3_Assessment.Rmd

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#Assessment

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##History Of Modeling Approaches Used For This Stock

Yellowtail Rockfish was previously modeled as an age-structured, 3-area stock north of  $40^\circ 10^\prime$  in 1999 [@Tagart2000] using a model written in ADMB [@Fournier2012]; an update of this assessment was last conducted in 2004 [@Wallace2005].  That assessment divided the stock into 3 INPFC areas based on the suggestion that there might be biological differences in the stock, however recent genetic studies don't support that [@Hess2011].  The INPFC area boundaries are not coincident with state boundaries; this is a concern in that recent reconstructions of historical catch are state-by-state along the West Coast.  Because we cannot produce data that conform to the areas previously assessed, we have made no effort to reproduce the previous model.

A data-moderate approach was used to evaluate stock status in 2013 [@Cope2013].  The data-moderate model used only indices of abundance and made simplifying assumptions about selectivity and growth since no length or age data were included in the model.  This approach is also  incompatible with the current model, and we have made no attempt to reproduce it, either. The same data-moderate was initially applied to the Southern model as well but due to a shortage of time during the review process, that model was never reviewed or put forward for management.

A data-poor assessment method, Depletion-Based Stock Reduction Analysis [@Dick2011] was applied to the Southern stock in 2011 [@Dick2010]. This method doesn't estimate biomass but provided the estimate of the OFL contribution for the southern stock to the complex in which it is managed.

###Previous Assessment Recommendations

The STAR Panel report for the 2005 Yellowtail Rockfish update assessment (for the area North of $40^\circ 10^\prime$ included three recommendations for future assessments:

1. \emph{Figure out the root cause of the low average weight at age in South Vancouver in 2002 and 2003. The actual cause of this problem is unclear, but may involve instability in fitting von Bertalanffy parameters, sampling, ageing, or penalties in the model.} The Northern model is no longer divided into sub-stocks and no longer uses empirical weights because weight at age is modeled using an internally estimated growth curve. The length compositions for 2002 and 2003 do not show anomolously small fish.

2. \emph{The major hindrance to Yellowtail stock assessments is lack of a credible abundance index. A major effort should be made to develop a credible abundance index for Yellowtail Rockfish. This may need to involve new survey technology.} The abundance indices used in both the Northern and Southern models in this assessment are all newly analyzed using updated statistical approaches, but there is no fishery independent survey that samples fish in the mid-water. In 2005, the NWFSC shelf-slope bottom trawl survey had only been in place for 2 years whereas it now represents a 14-year timeseries for the Northern stock. However, there remains the challenge of using bottom trawl gear to sample a rockfish often associated with mid-water or untrawable bottom habitat.

3. \emph{Considering that the last full assessment of Yellowtail was conducted in 2000, and the stock assessment model software currently in use is no longer being updated or maintained, a full assessment of Yellowtail should be considered in the next assessment cycle.} This is a full assessment conducting using the actively maintained Stock Synthesis software.


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##Model Description


###Transition To The Current Stock Assessment
These are the main changes from the previous model, and our rationale for them:

1. Transition to Stock Synthesis. \emph{Rationale}: The Pacific Fishery Management Council's preferred modeling platform for stock assessments is Stock Synthesis [@Methot2015], developed since the last full assessment of Yellowtail Rockfish.

2. Addition of Southern model. \emph{Rationale}: Hess, et al. determined that the West Coast Yellowtail stocks show a genetic cline occurring near Cape Mendocino, which is roughly  $40^\circ 10^\prime$ north latitude [@Hess2011].  This divides the stock into two genetically distinct substocks which we model independently.

3. Availability of recent data. \emph{Rationale}: Ten years of data collection have occurred since the last update assessment, and the data necessary for an assessment of the southern stock is now available.

4. Historical catch reconstructions. \emph{Rationale}:  Reconstruction of catch timeseries in California, Washington and Oregon clarify stock history as far back as 1889.

5. Collapsing the stock north of $40^\circ 10^\prime$ into one, heterogeneous stock. \emph{Rationale}: the previous full assessment of the Northern stock used three INPFC areas as proxies for sub-stocks thought to exhibit differential growth.  No attempt was made in this assessment to evaluate growth in those areas because the areas themselves have become obsolete with respect to data availability. In addition, the Hess, et al. study [@Hess2011] found that although there was notable heterogeneity in the Southern stock, there was very little in the North.  This suggests that differences in growth might be due to environmental factors that could change over time.  Evaluating growth patterns along the Northern Coast is among the recommendations for future research.


###Definition of Fleets and Areas

The Northern model comprises the area between Cape Mendocino, California, and the Canadian border.  The Southern model runs from Cape Mendocino to the Mexican border (Figure \ref{fig:assess_region_map}).

**Northern Model** 

\emph{Commercial}: The commercial fleet consists primarily of bottom and midwater trawl.  No attempt was made to analyze the fishery separately by gear, particularly since it seems that in the fishery in the 1980s and 1990s, "bottom trawl" gear was used in the midwater as well as on the bottom, and "midwater gear" was sometimes dragged across soft bottom (Craig Goode, ODFW Port Sampler, pers. comm).

The data associated with the commercial fleet includes age- and length-composition data from PacFIN and CalCOM, historical catch timeseries from CDFW, ODFW and WDFW. Observations of discards from the Pikitch research study provide lengths and discard rates; discard lengths and rates calculated from WCGOP data.  Sex was available for the comps in the retained catch, which is by-sex in the model, but was not available for the discards, so they are undifferentiated by sex.

The PacFIN logbook (fish ticket) index developed for the commercial fishery is in fish/tow.  Further information about how the data for the index was worked up is in the Abundance Indices section (\ref{abundance-indices}) above.

\emph{At-Sea Hake Fishery}: Yellowtail Rockfish are frequently caught in mid-water trawls associated with the At-Sea Hake Fishery (consisting of the Catcher-Processor and Mothership sectors). This fishery requires separate analysis than the shore-based commercial fishery because the at-sea catches are processed at sea (typically into fish meal). The catches are recorded and biological sampling takes place but the data are housed in a different database.  The At-Sea Hake fishery provides catches, length compositions by sex, and an index of abundance.

