Use of multiple selectivity patterns as a proxy for spatial structure Felipe Hurtado-Ferro 1, André E. Punt 1 & Kevin T. Hill 2 1 University of Washington, School of Aquatic and Fishery Sciences 2 NOAA, National Marine Fisheries Service

Outline What is the ‘fleets-as-areas’ concept A case study: Effect of spatial structure on Pacific sardine assessment Description of the problem Deeper look at selectivity estimates Some conclusions Which spatial factors have the largest effect Sardines have stage- dependent seasonal migrations Assessment assumes a single mixed stock with different selectivity in different areas PNW CA Ensenada

Spatial structure of stocks matters, but it can be difficult to deal with

One possible way out: Represent the areas using selectivity curves Assume that the stock is homogeneously distributed (i.e. fully mixed) Define fleets geographically Assign a different selectivity curve to each fleet

How well does the fleet-as-areas approach perform when applied to a spatially- heterogeneous stock? ? ?

A case study: Pacific sardine

Some issues suggest that the fully-mixed stock assumption may be violated Source: Lo et al., 2010 Large animals migrate north during summer and return during winter Commercial catches Fishery independent surveys PFMC, 2007

Some issues suggest that the fully-mixed stock assumption may be violated Demer et al. 2012

A few questions arise - What is the effect on the performance of Stock Synthesis 3 (SS3) of: occasional persistence in the PNW movement between CA and PNW Presence of southern subpopulation - Can the fleets-as-areas approach deal with these issues?

The analysis is based on a stock assessment evaluation framework Movement hypotheses Assessment data Spatially-structured operating model Data set 1Data set 2Data set n Assessment results Performance measures … Assessment model

The operating model is spatially explicit, with different fleets and movement. Spatially explicit modelSeasonal movement Weekly time steps Two types of movement: Advection and diffusion

How do you define ‘fleets’? Fishery composed by six “fleets” with different selectivities SCA and CCA are also divided by season. That is, catches in the first semester are assumed to be taken by a different ‘fleet’ than those in the second semester.

How do you define ‘fleets’? Fishery composed by six “fleets” with different selectivities However, in the OM, SCA and CCA selectivity curves were averaged to avoid confounding effects

Survey coverage Hill et al My model (that is, 2010)Stock assessment (2011) DEPM Aerial TEP

Sampling of age- and length-comps was designed to generate overdispersed samples c=1c=2c=3i=3 l=L max a=A c m=2 … i=3…… m=1 w=2i=1 l=2 a=2 w=1 i=2 l=1a=1 For a given fleet, pick which months (m) have non-zero catches In m, pick which weeks (w) and areas (c) have non-zero catches (i) From each i, sample n fish from the catches according to length comp Age comp samples (b) are conditioned on length Note this step can be catch- weighted or uniform

Scenarios on four non-exclusive processes were explored Movement (M) No migration (Ma) ‘Constant’ seasonal migrations (Mb) Migration is a function of SST (Mc) Southern subpop. influx (S) No influx (Sa) Periodic influx (Sb) Persistence in the PNW (P) No recruitment in the PNW (Pa) Uniform recruitment along the entire west coast (Pb) Data availability (L) Full length- and age- composition data (La) Data availability equal to that of the assessment (Lb)

Results with only diffusion show negative bias not related to spatial factors Large sample size Uniform sampling Actual sample size Uniform sampling Actual sample size Weighed sampling Scenarios MaSaPa

Migration, recruitment and sampling affect estimates of SSB in the last year (2010) Ma – Only diffusion Mb – Seasonal migration Mc – Migration following SST Sa – No influx from the S. subpop Sb – Influx of the S. subpop in summer Pa – Uniform recruitment Pb – Recruitment only in SCA La – Large composition sample sizes Lb – Comp. sample sizes same as assessment U – Uniform sampling W – Weighed sampling

Migration, recruitment and sampling affect estimates of SSB in the last year (2010) Ma – Only diffusion Mb – Seasonal migration Mc – Migration following SST Sa – No influx from the S. subpop Sb – Influx of the S. subpop in summer Pa – Uniform recruitment Pb – Recruitment only in SCA La – Large composition sample sizes Lb – Comp. sample sizes same as assessment U – Uniform sampling W – Weighed sampling Last year of assessment Average over the last 20 years FactorDf Sum Sq / Total Sum Sq Sum Sq / Total Sum Sq Seasonal movement Southern subpopulation Persistence in the PNW Length-composition data Sampling method Residuals Last year of assessment Average over the last 20 years Seasonal movement Mb-Ma Mc-Ma Mc-Mb Southern subpopulation Sb-Sa Persistence in the PNW Pb-Pa

Uncertainty in spatial structure can be captured by multiple fleets with different selectivity As migration rate increases, selectivity curves diverge, capturing this uncertainty. Adv. = 0.25Adv. = 0.50Adv. = 0.75

Selectivity estimates also change for the Pacific Northwest and the aerial survey These are the estimates for the peak of double normal selectivity, i.e. the length at which selectivity is 1 Length

So, does the “fleets-as-areas” approach work? Selectivity captures some of the variance from the spatial structure, but not all of it. Some biases due to spatial uncertainty were not solved by allowing multiple fleets. Furthermore, having more parameters can make models unstable. A spatially-explicit model might perform better.

The spoiler slide: An actual spatial model is better than a fleet-as-areas approximation

THANK YOU Acknowledgements: The organizers of this Workshop, Nancy Lo, Roberto Felix-Urraga, Richard Parrish Washington