H a r v e s t r u l e s f o r s t o c k s w i - - PowerPoint PPT Presentation

H a r v e s t r u l e s f

• r

s t

• c

k s w i t h c h a n g i n g r e c r u i t m e n t , l i k e B l u e w h i t i n g

D a n k e r t S k a g e n f

• r

P e l a g i c A C

DANKERT SKAGEN

Fisheries Science Consultant

Task

... to develop harvest rules that can work well with large unpredictable recruitment fluctuations, rather than to attempt to make predictions based

• n presumably realistic scenarios for the future.

Therefore, the suggestion is to set up a test-bench with a range of recruitment scenarios and transitions between scenarios, and to use that to explore the performance of harvest rules when recruitment fluctuates like it has done for blue whiting.

In brief: Outline harvest rules that can work for a stock like Blue whiting,

with

• Large and unpredictable variations in recruitment,
• Noisy assessments.

Harvest rules for Blue whiting have never survived very long.

The major challenge: Shifus in recruitment regimes:

Most harvest rules assume a stable recruitment regime

(variatjons around a stable relatjon between recruitment and SSB)

Limited experience with designing rules for regime shifus.

This slide is from the study in 2012. Still true!

Why is this so difficult?

• Variable recruitment
• Uncertain assessments
• Many interested parties, including scientists.

What can we do?

• Look for rules that can handle shifts in recruitment and 'strange' levels of

recruitment

• Reduce sensitivity to noise but keep sensitivity to changing production

capacity

• Start with conventional plan designs, and work from there.

A rational approach:

We are used to assume stationarity in dynamics and reference points. We cannot just assume that when recruitment changes. Clarify what becomes different.

Some key issues:

• Reference points may not be universally valid, safe values ain’t so safe.
• The timing of management action should be adapted to timing
• f change in stock dynamics and abundance

0.2 0.4 0.6 0.8 1 1.2 0.01 0.02 0.03 0.04 0.05 0.06 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Yield and SSB per recruit

Y/R SSB/R F0.1 90%Ymax 95%Ymax

Fishing mortality Yield/recruit SSB/recruit

Reference points: Yield and SSB per recruit

Depends on:

• Growth
• Maturation
• Selectivity in fishery
• Natural mortality.

Values from Blue whiting assessment 2016, but modified selectivity at age Actual catch and SSB is Y/R and SSB/R times the recruitment. Two key values: F=0.18: F0.1 F=0.32: Where Y/R is 95% of the maximum and ICES FMSY.

When recruitment (and growth and maturity) is has random variations, that translates into variation in catches and SSB: Here, we have assumed a constant mean recruitment at 10000 (arbitrary example!) and the variability used elsewhere in this study. If recruitment changes over time, beyond random variations, each recruitment regime will have its own set of such curves.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 100 200 300 400 500 600 700 800 900 1000 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Stochastic Yield and SSB per recruit

C10 C50 C90 SSB10 SSB50 SSB90 F0.1 FMSY

F Yield SSB

A new dimension! - reference points depend on recruitment.

Normally, we assume that recruitment varies around a stationary mean. We look at the yield and SSB as a function of F and the probability that SSB is below Blim (risk) as a function of F under that condition. But when recruitment is variable, we also have to consider how the risk depends on mean recruitment.

5000 10000 15000 20000 25000 30000 5 10 15 20 25 30

Risk to Blim at F0.1 and F95%

0.18 0.32 5.00%

Mean recruitment Risk %

One way to see this: For the two key F-values: How the risk to Blim depends

• n mean recruitment

5000 10000 15000 20000 25000 30000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

F at 5% risk

as function of mean recruitmetn

F at 5% risk

Mean recruitment F0.05

Another way to see this:

The F leading to 5% risk as a function of the mean recruitment. This is a straight line!

• Guidance for a rule where F depends on recruitment
• There is no specific F-value that is 'safe', even F0.1 is only safe if

there is enough recruits.

1 2 3 4 5 6 7 8 9 10 0.05 0.1 0.15 0.2 0.25

Age distribution in the SSB

Equilibrium distribution for 2 levels of F

0.18 0.32

Age Relative SSB

Timing of response

• 1. Spawning biomass is mostly ages 3-5.