\emph{Recreational}: The recreational fleet includes data from sport fisheries off Oregon, and northern California (Eureka and Del Norte counties), from MRFSS and RecFIN.  The index of abundance for the recreational fleet is in fish per angler-hour.  Length data for this fleet are undifferentiated by sex.

\emph{Washington-Sport}:  The Washington data (WA_Sport) provides catches, lengths and ages, and was treated as a separate fleet because the WA_Sport landings are not available by weight, so they are entered in the model as numbers, and Stock Synthesis internally converts them to weight using the combination of estimated selectivity for this fleet (informed by the length compositions), estimated growth, and the weight-length relationship.  Sex was available for the biological data, however many lengthed fish were not sexed, so the lengths for this fleet are undifferentiated by sex, although the ages are.

\emph{Research}:
The Alaska Fisheries Science Center's Triennial Trawl survey, provides age- and length-compositions, and an index of abundance.  This survey was conducted every third year from 1977-2004. 

The Northwest Fisheries Science Center's NWFSCcombo survey provides age- and length-compositions, as well as an index of abundance.  

\emph{Conditional Age-at-Length}:  Only the NWFSCcombo ages were used as conditional age-at-length in the model.  All other aged fleets (Commercial, Washington\_Sport, and Triennial) are present in the model as marginal ages due to the amount of noise in the age data for those fleets.

\emph{Indices}:  The NWFSCcombo and Triennial surveys provide indices based on biomass per area-towed.  The logbook survey for the commercial fleet is in units of biomass per tow and the At-Sea Hake Bycatch index is in units of relative biomass per hour.

**Southern Model**

\emph{Commercial}: The commercial fleet consists primarily of hook and line and trawl gear.  Hook and line gear account for 78% of the landings by weight in the recent period (1978-2016).  Commercial data were sexed, although there are many unsexed lengths.  To preserve the large numbers of lengths, the length data are entered in the model as undifferentiated, however the ages are sexed and provide the sole conditional age-at-length timeseries in the Southern Model. 

\emph{Recreational}: The recreational fleet includes data from sport fishery off the California coast south of Cape Mendocino.  The recreational lengths are unsexed.  The index is in fish per angler-hour.  Further information about how the index was worked up is included below. Changes in catchability and selectivity were estimated to have occurred in 1993 associated with a gap in the sampling.

\emph{California Onboard Recreational Survey}: Research derived-data include observations from the California Onboard recreational survey.  The length-compositions from this survey are undifferentiated by sex.  The index is in fish per angler-hour. This index included a sudden drop from 1998 to 1999 associated with a large change in the average length. This change appears to be more consistent with changes in sampling or fishing behavior than abundance so changes in catchability and selectivity were estimated associated with this time period.

\emph{NWFSC Hook-and-Line Survey}:  The data from this survey are used in the model as an index of fish per angler-hour, a single year of marginal age data by sex, and sexed length compositions.

\emph{Small Fish Study}: Length comps and a single year of ages reflect a small study of juvenile fish conducted by the SWFSC.

\emph{Juvenile Pelagic Survey}:  The SWFSC conducts an annual larval fish survey, and this provides an index of abundance of age-0 fish for the Southern Model.

###Modeling Software
The STAT team used Stock Synthesis [@Methot2015], which is the Pacific Fishery Management Council's preferred modeling platform for assessments. Version 3.30.03.05 (dated May 11, 2017) was primarily used, but tests with newer versions 3.30.03.07 and 3.30.04.02 produced identical results.

###Data Weighting
Commercial and survey length composition and marginal age composition data are weighted according to the method of Ian Stewart (pers.comm):

   Sample Size = 0.138 * Nfish + Ntows if Nfish/Ntows < 44, and Ntows * 7.06 otherwise.

Age-at-Length samples are unwieghted; that is, each fish is assumed to represent an independent sample.

Recreational trips (the analogue of tows in the commercial fishery) are difficult to define in most cases.  Since much of the recreational data are from the dockside interview MRFSS program, which didn't anticipate the need to delineate samples as belonging to particular trips, we chose to use all recreational data "as-is", with the initial weights entered as number of fish.

Weighting among fleets used the Francis method [@Francis2011] which is based on the model fit to the mean length or age relative to the expected variability for a given (adjusted) input sample size. The one exception was the age data from the Southern model's Hook and Line survey, where only a single year of ages were available and the Francis method cannot be used. For this single age-composition, the sample size was tuned using the McAllister-Ianelli harmonic mean method [@McAllister1997]. As a sensitivity analysis, the McAllister-Ianelli method was applied to all fleets in each model (described below).


###Priors \label{priors}
Log-normal priors for natural mortality were developed based on the method of Hamel [-@Hamel2015] as discussed under "Natural Mortality" in Section \ref{nat-mort} with point estimates for M of 0.15 and 0.12 for females and males for the Northern model and 0.18 and 0.135 for females and males in the Southern model. In the Northern model, both female mortality (with the prior) and male mortality as an offset (without a prior) were estimated. For the southern model, M was fixed at the median prior values for the two sexes.

The prior for steepness ($h$) assumes a beta distribution with parameters based on an update of the Thorson-Dorn rockfish prior (Thorson et al. [-@Thorson2017b], commonly used in past West Coast rockfish assessments) which was reviewed and endorsed by the Scientific and Statistical Committee in 2017. The prior is a beta distribution with $\mu$=0.718 and $\sigma$=0.158.


###General Model Specifications
Fecundity is represented in the models as:  $1.1185^{-11}W^{4.59}$.  This is a rescaling of the values provided in [@Dick2017].

Model data, control, starter, and forecast files can be found at ftp://ftp.pcouncil.org/pub/GF_STAR2_2017_Ytail_Yeye/.


