**Status of the Longnose Skate (*Raja rhina*)**

**off the continental US Pacific Coast in 2007**

**Vladlena V. Gertseva**

Cooperative Institute for Marine Resources Studies

Oregon State University

2030 SE Marine Science Drive

Newport, OR 97365

**Michael J. Schirripa**

Northwest Fisheries Science Center

NOAA Fisheries

2032 SE Marine Science Drive

Newport, OR 97365

July 9, 2007

[]{#__RefHeading___Toc167637157 .anchor}**TABLE OF CONTENTS:**

[TABLE OF CONTENTS: 2](#__RefHeading___Toc167637157)

[EXECUTIVE SUMMARY 4](#executive-summary)

[INTRODUCTION 15](#__RefHeading___Toc167637159)

[General information about the species
15](#general-information-about-the-species)

[Life history of longnose skate 15](#life-history-of-longnose-skate)

[Fishery off the US west coast 16](#fishery-off-the-us-west-coast)

[Fishery and assessment off Alaska and Canada
17](#fishery-and-assessment-off-alaska-and-canada)

[Management 17](#management)

[ASSESSMENT 18](#assessment)

[DATA 18](#data)

[Fishery dependent data 18](#fishery-dependent-data)

[Landed catch 18](#landed-catch)

[Discard 20](#discard)

[Biological data 20](#biological-data)

[Fishery independent data 21](#fishery-independent-data)

[NWFS slope survey 21](#__RefHeading___Toc167637172)

[NWFSC shelf-slope survey 21](#nwfsc-shelf-slope-survey)

[AFSC shelf (triennial) survey 22](#__RefHeading___Toc167637174)

[AFSC slope survey 22](#__RefHeading___Toc167637175)

[Survey biomass indices and length compositions
23](#survey-biomass-indices-and-length-compositions)

[Biological Parameters 23](#biological-parameters)

[MODEL DESCRIPTION 24](#model-description)

[Overview 24](#overview)

[Model parameters 25](#model-parameters)

[Natural mortality 25](#natural-mortality)

[Growth and maturity parameters 26](#growth-and-maturity-parameters)

[Stock-recruitment relationship 26](#stock-recruitment-relationship)

[Selectivity 26](#selectivity)

[NWFSC shelf-slope survey catchability *Q*
27](#nwfsc-shelf-slope-survey-catchability-q)

[Age-determination error 27](#age-determination-error)

[MODEL SELECTION AND EVALUATION 27](#model-selection-and-evaluation)

[Alternative model configurations 27](#alternative-model-configurations)

[Conversion criteria 28](#conversion-criteria)

[Likelihood profile analysis 28](#likelihood-profile-analysis)

[BASE RUN RESULTS 28](#base-run-results)

[Model fit 28](#model-fit)

[Model estimates 29](#model-estimates)

[State of the stock 29](#state-of-the-stock)

[UNCERTAINTY AND SENSITIVITY ANALYSIS
29](#uncertainty-and-sensitivity-analysis)

[Catch history 29](#catch-history)

[NWFSC shelf-slope survey catchability Q
31](#nwfsc-shelf-slope-survey-catchability-q-1)

[Maturity 31](#maturity)

[REFERENCE POINTS 31](#reference-points)

[HARVEST PROJECTIONS 31](#__RefHeading___Toc167637200)

[RESEARCH AND DATA NEEDS 32](#research-and-data-needs)

[ACKNOWLEDGMENTS 33](#acknowledgments)

[LITERATURE CITED 34](#literature-cited)

[TABLES AND FIGURES 39](#tables-and-figures)

[LIST OF TABLES 40](#list-of-tables)

[TABLES 41](#tables)

[LIST OF FIGURES: 60](#__RefHeading___Toc167637207)

[FIGURES 62](#__RefHeading___Toc167637208)

[APPENDIX 1: List of STAR Panel requests
117](#__RefHeading___Toc167637209)

[APPENDIX 2: Codes for the longnose skate assessment model
121](#__RefHeading___Toc167637210)

# EXECUTIVE SUMMARY

**Stock**

Longnose skates (*Raja rhina*) are found from Navarin Canyon in the
Bering Sea and Unalaska Island in Alaska to Cedros Island, Baja
California in Mexico. This assessment is for the population occupying
the waters off California, Oregon and Washington, bounded by Canada in
the north and Mexico in the south. Within this study area, the longnose
skate population is treated as one fishery stock, due to the lack of
biological and genetic data supporting the presence of multiple stocks.