2 4 6 8 10 12 14 16 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Time course of SSB after decreased recruitment

Recruitment from 30000 to 10000

0.04_5% 0.04_50% 0.04_90% 0.18_5% 0.18_50% 0.18_90% 0.32_5% 0.32_50% 0.32_90% 0.46_5% 0.46_50% 0.46_90%

Y ears SSB relative to year 1

2 4 6 8 10 12 14 16 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time course of SSB after increased recruitment

Recruitment from 10000 to 30000

0.04_5% 0.04_50% 0.04_90% 0.18_5% 0.18_50% 0.18_90% 0.32_5% 0.32_50% 0.32_90% 0.46_5% 0.46_50% 0.46_90%

Y ears SSB relative to year 1

• 2. Change in SSB is delayed and gradual

Two implications:

1.There is time to confirm a change in recruitment, but don't wait for too long 2.Using SSB as guidance means late and gradual response.

HCS: Workbench for testing harvest rules Brief tutorial on bootstrap simulation tools, like HCS.

Many elements are uncertain: Recruitment, growth, observations. These are represented by statistical distributions rather than exact numbers. We make many (1000) examples (iterations) with values for the uncertain elements drawn from their assumed statistical distributions. That translates these distributions into distributions of our performance parameters. We can then state the probability

• f outcomes of interest.

For example, we want to know the 'risk to Blim', which is the probability that SSB falls below the limit. We get that by counting the number out of the 1000 iterations where this happens - if it happens in 50 out of 1000 iterations, the risk is 5%. This way of accounting for uncertainty is called bootstrap or Monte Carlo methods.

Population model Observation model Decision rule Implementation Actual removal by the fishery True stock Apparent stock TAC Model sequence Data flow

HCS - how it works

An artificial stock that is updated every year. It is managed by TACs that are set according to a harvest rule and removed from the stock. A new year class recruits each year. Decisions are made according to 'observed' values for stock

• abundance. The

'observed' numbers have error that imitates a real assessment

The anatomy of a harvest rule.

Basis: Anything that informs about the state of the stock: SSB, TSB, Recruitment, something else.One or more. Rule: A formula that derives a measure of exploitation from the basis:

If Basis(1) < Btrig1: v = vstd*(1.0-alpha1*(btrig1-Basis(1))/btrig1). If that leads to v<0, set v = 0 If Basis(1) > Btrig1 and Basis(2) < Btrig2: v = vstd If Basis(1) > Btrig1 and Basis(2) > Btrig2: v=vstd*(1.0+alpha2*(Basis(2)-btrig2)/btrig2). If v<vmin so far, set v=vmin If v>vmax so far, set v=vmax

Measure of exploitation: F, harvest rate (HR=TAC/TSB) Translation: Derive TAC from measure of exploitation, typically using 'observed' stock numbers. Gives a primary TAC. Stabilizers: 50-50 rule: TAC = 0.5*TAC(y-1)+(1-0.5)*primary TAC) Percentage rule: TAC-change constrained if SSB > a trigger Maximum or minimum TAC

2000 4000 6000 8000 10000 12000 14000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 .18-1-1 .18-3-3 .32-1-1 .32-3-3 .18--0 .32--0

Model conditioning:

• Weights, maturities natural mortalities: As used by WGWIDE 2016.
• Selection in the fishery: Almost flat above age, different from most recent year.
• Initial numbers: Observation model applied to stock numbers at start of 2016.
• Recruitment:

Sequence of recruitment models with different means. Hockey stick with break-point at SSB = 1500,

 Lognormal ditribution with CV= 0.45,  Autocorrelation 0.75,  No truncation,  No exceptional year classes (spikes)

Probably somewhat more variable than the historical series.

• Observation model:

Random noise is a product: Year factor * Age factor.

 Age factor from assessment - CV of stock numbers at age.  Year factor: Autocorrelation 0.6 (a bit arbitrary) and CV scaled to give  a confidence interval of SSB in the initial year equal to that in the assessment.

This imitates a quite noisy assessment.