###Estimated And Fixed Parameters
The Northern model has a total of `r sum(!is.na(mod1$parameters$Active_Cnt) & substring(mod1$parameters$Label, 1, 8) != "ForeRecr")` estimated parameters in the following categories:

* equilibrium recruitment ($log(R_0)$) and `r sum(mod1$recruit$era %in% c("Early","Main","Late"))` recruitment deviations,
* 2 natural mortality parameters,
* 8 growth parameters,
* 1 index extra standard deviation parameter,
* `r length(grep("Sel", rownames(mod1$estimated_non_dev_parameters)))` selectivity parameters and `r length(grep("Retain", rownames(mod1$estimated_non_dev_parameters)))` retention parameters.

The Southern model has a total of `r sum(!is.na(mod2$parameters$Active_Cnt) & substring(mod2$parameters$Label, 1, 8) != "ForeRecr")` estimated parameters in the following categories:

* equilibrium recruitment($log(R_0)$) and `r sum(mod2$recruit$era %in% c("Early","Main","Late"))` recruitment deviations,
* 8 growth parameters,
* 1 index extra standard deviation parameter, and
* `r length(grep("Sel", rownames(mod2$estimated_non_dev_parameters)))` selectivity parameters.

The estimated parameters are described in greater detail below, and a full list of all estimated and fixed parameters is provided in Table \ref{tab:Model1_params} (Northern model) and Table \ref{tab:Model2_params} (Southern model).

**Growth**
Five parameters for female growth are estimated in each model: three von Bertalanffy parameters and two parameters for CV as a function of length at age  related to variability in length at age for small and large fish.

Three parameters are estimated for male growth in each model as offset from female growth.  The size for small fish and CV for small fish were assumed equal to females.

**Natural Mortality**
Natural mortality is estimated in the Northern model with an offset for males from females.  After much exploration of alternatives, natural mortality was fixed in the Southern model at the values estimated by the Northern model.

**Selectivity**
Selectivity for all fleets was initially estimated as a 4-parameter double normal, which allows selectivity to be dome shaped, with parameters controlling the position of the peak selectivity, the width of the peak, and the ascending and descending slopes. 

For all fleets where the estimated patterns were asymptotic, we fixed the parameters related to the dome, leaving only the position of the peak and the ascending slope as estimated parameters. For a few fleets, the position of the peak hit the upper bound, and was fixed at 55cm.

The two recreational fleets in the Northern model had a block on selectivity beginning in 2003 to allow a change in selectivity associated with management measures which constrained the depth range of recreational fishing.

The early and late Onboard Indices in the Southern model were treated as a single fleet with blocks on selectivity in earlier versions of the model. However, in the Final Southern Model, the Onboard survey from these two periods was split into separate fleets with independent selectivity.



**Retention**
Retention for commercial fishery in Northern model is a logistic function of size, with three parameters estimated: length at 50% retention, the slope of the curve, and the asymptotic retention fraction. The asymptote was allowed to be time-varying, with one value applied for the early years through 2001.  From 2002 through 2011 we applied annual time-blocks for theses years when the WCGOP program observed high discards.  The final block runs from 2012 forward, reflecting the current period in which the implementation of the IFQ program has led to low discard rates.

**Other Estimated Parameters**
Log(R0) is the equilibrium recruitment, which is estimated in each model.  

Recruitment deviations for the Northern model are estimated from `r min(mod1$recruit$Yr[mod1$recruit$era %in% c("Early","Main","Late")])` to 2016.  For the Southern model recruitment deviations are estimated from `r min(mod2$recruit$Yr[mod2$recruit$era %in% c("Early","Main","Late")])` to 2016. Both models also included estimated recruitment devations for the forecast years, although these have no impact on the model estimates for the current year.

A parameter representing extra standard deviation added to all years was estimated for each index that was included in the likelihood to allow the model to appropriately weight these data sources compared to other data types.

\clearpage

##Model Selection and Evaluation

###Key Assumptions and Structural Choices
Selectivity in both models is asymptotic, with the exception of the OR-CA MRFSS recreational fleet in the Northern model, and the Onboard recreational fleet in the Southern model.

For the Northern model, several options for developing a CPUE series for the recreational fishery were considered but rejected as sparse and noisy.  Similarly, the Washington\_Sport fishery data was evaluated a a possible source for an index, but the data was not available in a form useful for a recreational index, i.e., there was no data that provided for a trip-level analysis of catch and effort, as was used for the MRFSS index in the Southern model [@Stephens2004].

###Alternate Models Considered
The indices based on the Commercial Logbook CPUE and At-Sea Hake Bycatch were included during initial development of the Northern model but removed after further considerations and investigation at the STAR panel as described elsewhere.

Alternative structures for the time-blocked selectivity and retention were investigated in the Northern model, as were domed selectivities.

We also explored time-blocks on selectivity in the Southern model, and domed selectivity for the MRFSS/RecFIN data.  For early versions of the model, we allowed the model to estimate natural mortality.  There is very little discard of Yellowtail in the Onboard Survey, however it is the only information on discards in the south, so we attempted to include it in the model.

These approaches resulted in models that didn't converge, and so they were rejected.

Finally, we evaluated different assumptions pertaining to maturity ogives, modeling these parameters from the literature:

* Parameters in [@Gunderson1980]: L50% = 45.0, slope = -0.5315
* Parameters in [@Echeverria1987]:  L50% = 36.36, slope = - 0.4331

which we discovered made no significant changes in model outcomes.


###Convergence
Convergence testing through use of dispersed starting values often requires extreme values to explore new areas of the multivariate likelihood surface. Stock Synthesis provides a jitter option that generates random starting values from a normal distribution logistically transformed into each parameter's range [@Methot2015]. We used this function to find parameter values for convergence in the Southern model. 

The jitter analysis of the final Southern model post-tuning was run 100 times, and resulted in 75 models that returned to the base case.  No model resulted in a lower likelihood than the base model.

The Northern jitter analysis was run 100 times, and resulted in 88 models that returned to the base case.  No model resulted in a lower likelihood than the base model.

\clearpage

##Response To The Current STAR Panel Requests

The comprehensive explorations of the models conducted by the STAR panel are detailed in Appendix D.

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## Life History Results for both models

Maturity at length and mean weight at length are both estimated externally as described in Section \ref{bio-params} above (and shown in Figures \ref{fig:maturity} and \ref{fig:weight-length}).

