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

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

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 F init for west and south stocks Survey likelihoods robustified Corrected average November weights-at-age

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

Natural mortality Table k j,r /k j,N 1 Best constant M combinations are M j =1.0 or M j = 0.8 with M ad =0.8 Allowing M to change in Decrease in M j or increase in M ad (>M j ) - Non PDH Allowing M to differ by stock - Little difference (best fit with M south,ad <M west,ad )

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

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…(k r ) 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

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)

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

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

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 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

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

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

Other Comments N init estimated for ages 0-2 for west and 0 for south F init 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

Summary 2011 west stock 1+ biomass t (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…)

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

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