Spikes and autocorrelations

Tested including spikes and removing autocorrelation for two levels of fishing mortality

0.18 0.32 5 10 15

Risk to Blim

Baseline (autocorr and no spikes), Spikes, and No autocorrelation

Risk_base Risk_sp Risk_nauto

F Risk

0.18 0.32 200 400 600 800 1000 1200

Catches (10-50-90 percentiles)

C10_base C10_sp C10_noauto C50_base C50_sp C50_noauto C90_base C90_sp C90_noauto

F Catch

Baseline (autocorr and no spikes), Spikes, and No autocorrelation

Autocorrelation (here with ρ=0.75) broadens the distribution of catches (and biomasses) leading to higher risks. The median catch is almost unchanged. Spikes make little difference when the mean recruitment is adjusted accordingly.

Sequence of recruitments:

History: Standard test bench: 4 periods, shift in fixed years. Levels similar to the historical ones, but set up to test how rules can handle such recruitments and recruitment shifts.

1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 20000 40000 60000 80000 100000 120000 140000 Y early R Periods Rlow Rhigh 2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 10000 20000 30000 40000 50000 60000 Mean 10.00% 90.00%

Designing harvest rules for changing recruitment Blue whiting experience

1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 1 2 1 1 2 1 2 2 1 3 2 1 4 2 1 5 500 1000 1500 2000 2500 3000 Advice Catch ≈ MSY catch 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2000 4000 6000 8000 10000 12000 14000 10000 20000 30000 40000 50000 60000 70000 TSB SSB Recruits 19871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015 200 400 600 800 1000 1200 1400 1600 10000 20000 30000 40000 50000 60000 70000 Advice Recruits

Catch vs advice and 'MSY catch' Advice and recruits TSB, SSB and recruits

Tested several types of rules. Started with the conventional and moved towards slightly more innovative. The more innovative have different timing and strength of the response to changing productivity. Rules that have been examined: 1.The ICES standard MSY rule 2.Extensions of the standard rule 3.Using TSB and HR instead of SSB and F 4.Let F in the an extended standard rule be a linear function of recruitment 5.Escapement at high SSB: Leave enough behind, take the rest.

Performance criteria What do we want to know about?

Just catches and SSB is not meaningful here, they are just scaled with the recruitment, which is arbitrary here. We want rules that can handle the large changes in recruitment that we test. Generally, we would like to see:

• Low risk and rapid recovery if the stock gets low.
• High yield and timely response to changes in recruitment
• Low year - to -year variation.

Two measures that need explanation

IAV: Change in TAC as percentage of the mean of the two years: IAV(y) = (TAC(y) - TAC(y-1))/(TAC(y) + TAC(y-1)) MSY proxy catch: Approximately the catch you would get by applying FMSY TSB times the Yield/TSB ratio at F = FMSY.

For each harvest rule type, we present In the low recruitment period:

• How long it takes before the 5% limit is passed after the recruitment dropped
• The maximum percentage risk
• The minimum SSB (lowest value of 5 percentile)
• The time needed for 95% of those trajectories that have been below Blim

to recover above Blim after the recruitment returned to 'normal'.

In the high recruitment period:

• The catch in the high recruitment period as percent of the MSY proxy.
• How long it takes to reach 90% of the maximum that is obtained in the long run

This is the time it takes before the improved recruitment is picked up in the catches.

• IAV in the high recruitment period

The ICES standard MSY rule

Use F = FMSY when the SSB is estimated above the trigger biomass, and reduce it linearly towards the origin when SSB is lower.

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

ICES standard MSY rule

SSB F

FMSY = 0.32 Btrigger = 2250

Max in percent of MSY Time to 90% of max F=0.18,Alfa1=1 81 10 F=0.18,Alfa1=3 81 10 F=0.32,Alfa1=1 93 8 F=0.32,Alfa1=3 93 8 Years to Blim

• Max. risk

(%) Min of 5 percentile SSB Time to prob recovery > 95% F=0.18,Alfa1=1 8 28 1058 10 F=0.18,Alfa1=3 8 20 1064 7 F=0.32,Alfa1=1 5 52 689 10 F=0.32,Alfa1=3 5 39 865 9

The ICES standard MSY rule Low recruitment period High recruitment period

The ICES standard MSY rule

2010 2020 2030 2040 2050 2060 2070 1000 2000 3000 4000 5000 6000 10 20 30 40 50 60