The growth at the beginning of the year estimated by the models for the Northern and Southern stocks is shown in Figure \ref{fig:growth}.  Females grow faster in each case, but the Northern stock grows faster and attains larger maximum size.

## Northern Model Base Case Results

The data used in the Northern model by fishery is shown in Figure \ref{fig:data_plot.N}.  Estimated catches are shown in Figure \ref{fig:r4ss_total_catch_N}; estimated discards are in Figure \ref{fig:r4ss_discard_N}.  These show the large catches in the 1980s and 90s are being predicted by the model.  The large discards in latter years match the data well for those years.

The timeseries of estimated spawning output in trillions of eggs is shown in Figure \ref{fig:ssb.N}.  The model is estimating two periods of decline, one beginning in the forties and a steeper decline in the 1970s and 1980s, followed by an increase since 2000 to pre-1980 levels. There is a decrease in the final years of the timeseries coincident with increased uncertainty.


Figure \ref{fig:total_bio.N} shows the total biomass following a similar pattern; the ending value is `r round(mod1$timeseries$Bio_all[mod1$timeseries$Yr==2017])` metric tonnes.

The relative spawning output (Figure \ref{fig:depl.N}) went below the 40\% target in the early 1980s, and may have been below the minimum stock size limit of 25% in the late 1990s, but has rebounded since to `r round(100*mod1$derived_quants["Bratio_2017","Value"])`% (see Table \ref{tab:Timeseries_mod1}).

Figures \ref{fig:recruits1.N} and \ref{fig:recdevs1.N} address recruitments estimated the the model.  The first of these shows the age-0 recruits, and the second the recruitment deviations. There are no strong patterns in recruitment and the variability of the recruitment deviations was tuned to be 0.546 (based on the method of Methot & Taylor [-@Methot2011]) which is similar to what has been assumed or estimated for other rockfish in the California Current.  The stock-recruit curve, Figure \ref{fig:stock_recruit_curve.N} shows a shallow relationship between stock size and recruitment.}



### Selectivities, Indices and Discards

Selectivities in the Northern model (Figure \ref{fig:selex.N}) show the difference between the recreational fisheries and the commercial fishery and survey sampling.  All of the fish are fully selected by 50 cm, but the recreational fish are fully selected at 30 cm.

Retention by length (Figure \ref{fig:retention.N}) varies over time between 40\% and 100\%, with no clear pattern of interannual variation, except for the trawl-rationalization era 2011-present.

Discarding in the commercial fleet (Figure \ref{fig:r4ss_discard_fits.N}) is fit only by putting blocks on retention in the Northern model.  Discards were very low except during the 1990s and 2000s, until the trawl-rationalization program implementation.

Fits to the indices for the northern model (Figure \ref{fig:index_fits1}) demonstrate the utility of the NWFSCcombo survey. Although the model misses the uptick at the end of the timeseries, it is the only recent index and is well-fit by the model.  The other indices are noisier.  Most of the indices are fairly flat, indicating little change in abundance during each time-period.  Although the fit to the Triennial index is poor, the data nicely reflects the changes in management during it's tenure:  the CPUE was falling during the 1980s and 1990s, then rising after stringent restrictions began in 2000.

### Lengths
Bubble plots for the lengths in the fishery (Figure \ref{fig:comp_length_bubble_mod1_page1}) show the constancy of the commercial fleet, and the differences in growth between males and females; the females are larger, the males smaller.  The recreational fleet is represented by two different sampling regimes, and the changeover in the mid-2000s is clear in that panel.  

Commercial length comps are very well fit (Figures \ref{fig:mod1_1_comp_lenfit_flt1mkt2_page1} and \ref{fig:mod1_5_comp_lenfit_data_weighting_TA1.8_Commercial Fishery}).  Commercial discards are noiser and not well fit (Figure \ref{fig:mod1_6_comp_lenfit_flt1mkt1}) although the fit to the mean length (which is lower than for the retained fish), is reasonable (Figure \ref{fig:mod1_5_comp_lenfit_data_weighting_TA1.8_Commercial Fishery}). 

Lengths in the early period of the Hake Bycatch fishery are noisy (doubtless due to small sample sizes).  By 1992, the model is able to fit the data well (Figures \ref{fig:mod1_10_comp_lenfit_flt2mkt0} and \ref{fig:mod1_13_comp_lenfit_data_weighting_TA1.8_At-Sea Hake Fishery}).

The recreation OR+N.CA timeseries of lengths demonstrates the difference between the MRFSS sampling and RecFIN sampling.  The fits in the early period are good, those in the later period are noisy and model uncertainty is high (Figures \ref{fig:mod1_14_comp_lenfit_flt3mkt2} and \ref{fig:mod1_17_comp_lenfit_data_weighting_TA1.8_Recreational OR+CA}).

The WA_Sport length fits might have been improved with a better choice of maximum size bin for the model (Figures \ref{fig:mod1_18_comp_lenfit_flt4mkt2} and \ref{fig:mod1_21_comp_lenfit_data_weighting_TA1.8_Recreational WA}), however the data are noisy throughout the size range represented.

The Triennial lengths Figures \ref{fig:mod1_22_comp_lenfit_flt5mkt2} and \ref{fig:mod1_25_comp_lenfit_data_weighting_TA1.8_Triennial Survey} are fit well in some years and not in others.  The data is not noisy, however the intermittency of data collection may mean that the model is unable to capture interannual variation as well as for an annual timeseries.

NWFSCcombo lengths are not well fit, particularly in 2013, where the data show a large number of small fish that may represent a good recruitment several years earlier Figures \ref{fig:mod1_26_comp_lenfit_flt6mkt2} and  \ref{fig:mod1_29_comp_lenfit_data_weighting_TA1.8_NWFSC Combo Survey}.

Figure \ref{fig:mod1_30_comp_lenfit__aggregated_across_time} shows the relative fits among the data sources, aggregated across time.  The timeseries of presence-absence residuals indicated by filled- and open-bubbles Figure \ref{fig:comp_Pearson_length_mod1_page1} and Figure \ref{fig:comp_Pearson_length_mod1_page2} demonstrates the relative disappointment in model fits; the smaller the bubble, the better the match between the data and the model expectation.

