Tradeoffs between bias, model fits, and using common sense about biology and fishing behaviors when choosing selectivity forms Dana Hanselman and Pete Hulson Alaska Fisheries Science Center Juneau, AK

Outline Introduction Introduction Biology and fleet behavior Biology and fleet behavior Case study: GOA Pacific ocean perch Case study: GOA Pacific ocean perch Precision and estimability Precision and estimability Case study: Alaska sablefish Case study: Alaska sablefish Simulation tests Simulation tests Preliminary Conclusions Preliminary Conclusions

Introduction The slow creep of SS3 into AFSC The slow creep of SS3 into AFSC Paladins of parsimony Paladins of parsimony Highly parameterized models seem unstable Highly parameterized models seem unstable Can we use complicated models for research, but simpler models for management? Can we use complicated models for research, but simpler models for management?

Double Domes and steep drops WC Sablefish H&LBS Turbot Trawl fish. BS skate trawl fish. Ian-Stewart

BS P. Cod T. SurveyEBS Pollock Time varying everything Ian-Taylor Ian-Elli

GOA Pacific ocean perch Strong catch-history, rebuilt Strong catch-history, rebuilt Variable recruitment, clustered cohorts Variable recruitment, clustered cohorts Age structured (AMAK-like) Age structured (AMAK-like) Marginally good trawl survey Marginally good trawl survey 1000 otoliths per survey/fishery year (odd/even) 1000 otoliths per survey/fishery year (odd/even)

Gulf of Alaska POP – Problems Survey q drifting upward each assessment Survey q drifting upward each assessment Fishery selectivity was drifting domed but highly constrained Fishery selectivity was drifting domed but highly constrained q and selectivity interact q and selectivity interact Is it more likely that the survey q is changing in one direction or the fishery selectivity might have changed? Is it more likely that the survey q is changing in one direction or the fishery selectivity might have changed? Look for evidence of dome-shape selectivity in fishery Look for evidence of dome-shape selectivity in fishery

POP Fishery: Early Fishery versus Current

POP – Catch by depth

Fishery was catching greater than 25% over 25 years old in the 80’s

Fishery was catching a much higher proportion of older fish than survey in 80’s

The reverse has occurred recently

Fit selectivities to raw data by estimating selectivity curves and mortality Logistic looks pretty good for survey

Gamma fits about half as good, minimal dome suggested.

Logistic to the fishery fits acceptably except for pooled group…

But gamma has 20% of the residual error and fits pooled age well

POP – Final model New selectivity functions to describe fishing fleet New selectivity functions to describe fishing fleet Fit toward dome in three stages Fit toward dome in three stages 1961 to 1976: the beginning and end of the foreign fishing fleets massive catches 1961 to 1976: the beginning and end of the foreign fishing fleets massive catches 1977 to 1995: The domestication of the fishery, but large factory trawlers still dominant 1977 to 1995: The domestication of the fishery, but large factory trawlers still dominant 1996-Present: The emergence of catcher-boats, semi-pelagic trawling, fishing cooperatives, fishing shallower 1996-Present: The emergence of catcher-boats, semi-pelagic trawling, fishing cooperatives, fishing shallower

Better fit to fishery ages, 9 less parameters, slightly better but similar fit overall

POP – Model Results Recommended model, new selectivity Substantially better fit to fishery age comps (25% reduction in fishery age –lnL) Survey catchability parameter reduced below 2 Fit data better with 9 less parameters

Alaska sablefish Long survey time series (36 annual LL, 13 trawls) Long survey time series (36 annual LL, 13 trawls) High-value fish ($142 million in 2011, IFQ) Lots of data Split-sex 2 fishery (really at least 3) Huge area Mainly targeted

Alaska sablefish Two sexes made selectivity difficult to estimate Trawl survey and fishery should be descending (shallow) Simplified selectivities for better estimation

Trawl fishery selectivity Exponential LogisticGamma Females Males 6 parameters to 2 parameters

Trawl survey selectivity Exponential LogisticPower (1/a x ) Females Males 6 parameters to 2 parameters

Selectivity: Precision

Model Evaluation Parameter correlations greater than 0.4: Parameter correlations greater than 0.4: Model 1: 17 Model 1: 17 Model 2: 14 Model 2: 14 Model 3: 1 Model 3: 1 Model 3 fits about the same as Model 1 but with 13 less parameters, better model stability and less parameter correlation. Model 3 fits about the same as Model 1 but with 13 less parameters, better model stability and less parameter correlation.

