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

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 Finit 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 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

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)

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…(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

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 (1994-2011) 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 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

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 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

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…)

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