**Catches**

The longnose skate is not a commercially important target species. It is
caught primarily as bycatch in trawl fisheries, where most are
discarded. Although the landed catch of skates is documented through
fish tickets, most records are for a combined-skate category. There are
also apparent reporting inconsistencies with regard to the condition of
landed skates (e.g., as whole fish or as wings). The extent to which
landings in the combined-skate category were comprised by longnose skate
is informed by limited periods of species-composition sampling in Oregon
and Washington. Historical landed catch was reconstructed from variety
of sources. Over the last 57 years, longnose skate landings ranged
between 35 and 1,721 mt. Landings peaked in the mid-1990s, due to
increased demand from Asian markets. Discards rates were estimated at
93% prior to 1995 and 53% after 1995, which corresponds to changes in
skate markets in the mid-1990s.

**Table ES-1**. Recent landings (mt) for longnose skate by year and
state.

![](media/image1.wmf){width="4.282638888888889in"
height="1.9416666666666667in"}

![](media/image2.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

**Figure ES-1**. Reconstructed historical landings (mt) for longnose
skate.

**Data and Assessment**

This is the first assessment for longnose skate on the U.S. West Coast.
The Stock Synthesis 2 (version 2.00e) modeling program was used to
conduct the analysis and to estimate model parameters and management
quantities. Since there are no apparent differences in biological and
life history parameters as well as length and age frequencies between
females and males, the assessment uses a single-sex model. The model
starts in 1916, assuming an unfished equilibrium state of the stock in
1915. The assessment model includes one fishery that operates within the
entire area of assessment. Fishery dependent data used in the assessment
include combined-skate landings (1950-2006), fishery length compositions
(1995-2006) and limited age data (2003-2004). Fishery independent data
include biomass estimates (1980-2006) and length compositions
(1997-2006) from four NMFS surveys conducted on the continental shelf
and slope, as well as age data from one of the surveys (2003). The model
uses discard data from Rogers and Pikitch's study (1986-1987), the
Enhanced Data Collection Project (1996-1998), and the NMFS West Coast
Groundfish Observer Program (2005).

**Stock biomass**

Using the base model, the unexploited level of spawning stock biomass
for longnose skate is estimated to be 7,034 mt. At the beginning of
2007, the spawning stock biomass is estimated to be 4,634 mt, which
represents 66% of the unfished stock level.

**Table ES-2**. Recent trend in longnose skate spawning biomass and
depletion.

![](media/image3.wmf){width="5.551388888888889in"
height="2.4347222222222222in"}

![](media/image4.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

**Figure ES-2**. Estimated spawning biomass time-series with 95%
confidence interval.

**Recruitment**

In the assessment, we used the Beverton-Holt model to describe the
stock-recruitment relationship. Recruits were taken deterministically
from the stock-recruit curve. The level of virgin recruitment *R*~0~ was
estimated to assess the magnitude of the initial stock size. Steepness
of the stock-recruitment curve was fixed at a value of 0.4, to reflect
the *K*-type reproductive strategy of the longnose skate.

**Table ES-3**. Recent estimated trend in longnose skate recruitment.

![](media/image5.wmf){width="4.154861111111111in"
height="2.4368055555555554in"}

![](media/image6.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

**Figure ES-3**. Time-series of estimated recruitment for longnose
skate.

**Reference Points**

For the longnose skate, the management target is defined as 40% of the
unfished spawning stock biomass (SB~40%~), which is estimated to be
2,814 mt (95% Confidence Interval: 2,608-3,019 mt) in the base model.
The stock is declared overfished if the current spawning biomass is
estimated to be below 25% of unfished level. The MSY-proxy harvest rate
for longnose skate is SPR=F45%, which corresponds to an exploitation
rate of 0.043. This harvest rate provides an equilibrium yield of 1,264
mt (95% Confidence Interval: 1,194-1,334 mt) at SB~40%~. The model
estimate of maximum sustainable yield (MSY) is 1,268 mt (95% Confidence
Interval: 1,198-1,338). The estimated spawning stock biomass at MSY is
2,626 mt (95% Confidence Interval: 2,433-2,819 mt). The exploitation
rate corresponding to the estimated SPRmsy of F61% is 0.027.

