Fishery managers should consider Fishery managers should consider compensatory processes: compensatory processes: simulated responses to fishingsimulated responses to fishing

By By Rob Day, David Bardos, Rob Day, David Bardos,

Fabrice Vinatier and Julien SagiottoFabrice Vinatier and Julien Sagiotto

Zoology Dept, School of Physics, University of Melbourne Agronomy, INA-PG, Paris, France

Abalone are unusual fishAbalone are unusual fish

Sedentary adults – catch algae Short larval dispersal c 200m

- Thus hundreds of stocks Juveniles cryptic under rocks

Adults cannot be aged Aggregate to ‘hotspots’

- Divers can target these

- CPUE hyperstable

Current Dynamic pool modelCurrent Dynamic pool model

Fitted to adult survey data 1992-present – Nos, size distribution, catch– Complete catch history known

Stochastic growth model ‘Average’ M, growth parameters used Fecundity based on size distribution Fits relation of Fecundity- Recruitment (50 mm)

– One year recruitment lag

Experiments -with Industry help! Experiments -with Industry help! on compensatory mechanisms on compensatory mechanisms

Settlement, Post-larval survival?Cryptic juvenile survival, growth?Size at maturity?Adult survival, growth? Adult Fecundity?

2 m3 m

3 m

DD postlarval growth and survival

DD cryptic juvenile growth

DD time to maturity

DD growth of smaller adults

DD size-spcific fecundity in larger adults

What DD responses maintain stocks?What DD responses maintain stocks?

A Simulation ApproachA Simulation Approach

Explore consequences of each DD mechanism:

– compare responses to fishingNOT fitting a DD model to dataInspect the process – like IBM approachExplore variations of the models

– to determine sensitivity to model structure

Stage-Structured Matrix ModelsStage-Structured Matrix Models1, 1 1,1 1 5 5 6 6 7 7

2, 1 2,1 1 2,2 2

3, 1 3,1 1 3,2 2 3,3 3

4, 1 4,1 1 4,2 2 4,3 3 4,4 41

5, 1 5,1 1 5,2 2 5,3 3 5,4 4 5,5 5

6, 1 6,1 1 6,2

7, 1

0 0 0

0 0 0 0 0

0 0 0 0

0 0 0

0 0

n

n

n

nn

n

n

n

x g s f s f s f s

x g s g s

x g s g s g s

x g s g s g s g sx

x g s g s g s g s g s

x g s g

x

1,

2,

3,

4,

5,

2 6,3 3 6,4 4 6,5 5 6,6 6 6,

7,1 1 7,2 2 7,3 3 7,4 4 7,5 5 7,6 6 7 7,

0

n

n

n

n

n

n

n

x

x

x

x

x

s g s g s g s g s x

g s g s g s g s g s g s s x

xi,n is the population of size class i at time n

gij are growth transition probabilities from i to j assuming survivalfj is the number of post-larvae produced / individualsj is the survival probability over one time-step

The growth transitionsThe growth transitions

Fast abalone growth is modeled Best understood by a transition chart Some stages can grow 2-3 classes

Each model has 1 DD mechanismEach model has 1 DD mechanism

Used Beverton-Holt function– Adj. β to produce same initial equilibrium

Many possibilities!Many possibilities!Specify which stage is affected by densitySpecify which stages affect them (biomass / numbers)

Chose realistic optionsChose realistic options

e.g.

DD fecundity: fecundity of 3 adult sizes affected by density of adults + largest juveniles

Effects of fishing, Part 1Effects of fishing, Part 1Comparing DD modelsComparing DD models

Start with pop. at 10, 000 adults (equilibrium) Start fishing at step 5 90% of largest size class fished 12 types of DD effect modeled Examine, explain compare responses

– Especially time to fished equilibrium

DD FecundityDD Fecundity

Adults Juvs Postlarvae

0

25

50

75

100

125

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

IAL

AD

UL

TS

Adults Juvs Postlarvae

Post-larvaeAdults Juvs

After fishing:Higher fecundity: more post-larvae per adult.

Pop. stabilises in +/- 16 yr

DD Juvenile MortalityDD Juvenile Mortality

0

50

100

150

200

250

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

IAL

AD

UL

TS

Adults Juvs/10 Postlarvae/100

0

50

100

150

200

250

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

IAL

AD

UL

TS

Adults Juvs/10 Postlarvae/100

After fishing: Juvenile No.s reduced, then better survival stabilises population in <10yr

Note changes in scales!