### Ages

The NWFSCcombo survey was the only datasource used to inform growth as conditional age-at-length data for the Northern model; ages for other fleets were treated as marginal ages.  

The fits to the marginal commercial Figure \ref{fig:mod1_1_comp_agefit_flt1mkt2_page1} are quite good from about 1979 on, even fitting the tail where the ages beyond 55 are lumped.  The weightings panel Figure \ref{fig:mod1_5_comp_agefit_data_weighting_TA1.8_Commercial Fishery} shows the same thing:  fits are good after about 1979, and the decrease in mean age in the population corresponds with high catches in the 1980s and 1990s, with mean age increasing after 2000 as catches were curtailed.

The Washington Sport ages are noisy, and the fit is poor throughout the timeseries, see Figure  \ref{fig:mod1_6_comp_agefit_flt4mkt2} and Figure \ref{fig:mod1_9_comp_agefit_data_weighting_TA1.8_Recreational WA}.

The Triennial ages are noisy but are fit surprisingly well \ref{fig:mod1_10_comp_agefit_flt5mkt2}; \ref{fig:mod1_13_comp_agefit_data_weighting_TA1.8_Triennial Survey}.  That the model misses the influx of young fish in 1986 may be due to the timing of the survey; three-year surveys may not provide enough data for the model to fit recruitment events. 

Aggregated age comps for the Commercial, Washington Sport and Triennial fleets are shown in Figure  \ref{fig:mod1_14_comp_agefit__aggregated_across_time}, for comparison.  Agreggated fits for the Commercial and Triennial fleets are very satisfying.

The implied marginal age comps for the NWFSCcombo survey (Figure \ref{fig:mod1_16_comp_gstagefit_flt6mkt2}) are the conditional-age-at-length compositions for the survey aggregated over length.  This figure is included for informational purposes only; the marginal "ghost" comps are not included in the likelihood calculations. 

Pearson residuals for the marginal age comps, are shown in the bubble plots in Figure \ref{fig:comp_Pearson_age_mod1}.  The filled bubbles represent estimates greater than observations, and the open bubbles observations greater than estimates. The large filled bubbles at age 25 in a few years suggest that we might have chosen a slightly older age as the compilation age.

The residuals for the conditional age-at-length from the NWFSCcombo survey show that growth appears to be reasonably estimated with no strong patterns suggesting consistently older or younger fish than expected in any year (Figure \ref{fig:mod1_1_comp_condAALfit_residsflt6mkt2_page1}). However, the mean age aggregated across length bins shows more variability in the observations than expected by the model (Figure \ref{fig:mod1_3_comp_condAALfit_data_weighting_TA1.8_condAgeNWFSC Combo Survey}).  This may represent young fish recruiting to the fishery, which would happen approximately 5 years after a biological recruitment event.  The conditional age-at-length fits are also shown in Figure \ref{fig:mod1_3_comp_condAALfit_data_weighting_TA1.8_condAgeNWFSC Combo Survey}.  These plots explain the reason this survey was chosen to represent conditional age-at-length; the model was able to fit these data much better than other datasets, and improved fit, lower likelihood values and increased parsimony all contributed to a better model.

### Northern Model Parameters
For the Base model, the parameter estimates are given in Table \ref{tab:Model1_params}.  Status for all of the estimated parameters is good although the parameter for peak selectivity of the Triennial survey is estimated close to the 55 cm upper bound with a value of `r round(mod1$estimated_non_dev_parameters["SizeSel_P1_Triennial(5)", "Value"],2)`.

### Northern Model Uncertainty and Sensitivity Analyses
The following sensitivity analyses were conducted for the Northern model:
\begin{description}
\item[McAllister-Ianelli weights] We investigated tuning the model according to the method of McAllister and Ianelli [-@McAllister1997].
\item[M prior Age64] The literature value for maximum age is 64.  We centered the prior for female mortality at 0.0844, the value associated with that age, and estimated M for both females and males (with no prior on the offset for males).
\item[M prior Age64] The literature value for maximum age is 64.  We centered the prior for female mortality at 0.0844, the value associated with that age, and estimated M for both females and males (with no prior on the offset for males).
\item[M fixed Age64] We fixed mortality at 0.0844, the value associated with maximum age of 64, for both females and males.
\item[Add commercial index] We included the index based on commercial fishery logbook CPUE.
\item[Add hake bycatch index] We included the index based on bycatch in the at-sea hake fishery.
\item[Add commercial and hake indices] We included both the commercial CPUE and hake bycatch indices.
\end{description}

In general, the Northern model showed little change under these sensitivity analyses (Figures \ref{fig:sens.N.spawnbio} and \ref{fig:sens.N.Bratio} and Table \ref{tab:Sensitivity_model1}). The McCallister-Ianelli weighting method to the length and age composition data resulting in a higher overall scale of the population, with spawning output in 2017 at 82\% compared to 75\% for the base model. Applying the natural mortality prior centered at 0.0844 based on the maximum age of 64 reported in the literature instead of the base model prior centered at 0.15 had little impact on the estimated female natural mortality, reducing it from $M=0.174$ to $M=0.173$. However, fixing female and male natural mortality at 0.0844 had the largest impact of any of the sensitivity analyses explored for the Northern model. The likelihood profile over female natural (described below) indicated that there was information in the length and age data that strongly supported higher natural mortality than the value based on maximum age of 64. Furthermore, among the collection of over 138,000 ages available from the Commercial fishery, only 7 (0.005\% of the total) were older than 55 (including one listed as 110), suggesting that some of these outliers could have been data entry errors and applying a quantile to the distribution of ages to get an approximate maximum age for development of the prior is a more reliable method than taking the maximum of all observations. Adding either the index based on commercial logbook CPUE or bycatch in the at-Sea hake fishery, decreased the scale of the population a similar small amount and the combination of adding both of these indices resulted in a larger decrease (from 75\% of unfished spawning output in 2017 down to 63\%, Figure \ref{fig:sens.N.Bratio} and Table \ref{tab:Sensitivity_model1}).