Simulation – life history cases FishGadid (Pollock) Flatfish (Arrowtooth) Rockfish (POP) M N ages91324 Pop. TrendDecreasingIncreasing Survey CV~18%~8%~25% Survey q~1.00~0.73~2.00 RecVarHighLowMedium

Simulation – selectivity cases SelectivityParamsShape Logistic 2Asymp. Gamma 2Dome Exp. Logistic 3 Asymp. Or Dome Double-gamma 4 Dome or Double Dome Double-log 4 Asymp. Or Dome Double-normal 8Abstract art

Simulation – model SelectivityParamsForm Recruitment 38-53LMR + devs M 1Lognormal Q 1 Lognormal or fixed Age comps. - Multinomial Survey biomass - Lognormal Catch biomass 30Fdevs/Lognormal

Operating/Estimation One fishery, one survey, one SEX One fishery, one survey, one SEX Survey constrained to be logistic Survey constrained to be logistic 6 x 6 x 100 (fixed q) 6 x 6 x 100 (fixed q) 6 x 6 x 1000 (estimate q) 6 x 6 x 1000 (estimate q) Age comps only, no lengths Age comps only, no lengths Multinomial sample size of 200 Multinomial sample size of 200

Gamma (POP)

Double normal (POP)

Double normal (pollock, est. q)

Catchability (POP) (est. q)

LMR (POP, est. q)

Natural mortality (ATF)

Natural mortality (POP)

Ending SSB (POP)

Estimation/precision More parameters, more uncertainty, less convergence More parameters, more uncertainty, less convergence Even when biased, logistic and gamma are precise Even when biased, logistic and gamma are precise Models are more stable Models are more stable Correlations are lower Correlations are lower

CVs –Double normal

CVs –Logistic and gamma Logistic Gamma

CV of OFL (pollock)

Multiplier at P*=0.25 (pollock, est. q)

Preliminary conclusions Forcing the logistic can create bias in M Forcing the logistic can create bias in M For fishery selectivity, logistic not necessarily conservative For fishery selectivity, logistic not necessarily conservative Double normal can fit most shapes but at a cost: Double normal can fit most shapes but at a cost: Selectivity parameters are not precise Selectivity parameters are not precise Oddly, OFL and ending SSB are more precise (Hessian) Oddly, OFL and ending SSB are more precise (Hessian)

Preliminary conclusions Complicated selectivities are OK when: Complicated selectivities are OK when: There is a rationale that a fisherman can understand There is a rationale that a fisherman can understand The model can be reliably estimated with the number of selectivity parameters (e.g., easy convergence and CV<50%) The model can be reliably estimated with the number of selectivity parameters (e.g., easy convergence and CV<50%) Parameter correlations <0.5? Parameter correlations <0.5? Our simple simulations did not provide obvious results, selectivity IS complicated Our simple simulations did not provide obvious results, selectivity IS complicated

Introducing The TWINCE model

Introducing The Triple-Weibull-Inverse-Negative- Cauchy-Exponential The Triple-Weibull-Inverse-Negative- Cauchy-Exponential ONLY 19 parameters ONLY 19 parameters Can meet all your selectivity needs Can meet all your selectivity needs Flexible shapes (reversible, like overfished) Flexible shapes (reversible, like overfished) Stable until you add real data Stable until you add real data Estimable until you turn on the parameters Estimable until you turn on the parametersTHANKS!