Current developments on steepness for tunas Shelton Harley

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Current developments on steepness for tunas: Shelton Harley Pre-Assessment Workshop 4 -8 April 2011,

Current developments on steepness for tunas: Shelton Harley Pre-Assessment Workshop 4 -8 April 2011, Noumea

Three part presentation �My presentation to the ISSF Steepness workshop �Outcomes from the ISSF

Three part presentation �My presentation to the ISSF Steepness workshop �Outcomes from the ISSF steepness workshop �Preliminary meta-analysis of steepness in tunas

Outline �Estimating steepness �Meta-analysis �Modelling uncertainty in steepness �SR process for tropical tunas �Suggestions

Outline �Estimating steepness �Meta-analysis �Modelling uncertainty in steepness �SR process for tropical tunas �Suggestions

What we need Accurate estimates of recruits Accurate estimates of spawners Contrast in spawner

What we need Accurate estimates of recruits Accurate estimates of spawners Contrast in spawner abundance h Low recruitment variation

Estimating spawners �Definition of spawners - understanding the spawning process �Size based versus age-based

Estimating spawners �Definition of spawners - understanding the spawning process �Size based versus age-based processes? �Estimation of the spawning component – typically based on longline CPUE

Estimating recruits spawning �No ageing data and variable growth. . . in space and

Estimating recruits spawning �No ageing data and variable growth. . . in space and time Steepness �“Continuous” Moderate Low Very low Recruitment variation

Our options – meta-analysis � Appropriate level of ‘integration’? � Need to incorporate estimation

Our options – meta-analysis � Appropriate level of ‘integration’? � Need to incorporate estimation error in series � Assumptions of the underlying assessment s. .

Our options - uncertainty � Provide results across a range of assumed levels of

Our options - uncertainty � Provide results across a range of assumed levels of steepness � How do we weight them? � How do we ‘really’ include uncertainty in steepness?

Uncertainty in steepness? MSY=73, 480 mt Base model MSY=65, 840 mt h=0. 75 High

Uncertainty in steepness? MSY=73, 480 mt Base model MSY=65, 840 mt h=0. 75 High Sigma. R MSY=160, 000 mt h=0. 75 Low Sigma. R

A process for the relationship �Tuna are not salmon or reef fishes … where

A process for the relationship �Tuna are not salmon or reef fishes … where is the scope for density-dependence and compensation? �Tropical tunas spawn almost continuously when conditions are favorable (thought to be related to feed for condition and SST) �A process to maximize the time/space window for spawning – match/miss-match hypothesis?

Eggs and baskets �Aim to maximise the distribution of spawning in time and space

Eggs and baskets �Aim to maximise the distribution of spawning in time and space �Reduced spawning biomass. . . reduced time and space �Reduced probability of high recruitment and a higher probability of low recruitment �A variance-based process – expectations less relevant?

Mean or variance? More higher R at high SSB No apparent decline in recruitment

Mean or variance? More higher R at high SSB No apparent decline in recruitment variation More lower R at low SSB

Variation in recruitment �Recruitment variation typically higher at lower stock sizes in non-salmonid fishes

Variation in recruitment �Recruitment variation typically higher at lower stock sizes in non-salmonid fishes �Opposite trend to the constant CV assumption �But … confounded with time and emergence of surface fisheries and improved size data

The “P” word � Does the Precautionary Approach have a place in assumptions about

The “P” word � Does the Precautionary Approach have a place in assumptions about steepness? � Simulations suggest steepness most often over-estimated. . � Consequences – fishing effort too high and biomass reduced too low � Fishing strategies based on lower steepness – minimal lost yield, higher catch rates, and greater spatial extent of the stock � Is MSY a sensible concept for skipjack– in a deterministic sense?

Suggestions for a way forward �Direct ageing where possible �Research into meaningful estimates of

Suggestions for a way forward �Direct ageing where possible �Research into meaningful estimates of spawning potential �Revisit meta-analyses as info improves �Don’t base stock assessment advice on a single estimate (or assumed value) of steepness �Projections should consider alternative assumptions of recruitment variation

ISSF Workshop

ISSF Workshop

Summary of ISSF meeting �A workshop was held to examine two issues that significantly

Summary of ISSF meeting �A workshop was held to examine two issues that significantly affect scientific management advice: (1) Assumptions about the stock‐recruitment relationship, and (2) Evaluating the implications of changing mortality on juvenile and small tuna �These issues are not always being treated consistently in tuna stock assessments

ISSF Workshop recommendations 1. 2. That estimated values of steepness from individual assessments be

ISSF Workshop recommendations 1. 2. That estimated values of steepness from individual assessments be treated with considerable caution. Analysts should evaluate the extent to which the stock--‐recruitment estimation or assumptions influence the estimates of recruitment; RFMOs should collaborate towards undertaking a meta‐analysis of spawner‐recruitment data as initiated during this Workshop. It was recommended that analysts continue to develop this work with a view to provide further advice for the estimation of steepness in tuna assessments.