DD Juvenile GrowthDD Juvenile Growth

0

20

40

60

80

100

120

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

IAL

AD

UL

TS

Adults Juvs/100 Postlarvae/100

0

20

40

60

80

100

120

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

IAL

AD

UL

TS

Adults Juvs/100 Postlarvae/100 Prior to fishing: large no. juveniles, as growth is suppressed.

After fishing: Juvs begin to grow faster. This increases, then stabilises adult numbers

Stability after +/- 19 yr

(Depends on biomass density of population)

DD Growth - all stagesDD Growth - all stages

Prior to fishing: Most adults small: their growth is suppressed,so fishing has less effect

After fishing: increased growth of juvs restores adults, but juv nos decline, so slow decline of adults, over 30 years!

0

20

40

60

80

100

120

1 4 7 10 13 16 19 22 25 28 31 34

TIME

% I

NIT

AIA

L A

DU

LT

S

Adults Juvs/10 Postlarvae/100

(Juvenile, small adult growth depends on pop. biomass.Post-larvae growth depends on juvenile biomass)

Perturbation AnalysisPerturbation Analysis

Perturbations of +/- 10% to mortalities, fecundities and three growth parameters

– No changes substantially alter conclusionsAltered fishing pressures

– At over 50% little change in dynamics or even equilibrium stocks under fishing

Effects of fishing, Part 2Effects of fishing, Part 2Variations of the modelsVariations of the models

Change growth reduction process:– 1st models set increasing % to zero growth– In type 2 models growth reduced by 1 step

(some base growth transitions are 2 steps) From 1 to 2 adult size classes fished (90% pa) Fishing a set Quota Combine 2 DD responses (growth and mortality)

Type 2 DD growthType 2 DD growth

Type 2 compensation is weaker, as growth is not stopped – more realistic

But Nos. at equilibrium under fishing are similar for each model

Times to equilibrium even longer!

– Because less change in recruitment to fished sizes as adults are fished.

Changes to FishingChanges to Fishing

Few differences when 2 sizes fished– but fewer adults remain under fishing, except

DD adult growth models (few larger adults before fishing)

Quota fishing is more realistic– But real quotas are adjusted after the fish-down

phase– Time to mine down the stock below the quota

was examined– Thus sustainable quotas for each model found

Quota Fishing ResultsQuota Fishing Results

Sudden transition sustainable to unsustainable quota DD growth based on biomass : lowest quota

transitions Type 2 DD models had even lower transitions

(not shown) For each model, transitions reflect biomass under

high fishing pressure – i.e. recruitment With sustainable quotas, times & decreases to

equilibria under fishing similar to using F =0.9

Two DD responsesTwo DD responses

DD growth based on biomass + DD mortality– Realistic: at high density growth reduces,

then they die Effects appear additive, depend on ratio of βs For growth β = 10 - 10000 x mortality β:

– slow approach to equilibrium under fishing– Adult biomass remains at high level

EFFECT OF FISHING VERSUS RATIO OF DENSITY RESPONSES

0

0.2

0.4

0.6

0.8

1

1.2

1 4 7 10 13 16 19 22 25 28

TIME

AD

ULT

NU

MB

ER

S

0

0.001

0.01

0.1

1

10

100

1000

10000

β DD growth

Simulation SummarySimulation Summary

DD mortality, fecundity: rapid stabilisation Growth can lead to very slow stabilisation

– and complex responses– speeds up the generation time

This pattern holds for a range of models– and for combined growth and mortality

We know DD growth is strong in abalone DD growth “perhaps best established”

– Beverton & Holt 1957 most models assume simple, rapid DD recruitment

The Assessment problemThe Assessment problem

About 60 sites surveyed annually– Adult Nos & size distribution– Cannot survey every reef

Growth rates differ widely between reefsSize at maturity varies greatly

– 160 mm vs 70 mm

Model cannot fit DD growth effectModel cannot be fitted at local scale

Assessment at the local scale?Assessment at the local scale?

Every reef requires different management Local scale management by industry?

– Now happening in Victoria– Based on diver perceptions, guesses

Catch history at local scale known– But no time series except sample reefs

Can experiments reveal enough about dynamics? Can simulations guide local management?