1. Sardine Two-Stock Hypothesis: Results at the Posterior Mode
SPSWG Meeting
28th August 2013
Carryn de Moor
Doug Butterworth
Marine Resource Assessment and Management Group (MARAM)
Department of Mathematics and Applied Mathematics
University of Cape Town

2. SA sardine operating models
Two main hypotheses:
- single stock hypothesis
- two stock hypothesis, split at Cape Agulhas
Same data and modelling framework used for both hypotheses

3. Key differences since February 2013
Hockey stick SR relationship for “west” stock
Slope (b/K) of “south” SR relationship estimated
Initial numbers at age estimated, with different Finit for “west” and “south” stocks
Survey likelihoods “robustified”
Corrected average November weights-at-age

4. Similarities with February 2013
Hockey stick SR relationship for “south” stock
Time-invariant natural mortality
No additional survey variance
Movement modelled from
Variance parameters in distributions of commercial selectivity-at-length same for “west” and “south” stocks
Growth curves differ between stocks only in L

5. Natural mortality Table 2 0.5 ≤ kj,r/kj,N ≤ 1
Best constant M combinations are Mj=1.0 or
Mj = 0.8 with Mad=0.8
Allowing M to change in 2002
- Decrease in Mj or increase in Mad (>Mj)
- Non PDH
Allowing M to differ by stock
- Little difference (best fit with Msouth,ad<Mwest,ad)

6. Stock Recruitment Tables 3, 5 and Figure 1
Hockey stick (slightly) preferred to Beverton Holt
No SR relationship estimated within the model requires one to be fit to model output for use in projections, but allows model to estimate recruitment without any “influence”
No “west” SR relationship
- Better fit to data
- More “independent” parameters
- Model selection criteria not conclusive

7. Stock Recruitment Figure 4
“West” stock more productive than “south” stock
Median maximum recruitment for “south” stock more than halved compared to Feb2013 results
- slope much higher
-but…(kr)
Variability fixed for “west” stock; estimated on lower bound for “south” stock
west,r=0.5 and south,r=0.4; alternatives will also be run

8. Model Fits to Data: Hydroacoustic surveys
Figures 2-3
Generally good
Under-prediction of “south” stock 1+ biomass in early 2000s
Smaller residual in 2001 “south” stock recruitment (this ‘mis-match’ due to high catches on south coast prior to November)

9. Bias in Hydroacoustic surveys
Table 3
75% on hydroacoustic survey (November)
- 72% for single stock hypothesis
67% on May recruitment compared to November biomass
- 54% for single stock hypothesis
100% on “south” recruitment compared to “west” recruitment
- increase from former results
Bias for May survey thus 50% for both stocks
- 39% for single stock hypothesis

10. Movement of recruits Figures 5, 15 and Table 4
>50% of recruits move in 9 out of 18 ( ) years
Greatest movement from late 1990s to early 2000s
Model assumed uninformative independent priors so as to not bias results

11. Movement of recruits Figures 5, 15 and Table 4
Possible relationship with “south” 1+ biomass
Same year likely a reflection of 1+ biomass dependent on movement
Previous year possibly a reflection of natal homing; survey indices west of Cape Infanta actually a combination of “west” and “south” stock recruits [Future work]
Possible relationship with “south:west” 1+ biomass
- greatest median proportion of recruits move when “south:west” 1+ biomass is about about 1.5
- possibly indicative of entrainment : a higher “south” 1+ biomass in previous year relative to “west” 1+ biomass may better “facilitate” the movement of recruits in the current year
- possibly indicative of improved environmental suitability of south coast
High autocorrelation

12. Model Fits to Data: Survey Proportions-at-Length
Figures 6-8
Selectivity only estimated to deviate from 1 for minus and plus length classes
Acceptable given restrictions on time-invariant selectivity-at-length

13. Model Fits to Data: Commercial Proportions-at-Length
Figures 9-11,16
Higher selectivity about lower lengths for “west” than “south” stock
Non-random patterns in residuals; acceptable given time-invariant selectivity-at-length
Improving the fit to the peak in the average about higher lengths resulted in a poorer fit to survey abundance indices
Change in selectivity over time
- improved fit to the data
- non PDH

14. Other Comments
Ninit estimated for ages 0-2 for “west” and 0 for “south”
Finit estimated separately for each stock
for “west”
- <0.001 for “south”
Growth only differ slightly in L (Figures 12,13), and AIC suggests the difference is not necessary
Harvest rate on “west” stock decreased during early part of time series, then increased late 1990s-early 2000s when population as a whole peaked and high TACs were set
Harvest rate on “south” stock increased since mid-2000s
Maximum harvest rate on total population 0.25

15. Summary 2011 “west” stock 1+ biomass 280 000t (below average)
2011 “south” stock 1+ biomass t (above average)
7 out of 8 recent years below average recruitment to “west” stock
9 out of 13 recent years above average recruitment to “south” stock (but small…)

16. Summary “West” stock more productive than “south” stock
Results now estimate smaller median “south” stock recruitment, but greater proportion covered by the May hydroacoustic survey
Movement of recruits from “west” to “south” stock have a greater impact on “south” 1+ biomass than “south” stock recruitment
- possible relationship with “south” or “south:west” 1+ biomass

17. Sardine Two-Stock Hypothesis: Results at the Posterior Mode
Possible Discussion Points
Stock recruitment relationships and associated variability
Bias associated with the hydroacoustic surveys
Proportion of recruits moving from “west” to “south” stock
Thank you for your attention