### Northern Model Likelihood Profiles
We profiled the change in negative log likelihood for the data sources and model total likelihood for critical parameters in the model:  **$log(R_0)$**, the log of equilibrium recruitment; female natural mortality, **MF**; male natural mortality, **MM**; and steepness, **h**, the parameter that reflects how quickly the stock-recruit relationship allows the stock to rebound from depleted stock size.

The likelihood profile over a range of values (from 9 to 11) $log(R_0)$ are shown in Figure \ref{fig:profile_logR0.N}.  This plot shows the tension between the index data and the other data sources.  The indices are better fit with a smaller value of $log(R_0)$, near 9.6, while all other data sources are better fit at larger values.  The overall likelihood in the model is lowest at the estimated MLE value of `r round(mod1$parameters["SR_LN(R0)","Value"],1)`.  The likelihood contribution of the discard fractions is small over this range of $log(R_0)$, while the recruitments, ages and lengths are all best fit at values larger than 10.5.

The likelihood profile over female natural mortality, MF, is over a range from 0.10 to 0.24 (Figure \ref{fig:profile_M.N}).  In this figure, the indices are fit best when MF is 0.1, the ages and lengths are fit nearer 0.18, and the recruitments and total log likelihoods are minimized at 0.15.


Figure \ref{fig:profile_M2.N} shows the likelihood profile for male natural mortality, MM, over a range of negative values that are the offset from female mortality (FM).  Male natural mortality is represented as an offset from that for females based on the equation ${MM} = {MF}*e^{offset}$, such that an offset of 0 results in equal mortality for males and females, and an offset of -0.3 results in a male natural mortality which is about 74% of the female mortality ($exp(-0.3) = 0.7408$). The index data are at odds with the other data sources but would not be expected to be informative about natural mortality and show relatively little changes over the range of values considered. Both the age and length data support male mortality lower than female mortality (an offset less than 0).


The profile over values of steepness, $h$, from 0.5 to 0.9, Figure \ref{fig:profile_h.N}, shows the index data for once in the majority as all data sources except the lengths support 0.9 as minimizing the likelihood, while the lengths support a value closer to 0.5.  The scale of this plot differs from the others showing that the that the choice of h within this range has far less impact on likelihood in the model than choices for the other profiled parameters.  This suggests the stock is not depleted; the choice of steepness would have a much greater impact on a depleted stock. The MLE occurring at the maximum $h$ value also supports the choice to fix the steepness at the mean of the prior $h=0.718$.

### Northern Model Retrospective Analysis
The Northern model shows little influence of removing up to 5 years of data (Figure \ref{fig:retro.N}). Examination of the contributions of each index to the likelihood profile over $log(R_0)$ indicated that the NWFSCcombo survey, which is the only index available within the most recent data, had the least influence on the scale of the model, so shortening this time series wouldn't be expected to have a large contribution on the population estimates.


### Northern Model Reference Points


The estimated relative depletion level for the Northern model in 2017 is 
`r Depl_mod1` (~95% asymptotic interval: $\pm$ `r Depl_mod1_CI`, corresponding 
to an unfished spawning output of `r paste(round(Spawn_mod1,1), fecund_unit,sep=' ')` 
(~95% asymptotic interval: `r paste(Spawn_mod1_CI, fecund_unit, sep=' ')`) of 
spawning output in the base model (Table \ref{tab:Ref_pts_mod1}).  Unfished 
age `r min_age` biomass was estimated to be `r Ref_pts_mod1[2,2]` mt in the 
base case model. The target spawning output based on the biomass target 
($SB_{40\%}$) is `r paste(Ref_pts_mod1[7,2], fecund_unit,sep=' ')`, which gives 
a catch of `r Ref_pts_mod1[10,2]` mt. Equilibrium yield at the proxy $F_{MSY}$ 
harvest rate corresponding to $SPR_{50\%}$ is `r Ref_pts_mod1[15,2]` mt.

\clearpage

<!-- *************************MODEL 2 RESULTS****************************** -->

## Final Southern Model Results

The results offered here are for a version of the Southern model that was thought to be the most robust among sensitivites, and is not a "Base Case", as the model was deemed too uncertain for management.  The model was unable to estimate natural mortality (M), and was very sensitive to a range of alternates evaluated, responding to plausible values with large shifts in the scale of the population.  We investigated using the NWFSCcombo Survey as an index, however Yellowtail Rockfish do not occur in the survey trawls in large numbers in the south as they do in the north, therefore the Hook and Line Survey was the sole fishery-independent index available to inform the model.

Data used in the Southern model is shown in Figure \ref{fig:data_plot.S}. 

Estimated catches are shown in Figure \ref{fig:r4ss_catch2_S}.

The estimated spawning biomass in Figure \ref{fig:ssb.S} shows the size of the uncertainty in this model. Total biomass (Figure \ref{fig:total_bio.S}) shows a sharp upward trend in recent years, the decade in which there is only one year of age data, 2004, from the Hook-and-Line Survey.  Spawning depletion has likely never been below the 40% management target (Figure \ref{fig:depl.S}), since almost all variations of the model explored show a healthy stock well above that level.

Recruitments have been constant, except 2008 and 2010, when the model sees extra large recruitments with extra large recruitment deviations (Figures \ref{fig:recruits1.S} and \ref{fig:recdevs1.S}).  The spawner-recruit curve, Figure \ref{fig:stock_recruit_curve.S} shows a shallow relationship between stock size and recruitment, much like that in the Northern model.

### Final Southern Model Selectivities, Indices and Discards

Selectivity by fleet is shown in Figure \ref{fig:selex.S}.  Selectivities for all but the recreational Onboard fishery are modeled as asymptotic; both recreational fleets (MRFSS/RecFIN and Onboard) are fully selected at 30cm; the remaining fleets show full selectivity at 45cm, except for the Commercial fishery, which isn't fully selected until the maximum size, 55cm.

