options)?

• Sensitivity analysis common• Weighted model ensembles (“Grid”) used in CCSBT, WCPFC, IOTC

– Honest about arbitrary assumptions– Helps identify what’s important for management

The “Grid Approach” (model ensembles)?

From Davies et al (2013) SW Pacific swordfish stock assessment

CSIRO Growth

NMFS Growth Overfishing

SwordfishLife History Combinations: Growth, M, Maturity

MPD estimates from several hundred models summarised over 8 fixed life history parameter combinations

Tagging Data Issues

2011 CERN Headline: Neutrinos clocked moving at faster-than-light speed

• CERN scientists ask for confirmation of discovery that could rewrite laws of nature

Tuna Tagging Scientists Rise to the Challenge

• Tachyonic tuna observed in every large-scale tuna-tagging project• Curiously, some tachyonic tuna appear to change species as well!

Space

Tim

e

CERN retracts Neutrino claim!Due to a loose fibre optic cable and faulty timing chip

• Could there be errors in the tuna data as well?

Tag recovery data errors estimated from tag seeding experiments in Western Pacific:

Leroy et al. 201365% seeded tag

recovery dates wrong

Biased time-at-liberty

What’s going on?

• Recovered tags as currency• Fictional data to satisfy Tag Return Officer?

• What to do about it?• Use only reliable recovery sources?• Error structures that model human psychology?

Biases from good intentions?

• Tag data entry staff sometimes discard some obvious errors

• e.g. throwing out only negative errors will result in a positive bias

• Presumably measurement error

True

Negative error

Positive error

Positive bias

Can fish shrink? Marine iguanas shrink in length up to 20%

Wikelski and Thom 2002

http://en.wikipedia.org/wiki/GNU_Free_Documentation_License

Part II: Model Issues

Tuna RFMO Preferred growth functions• The usual suspects:

• Von Bertalanffy (VB)• Gompertz• Richards• …probably others

• More flexibility seems warranted for many tunas

Growth rate (cm/day) e.g. Indian Ocean tuna tag-recapture data

• YFT and BET data both suggest two phases of growth (e.g. possibly changing from one VB curve to another, based on two phases of linear declining growth rates)

• SKJ less clear, although appears to be an inflection point around 45 cm

Relaxing parametric functions

• Multifan-CLPenalized deviates

from classic von Bertalanffy

• SS3 Age-specific k(Sharma bigeye

assessment 2013) Western Pacific YellowfinDavies et al 2014

Indian Ocean Skipjack Indian Ocean Yellowfin

VBlogK – 2 stage von Bertalanffy with logistic weighting transition•5 parameters: Linf, k1, k2, logistic scale and amplitude•Continuous and differentiable

Derivation of VBlogK in LEP 2002

Selection of growth function

• Challenging to choose when data:•Don’t cover the age/length range of the population•Are highly variable (e.g. due to measurement error

and/or individual variability)

Selection of growth function

• Previous issues with choosing appropriate growth function apply to direct age and length data as well as tag-recapture data

• Even more issues with tag-recapture data since absolute age is unknown

Compare VB and VB log k fits to tag-recapture data for Indian Ocean skipjack

VB VB log k

• Fit using the method of Laslett et al. (2002), which models release and recapture lengths jointly, and age at tagging as a random effect;

• “t0” parameter chosen such that both curves give length of ~30 cm at an age of 0.5 years

• AIC supports VB log k, but examination of residuals not as conclusive

Growth Form Implications for management?

