Testing spatial heterogeneity with stock assessment models

This paper describes a methodology that combines meta-population theory and stock assessment models to gain insights about spatial heterogeneity of the meta-population in an operational time frame. The methodology was tested with stochastic simulations for different degrees of connectivity between sub-populations and applied to two case studies, North Sea cod (Gadus morua) and Northeast Atlantic sardine (Sardina pilchardus). Considering that the biological components of a population can be partitioned into discrete spatial units, we extended this idea into a property of additivity of sub-population abundances. If the additivity results hold true for putative sub-populations, then assessment results based on sub-populations will provide information to develop and monitor the implementation of finer scale/local management. The simulation study confirmed that when sub-populations are independent and not too heterogeneous with regards to productivity, the sum of stock assessment model estimates of sub-populations’ SSB is similar to the SSB estimates of the meta-population. It also showed that a strong diffusion process can be detected and that the stronger the connection between SSB and recruitment, the better the diffusion process will be detected. On the other hand it showed that weak to moderate diffusion processes are not easy to identify and large differences between sub-populations productivities may be confounded with weak diffusion processes. The application to North Sea cod and Atlantic sardine exemplified how much insight can be gained. In both cases the results obtained were sufficiently robust to support the regional analysis.


Introduction
This document shows the results from assessments made to dierent spatial aggregations of the North Sea cod stock data: all data combined as in the current stock assessment, data split according to a four sub-stock scenario and data split according to a three sub-stock scenario.
For each stock denition a comparison was also made between two dierent assessment approaches; a seperable model for shing mortality and a time/age variant model (tensor).
The initial putative sub-populations were taken from a synthesis of results from genetic, tagging, modelling of early life stages and knowledge of spawning areas presented to the ICES benchmark assessment of North Sea cod (ICES, 2015a). The areas identied were as shown in Figure 1 of the main text: "skagerrak" & viking: ICES sub-division IIIa and the North East part of ICES sub-division IVa "northwest": The remainder of ICES sub-division IVa (including waters around the Orkney and Shetland islands) and that part of ICES sub-division IVb north of a line running roughly north east from the east English coast at 55N to 57N 4E. "south": An area covering ICES sub-divisions VIId, and IVc and a part of ICES sub-division IVb dened by and then east to the Danish coast.
Input data for area-based analyses of stock dynamics and shing pressure were compiled by sub-areas for the years 2003-2013. Landings in weight by sub-areas were obtained from the EU STECF Fisheriesdependent information database, which includes landing information for EU countries by rectangle. For the UK and Denmark, the STECF estimates were supplemented by landings information from national sources. Norwegian landings, taken from ICES (2015b), were all allocated to the Viking sub-area. For the Skagerrak area, it was possible to supply landings back to 1987, available from national sources and ICES (2015b). The age distribution of landings by sub-areas was available from England & Wales and Denmark. If no area specic information was available the age distribution within the areas was taken to be equal to the overall North Sea wide age structure of landings and mean weights-at-age obtained from ICES (2015b). This was the case for the northwest area. For the skagerrak and viking areas Danish age compositions and mean weights at age were allocated to the total international landings; Denmark takes approzimately 70% and 23% of the landings for these areas. In the south area, age composition data were available from Denmark and England & Wales, that together take an average of 44% of the total landings in this area. An average age composition and mean weights-at-age from the two countries was allocated to the remaining landings to compute numbers-at-age.
For the Skagerrak area, discard numbers-at-age from monitoring programs were available from Denmark for the years 2000-2013. An average discard percentage in relation to landings for 2000-2005, was applied to derive discard estimates for 1987-1999. No discards assumptions were made for other countries. Only Danish discards were added to the international landings to derive catch-at-age. For the viking area, discard numbers-at-age from monitoring programs were available from Denmark for the years 2003-2013. The ratio between Danish discard and Danish landing numbers-at-age by year were applied to the total international landings to derive estimates of total discards in the area. For the northwest area discardsat-age were not available. The ratio between total North Sea wide landing and discard numbers-at-age from ICES (2015b) by year were applied to landings-at-age in the Northwestern area to derive discards. For the south area, discards-at-age estimates from monitoring programs were available for England & Wales and for Denmark for 2003-2013. The ratio between combined landings and discards-at-age from these countries by year was used to derive discard estimates for the rest of the countries shing cod in the area.
Survey cpue data was obtained from the International Bottom Trawl Survey (IBTS) Q1 and Q3 data available from the DATRAS website. A Delta-GAM model approach for tting numbers-at-age from DATRAS haul-by-haul exchange data was applied (Berg et.al, 2013). The indices are obtained by adding ltered model predictions over aspatial grid. The model is able to account for changes in gear, spatial coverage, and ship as well as steep depth gradients and country eects. The methodology is as used in ICES (2015b) but applied to each area seperately.
Mean weights-at-age in the stock for each area were estimated from the IBTS Q1 data. Natural mortality and maturity-at-age were kept as used by ICES (2015b).
Following the ideas of Cadrin and Secor (2009) it was considered that additivity of population abundances, such that N i = m j=1 N ij , where N is population abundance, i indexes ages and j indexes sub-populations could be used as a test on whether the assumption of largely closed sub-populations could be applied to these areas.
Using the tensor modelling approach the sum of the SSBs from assessments on the four sub-populations and the SSB obtained by tting to data over the whole area were comparable ( Fig. 19) but using the seperable model the sum of SSBs from the four sub-populations were approximately three times the SSB values obtained for the single whole area stock assessment. This lack of consistency between the four sub-population results and whole stock result and the lack of consistency between the separable modelling approach and tensor modelling approach implied the four (closed) sub-population assumption was awed.
While genetic analysis indicates a weak but temporally stable genetic dierence between north east North Sea and Skagerrak cod, tagging studies and the observed distribution of juveniles suggest that many juvenile cod that grow up in coastal Skagerrak waters migrate back towards the North Sea when reaching maturity. This is believed to be evidence of natal delity acting upon sh that were advected as eggs from North Sea spawning grounds (Andre et.al, 2016).
It was therefore decided that when it came to tting stock assessment models it was necessary to merge the Skagerrak and Viking areas. When the resulting three areas were tted the sum of SSBs form the individual areas were comparable to the SSB obtained tting to data over the whole area from both the tensor and separable models. The evidence for sub-populations from the literature does not contain any evidence for strong migrations of any age classes between the remaining three putative areas. This, combined with the consistent SSB results, lead the study to conclude the three sub-population scenario was the best to adopt given current scientic evidence.