Standard MSY rule

• FMSY. = 0.18, Breakpt SSB=2250, Alfa1=1

Prob Blim TAC10 TAC50 TAC90 SSB5% Recruit shift

Y ear TAC and SSB Risk to Blim

2010 2020 2030 2040 2050 2060 2070

• 200
• 150
• 100
• 50

50 100 150 100 200 300 400 500 600

Standard MSY rule

• FMSY. = 0.18, Breakpt SSB=2250, Alfa1=1

Perc MSY 10.00% 50.00% 90.00% Prob50%red Recruit shift

Y ear IAV Percent of MSY

ICES standard MSY rule.

Even at the low F = F0.1 = 0.18, there is a substantial risk to Blim in the low recruitment phase and a relatively low catch with high recruitment. The response to improved recruitment is slow. The FMSY = 0.32 gives very high risk to Blim in the low recruitment phase and still relatively low catch with high recruitment. The IAV is quite high, in particular in the low recruitment phase.

Extending the standard rule

A wide range of options were tested. Aim: Timely and adequate response to shifts in recruitment without un-necessary draconian actions. Options that were tested:

• Target F = 0.18 and 0.32
• Btrig1 (SSB below which F is reduced)
• Alpha1 (Slope of reduction towards low SSB)
• Btrig2 (SSB above which F is increased)
• Alpha2 (Slope of increase towards high SSB)
• Applying a filter (catch this year is the mean of the catch last year

and the TAC first calculated for this year), applicable when SSB > 2250 kt (BMSYtrigger).

• Applying a maximum TAC at 2500 kt.
• A minimum F = 0.025 and a maximum F = 0.6 were always applied.

Extending the standard rule - preferred option.

F=0.18, Alfa1=3, Alfa2=3, Btrig1=3000 Btrig2=6000 Min F: 0.025 Max F: 0.6 Filter 0.5 above 2250, MaxTAC = 2500

2015 2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 1000 2000 3000 4000 5000 6000 7000

Catch trajectories with and without filter and maxTAC

Target F = 0.18, Triiger 1=3000, Trigger2 = 6000, Alpha1=3, Aplha2=3

F&max 1 F&max 2 F&max 3 No 1 No 2 No 3 2000 4000 6000 8000 10000 12000 14000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

Extended standard rule

Preferred options

SSB F

Years to Blim Max. risk (%) Min of 5 percentile SSB Time to prob recovery > 95% Mean IAV Low (%) F=0.18,Alfa1=3, Alfa2=3, Btrig1=3000 Btrig2=6000 5 13 781 7 72 Preferred: F=0.18,Alfa1=3, Alfa2=3, Btrig1=3000 Btrig2=6000 Filter 0.5 above 2250, MaxTAC = 2500 5 16 719 6 51 F=0.32,Alfa1=3, Alfa2=3, Btrig1=3750 Btrig2=6000 5 16 528 6 76

Extended standard rule Low recruitment phase

Max in percent of MSY Time to 90% of max Mean IAV high R (%) F=0.18,Alfa1=3, Alfa2=3, Btrig1=3000 Btrig2=6000 99 7 68 Preferred: F=0.18,Alfa1=3, Alfa2=3, Btrig1=3000 Btrig2=6000 Filter 0.5 above 2250, MaxTAC = 2500 90 9 33 F=0.32,Alfa1=3, Alfa2=3, Btrig1=3750 Btrig2=6000 102 6 75

Extended standard rule High recruitment phase

2010 2020 2030 2040 2050 2060 2070 1000 2000 3000 4000 5000 6000 15 30 45

Modified MSY rule

Prob Blim TAC10 TAC50 TAC90 SSB5% Recruit shift

Y ear TAC and SSB Risk to Blim

2010 2020 2030 2040 2050 2060 2070

• 200
• 150
• 100
• 50

50 100 150 100 200 300 400 500 600 700 800

Modified MSY rule

Perc MSY IAV10 IAV50 IAV90 Prob50%red Recruit shift

Y ear IAV Percent of MSY

Extended standard rule

Extended standard rule - lessons learned.

