12_Appendix_2.Rmd

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#Appendix B. Fishery-Dependent Indices withdrawn from the Northern Model{-}
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**Commercial Logbook CPUE**   
The commercial logbook (fish-ticket) data in PacFIN was used to generate an index for the Northern model for the years 1987-1998, a period in which management of the fishery was stable, i.e., regulations weren't changing fishery practices.  

The data were first filtered using a modified Stephens-MacCall approach [@Stephens2004].  This approach uses the species composition (presence-absence) of the catch in a binomial generalized linear model (glm) to evaluate the per-haul probability of encountering a particular species; in this case, Yellowtail Rockfish.  The intent of the analysis is to eliminate all hauls with a very low probability of encountering Yellowtail Rockfish. 

For this analysis, the species effects were combined with fishery variables in a mixed-effects glm (a glmm). The species were modeled as binomial, and random effects were added for haul duration, depth, port, state agency, and month, and the interaction of year and vessel.  This approach reduced the number of hauls to be evaluated by 61%.

The hauls identified with a reasonable probability of encountering Yellowtail were then modeled in a delta-lognormal glm [@Stefansson1996] to produce an annual index of abundance, which was bootstrapped 500 times to evaluate uncertainty.  See Figures \ref{fig:Logbook_lognormal} and \ref{fig:Logbook_gamma} for Q-Q plots demonstrating that the lognormal glm fit the data better than the gamma.

**MRFSS Index**
MRFSS data was used to generate an index of abundance for 1980-2003.  The MRFSS data were aggregated as "trips" by staff at the SWFSC, and the Stephens-MacCall approach was used to filter the data to the set of fishing trips likely to have encountered yellowtail.  This was followed by application of a delta-lognormal glm using variables month and AREA_X (indicating offshore/onshore fishing) to generate the index, which was then jackknifed to produce estimates of uncertainty.  Q-Q plots for the MRFSS index are \ref{fig:MRFSSlognormal} and \ref{fig:MRFSSgamma}.

**Hake Bycatch Index**

The Hake bycatch data provided by the Alaska Fisheries Science Center (AFSC) was used to generate an index of abundance for 1985-1999.

Data on haul-by-haul catch of Yellowtail Rockfish and Pacific Hake for the period 1976-2016 were obtained from the At-Sea Hake Observer Program along associated information including the location of each tow and the duration. Previous Yellowtail assessments used an index of abundance for the years 1978-1999. The most recent assessment (Wallace and Lai, 2005) stated that the index was not updated to include years beyond 1999 “because subsequent changes in fishery regulations and behavior have altered the statistical properties of these abundance indices”.  The ending year of 1999 was retained for this analysis. However, the years up to 1984 have relatively few tows with adequate information for CPUE analysis, and fishing effort off the coast of Washington where Yellowtail are most commonly encountered (Figure \ref{fig:ASHOP_X1}). Therefore, for this new analysis, 1985 was chosen as the starting year.

The hake fishery was evolving during the chosen 15 year period (1985-1999), which included a transition from foreign to domestic fleets fishing for Pacific Hake (Figure \ref{fig:ASHOP_X2}). The index from the at-sea hake fishery used in previous assessments standardized for changes in catchability by using a ratio estimator relating Yellowtail catch to hake catch and then scaling by an estimate of fishing effort for hake (Equation 1 in Wallace and Lai, 2005). However, that approach does not take into account differences in the spatial distribution of the at-sea hake fishery relative to the distributions of hake and yellowtail.
 
For this new analysis, changes in catchability were estimated by comparing an index based on a geostatistical analysis of the hake CPUE from VAST [@Thorson2017] to the estimated available hake biomass from the most recent stock assessment (Berger et al. 2017). The relative catchability was then used to adjust an independent geostatistical index of Yellowtail CPUE (Figure \ref{fig:ASHOP_X3}). In order to capture the general trend in catchability, reducing the variability among years, linear, exponential, and locally smoothed (LOWESS) models were fit to the time series of individual estimates of hake index to available biomass (lower panel in Figure \ref{fig:ASHOP_X3}). Of these, the LOWESS model best captured the pattern of fastest change in the middle of the time series. The average rate of increase in the resulting estimated catchability time series is 13% per year.
 
VAST was then used to conduct a geostatistical standardization of the CPUE of Yellowtail caught as bycatch in the at-sea hake fishery. The resulting Yellowtail index after adjustment by the estimated changes in catchability is qualitatively more similar to the index used in previous assessments (Figure \ref{fig:ASHOP_X4}) than the index resulting from assuming constant catchability.