Continued 3. 4. 5. That stock status advice incorporate stock assessment structural and parameter

Continued 3. 4. 5. That stock status advice incorporate stock assessment structural and parameter uncertainty including a range of plausible steepness values; That RFMO decision‐makers consider management measures and/or Harvest Control Rules that are robust to uncertainty in steepness, noting the precautionary approach and the economic benefits of maintaining stocks at higher stock sizes. RFMOs should collaborate on methods for the incorporation of uncertainty of steepness into stock assessment advice, including approaches such as management strategy evaluation.

ISSF Other recommendations �The Workshop recommended that Fishery Impact plots be included routinely in

ISSF Other recommendations �The Workshop recommended that Fishery Impact plots be included routinely in tuna RFMO stock assessment reports. �The Workshop recommended that RFMOs facilitate meetings to compare the basic life history parameters being used in the tuna stock assessments, with a view to reconcile differences or improve consistency, if necessary.

ISSF results

ISSF results

SPC Preliminary analysis

SPC Preliminary analysis

Approach �Updating the analysis of Myers et al. (1999) Maximum reproductive rate of fish

Approach �Updating the analysis of Myers et al. (1999) Maximum reproductive rate of fish at low population sizes. CJFAS 56: 2404– 2419. �Focus on estimating the slope at the origin (α) of a ‘standardised’ spawner recruitment curve – both point estimates and likelihood profiles. �Translate into ‘steepness’

Models �Ricker: �Beverton-Holt:

Models �Ricker: �Beverton-Holt:

Need to standardize. . �Convert recruits into replacement spawners using the spawning biomass per

Need to standardize. . �Convert recruits into replacement spawners using the spawning biomass per recruit in the absence of fishing �So that

And then to steepness � represents the number of spawners produced by each spawner

And then to steepness � represents the number of spawners produced by each spawner over its lifetime at very low spawner abundance, i. e. , assuming absolutely no density dependence. �Steepness is:

Data sets � Albacore tuna � Skipjack • North Atlantic • North Pacific •

Data sets � Albacore tuna � Skipjack • North Atlantic • North Pacific • South Pacific • WCPO � Bigeye tuna • Atlantic • Indian Ocean • WCPO � Bluefin tuna • Eastern Atlantic � Yellowfin tuna • Indian Ocean • WCPO

Individual fits

Individual fits

Individual fits Stock Ricker BH ALB_AT 0. 73 0. 96 ALB_NP 0. 79 1.

Individual fits Stock Ricker BH ALB_AT 0. 73 0. 96 ALB_NP 0. 79 1. 00 ALB_SP 0. 37 0. 45 BET_AT 0. 73 0. 77 BET_IO 0. 94 0. 95 BET_WP 0. 90 1. 00 BFT_EA 0. 80 1. 00 SKJ_WP 0. 78 0. 96 YFT_IO 0. 60 0. 64 YFT_WP 0. 70 0. 81

The meta-analysis �A random effect meta-analysis undertaken using nlme() in R �Basic �Also model

The meta-analysis �A random effect meta-analysis undertaken using nlme() in R �Basic �Also model repeated for RK and BH: estimate BLUP �Transform back into steepness ‘space’

Preliminary results - BLUPs

Preliminary results - BLUPs

Preliminary results - Priors

Preliminary results - Priors

Next steps � Data • Refine data set – appropriate model runs • Increase

Next steps � Data • Refine data set – appropriate model runs • Increase number of stocks � Methods • nlme() …. Have there been improvements since 1999 • Incorporation of estimation error in recruitment time series • Incorporation of structural uncertainty – multiple assessment runs • Broken-stick model potential application � Potential ISSF support

Initial recommendations �Either fix steepness at the mode of the Ricker model based RE

Initial recommendations �Either fix steepness at the mode of the Ricker model based RE distribution �Or fix steepness at a range of values and derive a ‘point estimate’ for stock status weighting the values based on the RE distribution