Reference point results are calculated on both a per-recruit and
total-recruits basis (Table ES-9). The total-recruits results take into
account the spawner-recruitment relationship with the steepness as
defined in the base model (*h*=0.4). Because of this low steepness and
other reproductive characteristics of the stock, fishing at the target
SPR of 45% is expected to reduce the spawning biomass to less than 12%
of the unfished level over the long term. Conversely, fishing at a rate
that would maintain spawning biomass near 40% of the unfished level
would require a target SPR much higher than 45%. The Council's
Scientific and Statistical Committee should consider the appropriateness
of using the current proxy harvest rate for setting the Allowable
Biological Catch for longnose skate.

**Exploitation Status**

The assessment shows that the stock of the longnose skate in the US West
Coast is not overfished. Currently, the stock is at 66% of its unfished
level. Historically, the exploitation rate for the longnose skate has
been low. It reached its maximum level of 4.02 % in 1981. Currently, it
is at the level of 1.25 %.

**Table ES-4**. Recent trend in longnose skate exploitation.

![](media/image7.wmf){width="2.1194444444444445in"
height="1.9201388888888888in"}

![](media/image8.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

**Figure ES-4**. Exploitation rate and spawning biomass relative to
their target values (circle indicates the point that corresponds to
2007).

**Management**

The longnose skate is grouped with other unrelated species ("Other
Fish") for the purposes of specifying annual Allowable Biological
Catches and Optimum Yields (OY). Combined landings of species within
this category are typically well below the specified OY. As a result,
landings of species in this category are not actively monitored
throughout the year, nor have they been subject to trip-limit
management. In most areas of the world, management of skates has
generally been a low priority and where management and assessments are
implemented, the available data are generally inadequate. The longnose
skate, like other elasmobranches, presents an array of problems for
fisheries management. Given the low economic value of skates,
information about their fisheries and basic biology is scarce. However,
skate life history characteristics make them more susceptible to
overfishing than teleost fishes. Vulnerability of this group and the
past history of elasmobranch fisheries collapses are general causes for
concern. At the same time, the absence of a strong directed fishery for
skates in this region, combined with reductions in trawl effort
shoreward of 150 fm to promote rockfish stock rebuilding, reflect a
different fishing environment than has characterized these other
collapses.

**Forecast**

Projections of future catches, summary biomass, spawning biomass and
stock depletion were made based on F45%, as well as the current rate of
fishing mortality. The projected spawning biomasses are greater than 40%
of the unfished level for both approaches. No 40:10 harvest control rule
reductions were applied. Optimum yield catch values were equivalent to
ABC values.

**Table ES-5**. 10-year forecast of longnose skate catch, summary
biomass, spawning biomass and stock depletion estimated based on F45%.

![](media/image9.wmf){width="5.997222222222222in"
height="1.8541666666666667in"}

**Table ES-6**. 10-year forecast of longnose skate catch, summary
biomass, spawning biomass and stock depletion estimated based on current
rate of fishing mortality.

![](media/image10.wmf){width="5.997222222222222in"
height="1.8541666666666667in"}

**Rebuilding Projection**

Since the longnose skate stock is estimated to be above the overfished
level, no rebuilding is required.

**Unresolved Problems and Major Uncertainties**

The major uncertainties for the assessment include uncertainties in the
longnose skate catch history, particularly in proportion of longnose
skate in combined-skate landings, discard and discard mortality rates,
and Northwest Fishery Science Center (NWFSC) shelf-slope survey
catchability *Q*. To address uncertainties related to longnose skate
catches, alternative catch histories were developed, which reflect
variations in proportion of longnose skate in combined-skate landings,
as well as discard and discard mortality rates. These alternative
histories include the base scenario, which was reconstructed using the
best information available, along with "low" and "high" catch scenarios.
To explore uncertainty regarding the estimation of the NWFSC shelf-slope
survey *Q*, the base-case model (with *Q* fixed at 0.83) results were
contrasted with "low" and "high" *Q* scenarios. Alternative catch
histories and *Q* values were used to define alternative states of
nature and develop the decision table.

**Decision Table**

Three states of nature were defined based on the alternative longnose
skate catch history and values of NWFSC shelf-slope survey *Q*. The base
scenario uses the base catch history and base *Q* (*Q*=0.83), the "low"
scenario uses the low catch history and low *Q* (*Q*=0.654), and the
"high" scenario uses the high catch history and high *Q* (*Q*=1.046).
Ten-year forecasts for each state of nature were calculated based on
F45% for the base scenario. Ten-year forecasts were also produced with
future catch fixed at the average amount (using the base catch history)
for last three years (2004-2006) and at 150% of that three-year average.
Under the "high" scenario, the F45% harvest rate is projected to reduce
the spawning stock biomass below 40% of the unfished level within two
years. In all other scenarios covered by the decision table, the
spawning biomass remains above the target level throughout the 10-year
projection period. The current rate of fishing mortality is
significantly lower than F45% (current exploitation rate is 1.25%).
Therefore, it is very unlikely that the stock, even under the "high"
scenario will fall below 40% of its virgin state in the next 10 years.

