Growth Issues in Tuna RFMO Stock Assessment A

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 ntr Co • Have we sorted out the basics? ers ov y m cis pti • Keeping it in perspective • How not to understate the uncertainty? Sce • Assessment Model Integration Issues m icis • Favourite functions and error models • Space/time variability • Size selectivity Cyn • Model Issues

Research $$$ / fish The 5 Tuna Regional Fisheries Management Organizations Tuna and Tuna-like species CCSBT IOTC

FAO Global Tuna Catch Estimates (excluding neritics) Catch (Million tonnes) 5. 0 2012 Landed value US$ 12+Billion 4. 0 3. 0 2. 0 5% of global capture fisheries 1. 0 0. 0 1950 -2014 (tonnes) 1970 1990 2010

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 (R 0 and devs), catchability, selectivity, length-at-age, movement Most tuna and billfish assessments are spatially aggregated

Processes governing Size-at-Age: Length Individual level: Size dependent natural and fishing mortality e. g. Risky foraging behaviour causes high predation risk • Genetics (e. g. Sex dimorphism) • Seasonal foraging success, migration and spawning costs • Local environment e. g. Starvation and disease Time Different spawning timing Population level: Above average Below average • Spatial and Temporal variability: • Regional Environmental Variability • Density dependent effects • Evolutionary changes

Size and Age Data – Observations Size selective fishing gear Length error Length Size selective catch sampling Age Error Observations may be integrated over a time window Time

Length Growth Models in most t. RFMO assessments Mean length-at-age Variability in length-at-age 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” (Knife-edge partitioning) Age 20+ Age 13 Age 7 Age 2 Age 0

SBT “cohort-slicing” age estimation error simulations Constant M(age), F(age) Not bad to age 10 From Eveson and Polacheck 2001 Estimated M(age), F(age) 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

Frequency Catch Length Frequency Data Length 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: Poor annual rings for most tropical tunas Daily counts to ~ 4 years max Indian Ocean Yellowfin Eastern Pacific Bigeye Linfinity ? Dortel et al. 2014 Da Silva et al. 2014

Direct Age estimates Annual counts for temperate tunas and billfish South Pacific Albacore otoliths Williams et al. 2012 North Pacific Swordfish fin spines De Martini et al. 2007

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 16 14 12 10 CSIRO • Difference between NMFS and CSIRO curves largely attributable to lab variability Swordfish Fin Spine Age Estimate Comparison (jittered) 8 6 • No independent age validation (Fukushima? ) 4 2 0 0 5 NMFS 10 From Young et al. 2008 15

Age Validation of tuna otoliths • OTC or Sr. Cl injections at tag release • Count rings at recapture and compare with time at liberty

Indian Ocean tuna otoliths – validation of daily increments Yellowfin Bigeye Skipjack • For YFT and BET, daily counts appear validated, but not perfect • For SKJ, daily counts are not supported (in Indian Ocean).

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)? MPD estimates from several hundred models summarised over 8 fixed life history parameter combinations CSIRO Growth NMFS Growth Swordfish. Life History Combinations: Growth, M, Maturity From Davies et al (2013) SW Pacific swordfish stock assessment Overfishing

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

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: 65% seeded tag recovery dates wrong Biased time-at-liberty Leroy et al. 2013

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 Positive bias True Negative error

Can fish shrink? Marine iguanas shrink in length up to 20% http: //en. wikipedia. org/wiki/GNU_Free_Documentation_License Wikelski and Thom 2002

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 tagrecapture 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-CL Penalized deviates from classic von Bertalanffy • SS 3 Age-specific k (Sharma bigeye assessment 2013) Western Pacific Yellowfin Davies et al 2014

VBlog. K – 2 stage von Bertalanffy with logistic weighting transition • 5 parameters: Linf, k 1, k 2, logistic scale and amplitude • Continuous and differentiable Indian Ocean Skipjack Indian Ocean Yellowfin Derivation of VBlog. K 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 tagrecapture 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; • “t 0” 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) SKJ M estimates • Management implications? …awaiting IOTC assessment 0. 5 0. 4 0. 35 0. 3 0. 25 0. 2 0. 15 0. 1 0. 05 0 0 0. 5 1 1. 5 2 VB, PS mix 2. 5 3 VBLK, PS mix 3. 5 4 4. 5

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 LEP: random Linf + meas error Fabens-blue LEP: meas error only (v. similar to da Silva) LEP with measurement error only -green

LEP Bias Simulations Low meas error, Low indiv variability Low meas error, High indiv variability High meas error, Low indiv variability (Eveson et al 2007) Meas error only Length Bias Random Linf + meas error Random k + meas error Random Linf & k + meas error Age

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 Albacore Williams 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? Swordfish Sun 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 2010 s 1950 s Is growth variability the norm?

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 B 0 and projections)? – With selection is it permanent or transitory with an easing in fishing pressure reversing the effect? Timescales?

Spatial Variability in tuna growth Rarely tested with simultaneous samples and the same age readers -probably the norm? Female Male South Pacific Albacore Williams et al. 2012

What to do about spatial variability in growth? Albacore assessment domain, Hoyle et al 2012 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?

e. g. What to think of some curious genetic studies Fine-Scale Differentiation within each region reported 1 YFT Dammannagoda et al. 2008 2 YFT Swaraj et al. 2013 3 SKJ Dammannagoda et al. 2011 4 SKJ Menezes et al. 2012 5 BET Nugraha et al. 2011 WPTT-15 -2013: YFT WP 36; BET WP 21

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 • Purely length-based FAD and Free-school selectivity • 2 stage Growth, plus Linf bias • Looks a lot like the two-stage Growth curves? Kolody 2008

Size selectivity due to spawning (location) Larger fish for partially mature ages more likely caught on spawning grounds Southern Bluefin Farley et al 2014 Albacore 140 -170 W Farley, pers. comm.

What about skipjack 2 stage growth? 1000 Longline SKJ Catch-at-Length 500 0 20 33 46 59 72 85 98 • Where are the big skipjack? ?

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 Scenario 1 Equilibrium B/B 0 = 0. 37 • Different levels of depletion Scenario 2 Equilibrium B/B 0 = 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

Growth Curve Quality Where is the “best” growth curve relative to where we think it is? Spatial and temporal variability Biased sampling, etc. Growth modelling Investment How much data to get there?

• IOTC 2012 Tagging Symposium (Fish Res tagging special issue in prep): • 4 papers estimate growth • 1 paper estimates M, F and/or N

Non-Growth issues • • • Total Catch Data in some cases Abundance indices Stock connectivity and migration M Stock Recruitment

Taiwan Indian Ocean Bigeye Longline Standardised CPUE 2008 LL Effort Japan Korea 2011 LL Effort

Pacific Tag Analyses 2011 Skipjack assessment model region Tag Release Area • Clearly not mixed throughout the fishery • Expect estimator biases Tag Recoveries Tag Recaptures and catch from the same time window Catch contours From Kolody and Hoyle in press

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 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