Sardine Two-Stock Hypothesis: Results at the Posterior Mode

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 1994-2011 • 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 (1994-2011) 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 - 0.50 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 870 000t (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