**Research and Data Needs**

This assessment reflects a data-moderate to data-poor circumstance with
respect to several influential model elements, including catch history,
survey catchability, and some life history characteristics.
Consequently, some critical assumptions were based on very limited
supporting data and research. There are several data and research needs
which, if satisfied, could improve the assessment.

Data needs:

1)  Continue species-specific identification in fishery to improve the
    accuracy of fishery catch data;

2)  Continue monitoring discard of the longnose skate;

3)  Resume collecting and processing of vertebra samples for age
    determination to improve the accuracy of growth model parameters and
    size-at-age relationships.

Research needs:

1)  Conduct studies to determine survival rates of discarded longnose
    skate, especially with trawl gear, so that total fishing mortality
    can be estimated more precisely;

2)  Conduct studies on life history characteristics, especially those
    related to maturity and reproduction;

3)  Conduct age-validation studies;

4)  Conduct studies of longnose skate catchability by survey gear types.

**Table ES-7**. Decision table based on three states of nature, defined
based on alternative catch histories

and levels of NWFSC shelf-slope survey catchability *Q*.

> ![](media/image11.wmf){width="8.990972222222222in"
> height="5.090972222222222in"}
>
> **Table ES-8**. Summary of recent trends in longnose skate
> exploitation and estimated population levels.
>
> ![](media/image12.wmf){width="8.990277777777777in"
> height="1.9902777777777778in"}

\* indicates values calculated as the average for the last three years
(2004-2006)

> **Table ES-9**. Summary of longnose skate reference points.
>
> ![](media/image13.wmf){width="5.9222222222222225in"
> height="3.561111111111111in"}

[]{#__RefHeading___Toc167637159 .anchor}**INTRODUCTION**

## General information about the species

Skates are the largest and most widely distributed group of batoid fish
with approximately 230 species ascribed to two families (Martin and
Zorzi 1993, McEachran 1990). Skates are benthic fish that are found in
all coastal waters but are most common in cold temperatures and polar
waters.

There are about 12 species of skates from either of two genera (*Raja*
and *Bathyraja*) present in the northeast Pacific Ocean off California,
Oregon and Washington. Of that number, just three species (longnose
skate *Raja rhina*, big skate *Raja binoculata*, and sandpaper skate
*Bathyraja interrupta*) make up over 95% of survey catches in terms of
biomass and numbers, with the longnose skate leading in both categories
(62% of biomass and 56% of numbers). Species compositions of fishery
landings also show that longnose skate dominates commercial catches. On
average, longnose skate represents 75% of total skate landings in Oregon
for the last 12 years and 45% in Washington for the last three years.
There are no species composition data available for commercial landings
in California, but anecdotal evidence suggests that the majority of
skates landed there are longnose skates.

The longnose skate or *Raja rhina* belongs to the family Rajidae
(skates), the order Rajiformes (skates and rays), and the subclass
Elasmobranchii (cartilaginous fish) that includes skates, rays and
sharks (Compagno1999, McEachran and Aschliman 2004). Like other skates,
longnose skate is a dorso-ventrally compressed animal with large
pectoral fins (often called "wings"), a long whip-like tail and a stiff,
long snout (Compagno 1999). A photograph of the longnose skate is shown
in Figure 1.

The distribution of the longnose skate is limited to the eastern Pacific
Ocean between 61^o^ N Lat. and 28^o^ N Lat. It is found as far north as
Navarin Canyon in the Bering Sea and Unalaska Island in Alaska to as far
south as Cedros Island, Baja California in Mexico at depths of 25-684 m
(Lamb and Edgel 1986). Longnose skates do not exhibit a size-specific
pattern in distribution relative to bottom depth; average fish size does
not vary greatly with depth (Figure 2).