Index fits are shown in \ref{fig:index_fits2}.  The estimated change in catchability in 1993 for the MRFSS index is small and both the observed and expected index values show little trend.  The Onboard survey fits to the two periods are flat in each period with a large change in catchability estimated between the two periods.  The Hook-and-Line survey fit does not seem to capture trends in time.  However, the model fits the data from the Juvenile Pelagic remarkably well, capturing the downward trend at the end of the period, which the other fits for the current period do not.  During model tuning, we tried introducing a time-blocked index for the two periods of the MRFSS and the two periods of the Onboard survey, however it didn't improve the fit to the index until we also introduced the Northern model's estimates of natural mortality.  These two changes had to be made in concert, since either in isolation destabilized the model further.

There was little information to inform this model of discard behavior, except in the Onboard survey, where it was represented by extremely small numbers.  We included these discards in the retained fishery, since attempts to include it as a type-1 "retained plus discards" fishery prevented the model from converging.

### Final Southern Model Lengths
Lengths in the Southern model were entered as unsexed, except for the Hook-and-Line fishery.  There were sexes for the Commercial lengths, however there were also large numbers of unsexed lengths, and we chose to model the lengths as unsexed, to include as much of the data as possible.  This was true of the Small-Fish study, as well.

Bubble plots of the lengths by year in each fishery are in Figure \ref{fig:comp_length_bubble_mod2}.  The plot for the recreational fishery clearly shows the transition from the MRFSS sampling program to RecFIN in 2003/2004, as well as suggesting the existence of larger fish in the 1980s.  The Commercial fishery data has been sparse in recent years; however the fish taken in the Commercial catch are consistently larger than those in the recreational fishery, no doubt reflecting trawling in deeper waters.  The Onboard survey lengths reflect two eras of sampling, again with larger fish in the earlier period.  The panel for the Hook-and-Line survey shows that the females landed are always larger than the males, in agreement with the model estimates of growth: Figure \ref{fig:growth}.

The fits to the lengths in the Recreational fishery Figure \ref{fig:mod2_1_comp_lenfit_flt1mkt2} show variable fits through the years, with the noisy and sparse data in 2004 heralding the transition between MRFSS sampling and RecFIN.  Overall, the timeseries of mean lengths is fit fairly well (Figure \ref{fig:mod2_4_comp_lenfit_data_weighting_TA1.8_Recreational Fishery}).

The Commercial length comps are fit well through 2005, when data becomes sparse and noisy Figure \ref{fig:mod2_5_comp_lenfit_flt2mkt2}; and Figure \ref{fig:mod2_8_comp_lenfit_data_weighting_TA1.8_Commercial Fishery}.

Fits for the Onboard Survey lengths are reasonable for both the early and late periods (Figures \ref{fig:mod2_9_comp_lenfit_flt3mkt2} - \ref{fig:mod2_16_comp_lenfit_data_weighting_TA1.8_Rec. Onboard Survey Late}.  Previous attempts to apply a time-block to this data resulted in poor convergence, but splitting the onboard index into separate fleets (along with revising the indices) during the STAR panel resulted in better fits and model performance.

The Hook-and-Line Survey lengths are noisy (Figure \ref{fig:mod2_17_comp_lenfit_flt5mkt0}), but the fits are acceptable, and follow the trend of the data better than those for the other datasets:  Figure \ref{fig:mod2_20_comp_lenfit_data_weighting_TA1.8_Hook & Line Survey}.

The Small Fish Study lengths are not fit badly (Figures \ref{fig:mod2_21_comp_lenfit_flt7mkt2} and \ref{fig:mod2_24_comp_lenfit_data_weighting_TA1.8_Small Fish Study}), and it is perhaps a shame that there are so few years to this timeseries.

The aggregate fits to the length comps for all five datasets is shown in Figure \ref{fig:mod2_25_comp_lenfit__aggregated_across_time}, and Pearson residuals for the lengths in Figure \ref{fig:comp_Pearson_length_mod2}.  Filled bubbles represent under-estimation of the data, open bubbles represent overestimation.


### Final Southern Model Ages
There are few marginal ages in the model.  Bubble plots for the Southern model ages (Figure \ref{fig:comp_age_bubble_mod2}) show the small sample from the Small Fish Study and the single year of ages from the Hook-and-Line Survey.  The samples are too small to show any inter-annual variation, and are noisy within-year.

Figure \ref{fig:mod2_5_comp_agefit_flt7mkt2} shows the fit to the Recreational Fishery samples, which is poor in all four years.  The mean age in this data is shown in Figure \ref{fig:mod2_8_comp_agefit_data_weighting_TA1.8_Small Fish Study}, at 10 years.

The Hook-and-Line Survey age fit is shown in Figure \ref{fig:mod2_1_comp_agefit_flt5mkt0}.  The Francis tuning method could not be applied in this case as it depends on the fit to multiple years of data.

The aggregated fits for the marginal ages are shown in Figure \ref{fig:mod2_9_comp_agefit__aggregated_across_time}.

The implied marginal age distribution from the commercial conditional-age-at-length compositions is shown in Figure \ref{fig:mod2_11_comp_gstagefit_flt2mkt2}.  This figure is included for informational purposes only; as it does not contribute to the model likelihood calculations.  The fits here are quite good 1981-1999, however the last three years of data are very sparse and not well fit.

Pearson residuals for the Small Fish Study and the Hook-and-Line Survey are shown in Figure \ref{fig:comp_Pearson_age_mod2}.  Bubble size indicates the amount of disappointment in the fits.  The filled bubbles indicate underestimates by the model; the open bubbles indicate overestimates.

The good news age-data comes from the commercial fleet, as was foreshadowed by the implied marginal ages.  Figure \ref{fig:mod2_4_comp_condAALfit_data_weighting_TA1.8_condAgeCommercial Fishery} shows the interannual fits to the mean age in the commercial age-at-length data.  Except for 1981, 1982 and 1989, the model is able to fit the data reasonably well, detecting the downward trend in the late 1980s and into the mid-1990s.

The annual plots of age-at-length fits (Figure \ref{fig:mod2_5_comp_condAALfit_Andre_plotsflt2mkt2_page1}) show good fits in all years except 2001-2002.

### Final Southern Model Parameters

For the Final Southern model, the parameter estimates are given in Table \ref{tab:Model2_params}. Status for all of the 161
estimated parameters is good.