• For Indian Ocean skipjack, the VB and VB log k growth models are very different

• Lead to very different estimates of natural mortality at age (derived from a Brownie tag-recapture model applied to the data)

• Management implications?…awaiting IOTC assessment

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.05

0.1

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0.25

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0.35

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SKJ M estimates

VB, PS mix VBLK, PS mix

Selection of error structure• Fabens• Joint distribution of release and recovery length

•LEP–Individual Linf– Individual K

•Da Silva

Implications of error structure for Indian Ocean skipjack

Fabens-blue

LEP with measurement error only -green

LEP: meas error only(v. similar to da Silva)

LEP: random Linf + meas error

Low meas error,Low indiv variability

Low meas error,High indiv variability

High meas error,Low indiv variability

Meas error only

Random Linf + meas error

Random k + meas error

Random Linf & k + meas error

Leng

th B

ias

Age

LEP Bias Simulations (Eveson et al 2007)

Length-based tuna models:

• Ageing error for rapidly growing tunas can be problematic• Length a more “natural” currency than age for some processes• Length-based transition matrix approaches potentially useful• Can accommodate fully probabilistic growth naturally• Is dealing with tags by length a better way in assessments?

• Potential benefits likely to be situation-dependent – Skipjack most likely candidate

• Examples: – Experimental Eastern Pacific skipjack models (Maunder-not to be cited)– Indian Ocean skipjack Brownie tag model (Hillary and Eveson 2014)

Growth variability by sex

Tunas• Males > females(ALB, BET, SBT, YFT)

• Most or all assessments sex-aggregated• few sex data

AlbacoreWilliams et al. 2012

Growth variability by sex

Billfish• Females > males• Some sex-disaggregated swordfish

assessments• North Pacific (Wang et al 2007)• Indian Ocean (Kolody et al 2011)• ISC 2013

• More realistic, but advantage for management not yet demonstrated

• Few sex-specific data• Most useful for MSE?

SwordfishSun et al. 2002

Temporal Variability

• Seasonal growth variability explored for southern bluefin – not pursued

• MULTIFAN-CL – optional density dependent term • cohort-specific k

Southern Bluefin experienced strong growth changes over time

• 4 tagging programmes• 4 growth curve shifts

Is growth variability the norm?

1950s

2010s

Southern Bluefin experienced strong growth changes over time• Temporally variable growth included in the assessment, but what

about other length-based processes?– natural mortality and maturity

Why did Southern Bluefin growth change?

• Density-dependence: • correlation between mean length(a) and log(N) ≈ -0.75

• Cannot discount genetic selection effect or environmental

• Makes determination of stock status and projections complicated...

– With D-D would growth revert as stock rebuilds or is there any hysteresis likely (impacts very idea of B0 and projections)?

– With selection is it permanent or transitory with an easing in fishing pressure reversing the effect? Timescales?

Spatial Variability in tuna growth

South Pacific AlbacoreWilliams et al. 2012

Rarely tested with simultaneous samples and the same age readers-probably the norm?

Female

Male

What to do about spatial variability in growth?

1) Independent growth curves by area?2) Clever fix to model growth by area with movement?3) Is the real issue growth variation or population structure?

Albacore assessment domain, Hoyle et al 2012

e.g. What to think of some curious genetic studiesFine-Scale Differentiation within each region reported

1 YFT Dammannagoda et al. 20082 YFT Swaraj et al. 20133 SKJ Dammannagoda et al. 20114 SKJ Menezes et al. 20125 BET Nugraha et al. 2011

WPTT-15-2013: YFT WP36; BET WP21

What to do about spatial/temporal variability in Growth?

• Quantify where possible• Express uncertainty for management (e.g. MSE Operating Models)

What about size-dependent processes?

• Variants on Rosa Lee’s phenomenon (1912)?• Size-based mortality, selectivity or sampling bias

• Where do we see it?

Indian Ocean yellowfin otolith data – is there really two stage growth, or is it size selectivity?

A quick simulation

Kolody 2008

•Purely length-based FAD and Free-school selectivity

•2 stage Growth, plusLinf bias

•Looks a lot like the two-stageGrowth curves?

Size selectivity due tospawning (location)

Southern Bluefin Farley et al 2014

Albacore 140-170W Farley, pers. comm.

Larger fish for partially mature ages more likely caught on spawning grounds

What about skipjack 2 stage growth?