Large number of possible options. Coarse screening here, but still 270 sets of options tested. Improvements, but not quite satisfactory. Quicker response to changes in recruitment, but the Alphas and Btriggers need to be scaled quite carefully Still quite high IAV Filter and max. catch improve IAV, but cost something of catch. The risk with low recruitment is bad, SSB can become very low. Recovery looks ok,

TSB and harvest rate instead of SSB and F

Similar exploration as for extended standard rule. HR: 0.11 or 0.17. corresponding roughly to F = 0.18 and 0.32. Alph1: 1 or 3 Alpha2: 0 or 2. Btrig1: TSB at 2500 or 4000 Btrig2: TSB at 8000 or no trigger Min HR: 0.04 Max HR: 0.18 or 0.30 MaxTAC: 2500 or infinity Filter: No filter or 50%, with derogation at SSB below 2250. Results with the most promising choice are tabulated.

Years to Blim Max. risk (%) Min of 5 percentile SSB Time to prob recovery > 95% Mean IAV Low (%) HR=0.11, Btrig1=4000,Alfa1=3, Btrig2=8000, Alfa2=2, Max HR = 0.3 Min HR = 0.04 Filter 0.5 above 2250, MaxTAC = 2500 7 9 1324 7 35 Max in percent of MSY Time to 90% of max Mean IAV high R (%) HR=0.11, Btrig1=4000,Alfa1=3, Btrig2=8000,Alfa2=2, Max HR = 0.3 Min HR = 0.04 Filter 0.5 above 2250, MaxTAC = 2500 90 8 28

TSB and harvest rate instead of SSB and F

Low recruitment phase High recruitment phase

2010 2020 2030 2040 2050 2060 2070 1000 2000 3000 4000 5000 6000 10 20 30 40 50 60

HR and TSB - rule

Prob Blim TAC10 TAC50 TAC90 SSB5% Recruit shift

Y ear TAC and SSB Risk to Blim

2010 2020 2030 2040 2050 2060 2070

• 150
• 100
• 50

50 100 150 100 200 300 400 500 600 700

HR and TSB rule

Perc MSY IAV10 IAV50 IAV90 Prob50%red Recruit shift

Y ear IAV Percent of MSY

TSB and harvest rate instead of SSB and F

TSB and harvest rate instead of SSB and F Lessons learned.

Performs better than the SSB-F rule.

• Lower risk, develops more slowly
• Lower IAV, in particular with low recruitment
• Similar average catch
• Similar recovery

• vstd = v0 + gain*R
• If Basis(1) < Btrig1: v = vstd*(1.0-alpha1*(btrig1-Basis(1))/btrig1).

If that leads to v<0, set v = 0

• If Basis(1) > Btrig1 and/or Basis(2) < Btrig2: v = vstd
• If Basis(1) > Btrig1 and Basis(2) > Btrig2:

v=vstd*(1.0+alpha2*(Basis(2)-btrig2)/btrig2).

• If v<vmin so far, set v = vmin
• If v>vmax so far, set v=vmax

R dependent F - rule

The general formula for the rule is: Basis(1) and Basis(2) are both SSB, the v's are F's The difference from the extended standard rule is that the standard exploitation measure (F) now depends on a measure

• f recruitment R

The relation between F and R is a straight line which crosses the y-axis at v0 and with a slope called gain. For R we use the median of assessed recruitments for years -4 to -2 relative to the TAC year. We skip the rise in F towards high SSB, since that is well enough covered by the high F at high recruitment.

R dependent F - rule

Scanned over a wide range of options, like it was done for previous rules. A gain = 0.23 and a v0 = -0.10 is the relation between recruitment ant the F having a 5% risk in long term equilibrium, as seen earlier:

5000 10000 15000 20000 25000 30000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

F at 5% risk

as function of mean recruitmetn

F at 5% risk

Mean recruitment F0.05

This seemed to be a good choice. A filter and a maximum TAC improved the performance without reducing catch very much, but increased risk in the low phase somewhat.