### Southern Model Uncertainty and Sensitivity Analyses

The Southern model was investigated in these 16 analyses:

* **Drop Biological Datasets** The data from each source in turn was dropped from the model.
* **Drop Indices** Each index in turn was dropped from the model.
* **Changes to M** Two sensitivities to M were run:  we let the model estimate M and we fixed M at a value that Hamel [-@Hamel2015] estimated for a maximum age of 64, the value reported in [@Love2011].
* **add NWFSCcombo** Samples South of Cape Mendocino in the NWFSCcombo shelf-slope bottom trawl survey were too sparse to create an index, but as a sensitivity, the VAST analysis that produced the index for the Northern model was re-run at a coastwide scale with the output stratified at Cape Mendocino. The estimates for the Southern area were input to the Southern model as an additional fleet with catchability and selectivity assumed equal to the estimated values from the Northern model.
* **Tuning**  We investigated tuning the model according to the method of McAllister and Ianelli[-@McAllister1997].  

The Southern model is very reactive to many of these sensitivity analyses (Tables \ref{tab:Sensitivity_model2A} and \ref{tab:Sensitivity_model2B}), and not so much to others. Removing different subsets of the biological data (Figures \ref{fig:sens_S_bio1} and \ref{fig:sens_S_bio2}) had a large impact only in a few cases: removing all ages or removing all lengths resulted in large changes as expected. Commercial Fishery biological data and removing the Recreational (MRFSS) biological data also had large changes, which.  In Figures \ref{fig:sens_S_indices1} and \ref{fig:sens_S_indices2} we can see that the model is not very sensitive to removal of the indices.  The remaining fleets (all of which had shorter time-series of biological data) had much smaller impacts.

Removing all indices of abundance has relatively little impact on the model results, with removal of the Hook and Line index causing the largest impact (though still small). However, removing the Juvenile Index (or all indices, including this one) resulted in large changes to the estimates of recruitment in the most recent years \ref{fig:sens_S_indices3}. This is likely caused by recent recruitment getting information from the Juvenile Survey which is assumed to index only age-0 fish.

The impact of the remaining sensitivies on estimates of spawning output are shown in Figures \ref{fig:sens_S_Other1} and \ref{fig:sens_S_Other2}. 

Adding an index from the NWFSCcombo Survey with catchability fixed at the value estimated in the Northern model resulted in a low biomass at the end of the time series, and in order to sustain the observed history of removals, the model estimated very high recruitment causing an implausible increase in biomass prior to the period of peak removals in the 1980s. 

Estimating M resulted in estimates of $M = 0.21$ for females and $M = 0.23$ for males, along with a much highest stock size. Fixing mortality at the low $M = 0.08$ (the value associated with a maximum age of 64) resulted in a much lower estimate of the scale of the model. Tuning based on the McAllister-Ianelli method had very little impact.


### Final Southern Model Likelihood Profiles

The Southern model likelihood profiles shown here are those for one of the many sensitivities, and may be slightly different than those that would be the result of profiles on the "final" Southern model.  These likelihood profiles show the general pattern of likelihood profiles for the Southern model, which was not found to be sufficient for management purposes.

We profiled the change in negative log likelihood for the data sources and model total likelihood for critical parameters fixed in the model:  **$log(R_0)$**, the log of equilibrium recruitment; female natural mortality, **MF**; male natural mortality, **MM**; and steepness, **h** the parameter that reflects how quickly the stock-recruit relationship allows the stock to rebound from depleted stock size.

The likelihood profile for **$log(R_0)$** is shown in Figure \ref{fig:profile_logR0.S}.  The parameter $log(R_0)$ was profiled over values from 8.6-11.0.  The figure shows that best fit to the age and length data all occur in the range of 9.0 to 9.6 but the indices are best fit at the upper end of the range: 11.0.  The overall negative-log-likelihood is minimized at `r round(mod2$parameters["SR_LN(R0)","Value"],1)`.

The female natural mortality (FM) profile, \ref{fig:profile_M.S} ranges from 0.1 to 0.24.  This shows that the indices and length data show the greatest change in likelihood associated with changing M and all support a higher value (consistent with the sensitivitiy analysis where mortality was estimated).

Male natural mortality (MM) is profiled over a range from -0.4 to 0.  Male natural mortality is represented as an offset from that for females based on the equation ${MM} = {MF}*e^{offset}$, such that an offset of 0 results in equal mortality for males and females, and an offset of -0.3 results in a male natural mortality which is about 74% of the female mortality ($exp(-0.3) = 0.7408$).  All roads lead to Rome in this figure (Figure \ref{fig:profile_M2.S}); since all data sources and the overall likelihood are minimized at zero.  Likelihoods for recruitments and indices are flat over the range of MM; the other data sources show changes of about 20 (lengths) and 40 (ages) likelihood values. However, given the larger amount of data available to the Northern model supporting lower mortality for males than females (Figure \ref{fig:profile_M2.N}), the choice to fix the male mortality at the value from the Northern model, resulting in lower mortality for males than females, seems reasonable.

The profile over stock-recruit steepness (Figure \ref{fig:profile_h.S}) shows little information about steepness, with the change in total likelihood less than 0.7, over a range of $h = 0.5$ to $h = 0.9$. This supports the conclusion that the stock was never at a very low biomass.  For a more depleted stock, steepness would have a larger impact on the likelihood. The lack of information on steepness supports the choice to fix the value at the mean of the prior: $h=0.718$.

### Final Southern Model Retrospective Analysis

The Southern model retrospectives shown here are those for one of the many sensitivities, and may be slightly different than those that would be the result of arun on the "final" Southern model.  These retrospectives show the general pattern of retrospectives for the Southern model, which was not found to be sufficient for management purposes.

The Southern model shows a retrospective pattern in which removing one year of data at a time leads to slightly higher estimates of spawning output (Figure \ref{fig:retro.S}). The changes associated with 1 or 2 years of data removed are relatively small, but removing years of data had a larger impact on spawning output, with equilibrium value increasing from 2.8 trillion eggs to 3.5 trillion eggs when 5 years of data were removed. 

### Final Southern Model Reference Points

Reference points are not reported for the Southern model because it is not being recommended for management of the species.