1. Fishery managers should consider compensatory processes: simulated responses to fishingBy
Rob Day, David Bardos,
Fabrice Vinatier and Julien Sagiotto
Zoology Dept, School of Physics, University of Melbourne
Agronomy, INA-PG, Paris, France

2. Abalone 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

3. Current 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

4. Experiments -with Industry help! on compensatory mechanisms
Settlement, Post-larval survival?
Cryptic juvenile survival, growth?
Size at maturity?
Adult survival, growth?
Adult Fecundity?
2 m
3 m

5. What DD responses maintain stocks?
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

6. A Simulation Approach Explore consequences of each DD mechanism:
compare responses to fishing
NOT fitting a DD model to data
Inspect the process – like IBM approach
Explore variations of the models
to determine sensitivity to model structure

7. Stage-Structured Matrix Models
xi,n is the population of size class i at time n
gij are growth transition probabilities from i to j
assuming survival
fj is the number of post-larvae produced / individual
sj is the survival probability over one time-step

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

9. Each model has 1 DD mechanism
Many possibilities!
Specify which stage is affected by density
Specify which stages affect them (biomass / numbers)
Chose realistic options
e.g.
DD fecundity: fecundity of 3 adult sizes affected by density of adults + largest juveniles
Used Beverton-Holt function
Adj. β to produce same initial equilibrium

10. Effects of fishing, Part 1 Comparing 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

11. DD Fecundity After fishing:
Adults
Juvs
Postlarvae 25 50 75
100
125 1 4 7 10 13 16 19 22 28 31 34
TIME
% INITIAL ADULTS
Post-larvae
After fishing:
Higher fecundity: more post-larvae per adult.
Pop. stabilises in +/- 16 yr

12. DD Juvenile Mortality Note changes in scales! After fishing:50
100
150
200
250 1 4 7 10 13 16 19 22 25 28 31 34
TIME
% INITIAL ADULTS
Adults
Juvs/10
Postlarvae/100
After fishing:
Juvenile No.s reduced, then better survival stabilises population in <10yr

13. DD Juvenile Growth (Depends on biomass density of population)20 40 60 80
100
120 1 4 7 10 13 16 19 22 25 28 31 34
TIME
% INITIAL ADULTS
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

14. DD Growth - all stages
(Juvenile, small adult growth depends on pop. biomass.
Post-larvae growth depends on juvenile biomass) 20 40 60 80
100
120 1 4 7 10 13 16 19 22 25 28 31 34
TIME
% INITAIAL ADULTS
Adults
Juvs/10
Postlarvae/100
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!

15. Perturbation Analysis
Perturbations of +/- 10% to mortalities, fecundities and three growth parameters
No changes substantially alter conclusions
Altered fishing pressures
At over 50% little change in dynamics or even equilibrium stocks under fishing

16. Effects of fishing, Part 2 Variations 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)

17. Type 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.

18. Changes 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

20. Quota 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

21. Two 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 = x mortality β:
slow approach to equilibrium under fishing
Adult biomass remains at high level

22. β DD growth

23. Simulation Summary Beverton & Holt 1957
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

24. The Assessment problem
About 60 sites surveyed annually
Adult Nos & size distribution
Cannot survey every reef
Growth rates differ widely between reefs
Size at maturity varies greatly
160 mm vs 70 mm
Model cannot fit DD growth effect
Model cannot be fitted at local scale

25. 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?