Currently, there is no information available that indicates the
existence of multiple breeding units in the Northeast Pacific Ocean.
Several tagging studies have found that elasmobranchs, such as sharks
and skates, can undertake extensive migrations within their geographic
range (Martin and Zorzi 1993, McFarlane and King 2003). This behavior
suggests the likelihood that there is a high degree of genetic mixing
within the population, across its range. As a result, the longnose skate
population off California, Oregon and Washington is modeled in this
assessment as a single stock. A map depicting the scope of the
assessment is presented in Figure 3.

## Life history of longnose skate

The life history of skates is characterized by late maturity, low
fecundity and slow growth to large body size (King and McFarlane 2003,
Moyle and Cech 1996, Walker and Hislop 1998). The characteristics are
associated with a *K*-type reproductive strategy, as opposed to *r*-type
strategy, wherein reproductive success is achieved by high productivity
and early maturity (Hoenig and Gruber 1990).

The longnose skate is oviparous (egg-laying) and invests considerable
energy in developing a few large, well-protected embryos. There are
three major stages in the life cycle of the longnose skate: the egg, the
juvenile and the adult stages. After fertilization, the female forms a
large tough, leathery yet permeable egg case (about 10×6 cm) that
surrounds one or more eggs. After several months the female deposits the
egg case onto the sea floor. The eggs incubate for several months in a
benthic habitat where there is some exposure to predation and damage.
Inside the egg case, the embryos develop with nourishment provided by a
yolk. When the yolk is depleted and the juvenile fully formed, it exits
the egg case. Once hatched, the young skate is similar in appearance to
an adult, but smaller in size. The juvenile stage lasts from the time of
hatching to the onset of maturity (Frisk et al 2002, Pratt and Casey
1990). On average, longnose skate mature at ages ranging from six to
nine years. Upon reaching maturity, skates enter the reproductive adult
stage, which characterizes the remainder of their lives. The life span
of this species is not well known, although individuals up to 23 years
of age have been found. Longnose skates attain a maximum length of about
145 cm (Zeiner and Wolf 1993). The average size is about 60-90 cm
(Thompson 2006, Zeiner and Wolf 1993).

The reproductive cycle of oviparous skates has been observed for a few
species but not for longnose skate. These studies indicate that egg
production generally occurs throughout the year although there have been
some instances where seasonality in egg laying was observed (Hamlett and
Koob 1999). Information on fecundity of longnose skate is extremely
limited. Holden (1974) found that species of genus *Rajidae* are the
most fecund of all elasmobranches and can lay 100 egg cases per year,
although eggs may not be produced every year. Frisk et al. (2002)
estimated that annual fecundity for medium-sized skates like longnose
may be less than 50 eggs per year; however, those eggs exhibit high
survival rates due to the large parental investment. Typically, an egg
case houses 4-5 embryos although the numbers can go as low as one to as
high as seven (Thompson 2006). Overall, little is known about breeding
frequency, egg survival, hatching success and other early life history
characteristics of the longnose skate.

## Fishery off the US west coast

Historically, skates in general, and longnose skate in particular, have
not been high-priced fishery products. They are taken mostly as bycatch
in other commercially important fisheries (Bonfil 1994). Although skates
are caught in almost all demersal fisheries and areas off the U.S. West
Coast, the vast majority (almost 97%) are caught with trawl gear. Figure
4 shows the distribution of skate landings among gears, averaged over
the last 25 years.

Landing records indicate that skates have been retained on the U.S.
Pacific Coast at least since 1916 (Martin and Zorzi 1993). Little is
known about the species composition of West Coast skate fisheries,
particularly prior to 1990. With few exceptions, longnose skate landings
have been reported, along with other skate species, under the market
category "unspecified skates." In recent years, the species composition
of this market category has been sampled by state port samplers in
Oregon and Washington.

Skate retention is probably influenced by the success of the target
fisheries in which they occur as bycatch. A high catch of the target
species could result in limited storage space for skate and subsequent
drop in skate landings (Martin and Zorzi 1993). Martin and Zorzi (1993)
have found that skate landings do partially reflect changes in landings
in other trawl fisheries, particularly rockfish and flatfish, but
findings of direct correlations are inconsistent and there is often a
time lag of several years. Frey (1971) found that fluctuations in skate
landings roughly followed general economic trends such that peaks in
production occur at about the same period as economic peaks.