Years to Blim

• Max. risk

(%) Min of 5 percentile SSB Time to prob recovery >95% Mean IAV Low (%) Gain=0.23, Vmax=0.32, Vmin=0.025, V0=-0.1 R is median for years -4 to -2, 50% filter above SSB = 2250 5 9.6 1110 7 42 Max in percent of MSY Time to 90% of max Mean IAV High (%) Gain=0.23, Vmax=0.32, Vmin=0.025, V0=-0.1 R is median for years -4 to -2, 50% filter above SSB = 2250 95 7 28

R dependent F - rule

Low recruitment High recruitment

2010 2020 2030 2040 2050 2060 2070 1000 2000 3000 4000 5000 6000 10 20 30 40 50 60

F from R - rule

Prob Blim TAC10 TAC50 TAC90 SSB5% Recruit shift

Y ear TAC and SSB Risk to Blim

2010 2020 2030 2040 2050 2060 2070

• 200
• 150
• 100
• 50

50 100 150 200 100 200 300 400 500 600 700

F from R - rule

Perc MSY IAV10 IAV50 IAV90 Prob50%red Recruit shift

Y ear IAV Percent of MSY

R dependent F - rule

Escapement rule

This is the standard type of rule, using F and SSB, but with an additional clause: If SSB is above a treshold and the difference between the actual SSB and the treshold is bigger than the TAC calculated by the ordinary rule, then set the TAC equal to the difference. “If there is plenty fish, why not take it.” Explored only with the 'best' options for the extended standard rule. but no increase of F above Btrigger2, no filter, but maximum TAC at 3000 kt.

Years to Blim

• Max. risk

(%) Min of 5 percentile SSB Time to prob recovery > 95% Mean IAV Low (%) F=0.18,Alfa1=3, Alfa2=0, Btrig1=3000 MaxTAC = 3000 Escapement biomass = 6000 7 12 1439 7 67 Max in percent

• f MSY

Time to 90% of max Mean IAV high R (%) F=0.18,Alfa1=3, Alfa2=0, Btrig1=3000 MaxTAC = 3000 Escapement biomass = 6000 91 8 56

Escapement rule

Low recruitment High recruitment

Escapement rule

2010 2020 2030 2040 2050 2060 2070 1000 2000 3000 4000 5000 6000 10 20 30 40 50 60

Escapement - rule

Prob Blim TAC10 TAC50 TAC90 SSB5% Recruit shift Y ear TAC and SSB Risk to Blim 2010 2020 2030 2040 2050 2060 2070

• 200
• 150
• 100
• 50

50 100 150 200 100 200 300 400 500 600 700

Escapement - rule

Perc MSY IAV10 IAV50 IAV90 Prob50%red Recruit shift

Y ear IAV Percent of MSY

Comparing rules

2010 2020 2030 2040 2050 2060 2070

• 10

10 30 50 70 90 110 130 150 5000 10000 15000 20000 25000 30000 35000 40000

Comparing types of harvest rules

Mean annual catch in percent of MSY

Mean Recruitment ICES Std Modified std HR & TSB F from R Escape

Year Percent Recruits 2010 2020 2030 2040 2050 2060 2070 10 20 30 40 50 60 70 80 90 5000 10000 15000 20000 25000 30000 35000 40000

Comparing types of harvest rules

Mean annual IAV

Mean Recruitment ICES Std Modified std HR & TSB F from R Escape

Y ear IAV Recruits

Mean F Mean catch relative to MSY proxy IAV

2010 2020 2030 2040 2050 2060 2070 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 5000 10000 15000 20000 25000 30000 35000 40000

Comparing types of harvest rules

Mean annual F

Mean Recruitment ICES Std Modified std HR & TSB F from R Escape

Y ear F Recruits

The ICES standard MSY-rule is not the best F does not adjust properly to changes in productivity. Impossible trade-off between high catch when productivity is big and low risk when productivity is low Modifying it improves performance: Steeper and earlier reduction of F at low SSB and incresded G at high SSB, applying a filter stabilizer and a maximum catch Letting F depend on recruitment seems to work well, low risk, satisfactory catches and low IAV Using TSB as basis (here combined with using HR rather than F) also works well. Applying an escapement rule at high SSB does not improve mean catch but increases IAV very much. The F depending on R and the TSB-HR rules seem most promising, and are candidates (with some further refinement) for a better management

• f the Blue whiting.

T