• Where are the big skipjack?

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101

102

0

500

1000

Longline SKJ Catch-at-Length

?

Maybe tuna modellers need to be more explicit about size-based processes in assessments?

1) Pseudo length-based selectivity, - i.e. fit CL, but do not retain differential age-length effects

3) Growth morphs (platoons) – probably describe most of the length-based selectivity effects

4) Joint age-length model (e.g. Parma 1989 shortcuts)

Estimating the growth curve inside or outside of the assessment?

• Pro-Inside: – Convenient one step process for handling parameter uncertainty – Internal consistency with a unified framework including size selectivity

issues– Maybe da Silva et al (in press) approach resolves internalization of tag

increments for the tropical tunas

Estimating the growth curve inside or outside of the assessment?

• Anti-Inside: – cannot use more computationally intensive error assumptions– Other assessment data might not be informative about growth

• Wrong fixed M or faulty selectivity may bias growth– Limited older age data for some species (need new tag increment methods)– Need growth curve-dependent tag age assignments

Interactions among growth, M and selectivity:• Quick simulation comparing CL distributions with different

parameters• Roughly based on Atlantic BET growth and M• Different Growth, M, Selectivity and Catchability• Equilibrium population structure with constant Recruitment

• (estimated q and selectivity for red by fitting CL to black)

Interactions among growth, M and selectivity:• Same equilibrium CL distributions• Different levels of depletion Scenario 1 Equilibrium B/B0 = 0.37

Scenario 2 Equilibrium B/B0 = 0.74

Implications:• Suggests its probably a bad idea to do internal growth estimation

without considering uncertainty in M and selectivity (functional form)

Putting tuna growth in perspective

Imagine appropriate copyrighted cartoons here• Nero fiddling while Rome burns• Drunk searching for keys under the lamp-post

Where is the “best” growth curve relative to where we think it is?

Investment

Gro

wth

Cur

ve Q

ualit

y

How much data to get there?

Growthmodelling

Spatial and temporal variabilityBiased sampling, etc.

•IOTC 2012 Tagging Symposium (Fish Res tagging special issue in prep):

•4 papers estimate growth• 1 paper estimates M, F and/or N

• Total Catch Data in some cases• Abundance indices• Stock connectivity and migration • M• Stock Recruitment

Non-Growth issues

Indian Ocean Bigeye Longline Standardised CPUE

Taiwan

Japan

Korea

2008 LLEffort

2011 LLEffort

Pacific Tag Analyses

• Clearly not mixed throughout the fishery

• Expect estimator biases

From Kolody and Hoyle in press

Tag Recoveries

Catch contours

Tag Release Area2011 Skipjack assessment model region

Tag Recaptures and catch from the same time window

Key Conclusions• Many tuna and tuna-like species currently lack quality data to estimate length-at-age

relationships, including basic age estimation validation.

• Tags are probably critical for estimating tropical tuna growth.

• There are a range of growth modelling techniques available, some of which should minimize some obvious biases.

• There is little data with which to evaluate temporal and spatial growth variability, but where there is data, there is variability.

• Size-based processes (e.g. selectivity) could probably be represented better in most tuna models.

• Tuna growth is only one uncertainty among many, and probably not the most important. Efforts should be taken to fully represent the uncertainties due to growth in conjunction with other assessment issues in a framework that is appropriate for providing robust management advice.

Suggest spending less time seeking the “best” growth curve, and more time describing the uncertainty and developing robust management procedures e.g. SW Pacific Swordfish Harvest Strategy Evaluation

Increases Catch from Optimistic Operating

Model

Avoids Stock Collapse in Pessimistic Operating

Models

Thanks! With thanks to CAPAM & ISSF/SWMFSC and many individuals associated with the CCSBT, IOTC, WCPFC, IATTC and ICCAT, who have agonized over otoliths, tag recoveries and growth equations over the years

OCEAN & ATMOSPHERE FLAGSHIP