Historically, only the skinned pectoral fins, or "wings" were sold,
although a small portion of catch would be marketed round. The wings
were cut onboard the boat and the remainder discarded. Currently, West
Coast skates are marketed both whole and as wings. Skates wings are sold
fresh or fresh-frozen, as well as dried or salted and dehydrated, for
sale predominantly in Asian markets (Bonfil 1994, Martin and Zorzi
1993). There is no information to suggest change in skate markets prior
to the mid 1990s. However, it appears that the demand for whole skates
did increase greatly during the mid-1990s, as evidenced by the increase
in the number of trips where skates were landed (Figure 5). While skates
were encountered predominantly as bycatch previously, landings data from
this period reveal greater targeting of skates by some vessels. After a
few years, the whole-skate market cooled due to downturns in Asian
financial markets (Peter Leipzig, Fishermen\'s Marketing Association,
personal communication).

## Fishery and assessment off Alaska and Canada

In Alaska, skates were primarily taken as bycatch in both longline and
trawl fisheries until 2003 when a directed skate fishery developed in
the Gulf of Alaska. Longnose skates, as well as big skates, comprise the
majority of the skate biomass in the Gulf of Alaska. In 2003 skate
species in the Gulf of Alaska, and the Bering Sea and Aleutian Islands
were assessed as a group rather than as separate species. In 2005 the
skate assessments were updated, with the recommendation that no directed
fisheries for skates be conducted in the Gulf of Alaska due to high
incidental catch in groundfish and halibut fisheries. Also, the
area-specific Allowable Biological Catches for big and longnose skates
were recommended (Gaichas et al. 2003, Matta et al. 2006).

In Canada historic information regarding skate catches goes back to the
1950's. Prior to 1990's skates were taken mostly as bycatch and landings
were reported as part of a skate complex (not by species). As with the
West Coast, the trawl fishery is responsible for the largest amount of
bycatch. Skate catches off British Columbia accelerated in the early
1990's, partly due to emerging Asian markets. Since 1996, longnose skate
has been targeted by the B.C. trawl fishery and, as a result, catches
have been more accurately reported. A longnose skate assessment has not
been done for B.C., but in 2001 a review of elasmobranch biology,
fisheries, assessment, and management was conducted to assess the
current state of knowledge and to examine possible methods for assessing
elasmobranch species, including longnose skates (Benson et al. 2001).

## Management 

On the West Coast, longnose skate has been grouped with other species in
an "Other Fish" category, for purposes of setting Allowable Biological
Catches and Optimum Yields (OY). Since landings are routinely well below
OYs for this category, trip limits have not been used for inseason
management. In most areas of the world, management of skates has been a
low priority, and where management and assessments are implemented, the
available data are generally inadequate (Shotton 1999). The longnose
skate, like other elasmobranches, present an array of potential problems
for fisheries management. Skates' life history characteristics make them
more susceptible to overfishing than teleost fishes. The most extreme
case of overexploitation has been reported in the North Atlantic, where
the common skate *Dipturus batis* has dissapeared from the Irish Sea
(Brander 1981) and much of the North Sea (Walker and Hislop 1998).
However, given the low economic value of skates, information about their
fisheries and even their basic biology is scarce, patchy and scattered
(Bonfil 1994). The vulnerability of these species, combined with past
collapses of elasmobranches fisheries elsewhere, underscores the
importance of ascertaining the status of longnose skate on the West
Coast.

# ASSESSMENT

## DATA

For this assessment we used the following data sources: (1) commercial
landings (1950-2006), (2) fishery biological data (1995-2006), (3) NWFSC
slope survey (1999-2002), (4) NWFSC shelf-slope survey (2003-2006), (5)
AFSC shelf (triennial) survey (1980-2004), and (6) AFSC slope survey
(1997-2001). These data sources are divided into two major categories:
fishery-dependent and fishery-independent data. Summaries of the
fishery-dependent and fishery-independent data used in this assessment,
by source and year, are presented in Tables 1 and 2, respectively.

### Fishery dependent data

#### Landed catch

Historically, landed catch of longnose skate has been reported under the
market category "unspecified skates" along with other skate species.
Hence, skate landings records, themselves, are not species-specific. In
order to reconstruct landed catch of longnose skate we first,
reconstructed the historical landings of "unspecified skates" market
category, and then estimated the proportion of the longnose skate within
this category.

To reconstruct the time series of combined-skate landed catch, we used
several data sources that included both published reports and databases.
The most recent and detailed information, for the period between 1981
and 2006, was obtained from the Pacific Fisheries Information Network
database (PacFIN, Daspit et al. 1997). For the period between 1950 and
1980, combined-skate landings were obtained from annual publications of
Fisheries Statistics of US. From historical data, we excluded all skate
catches landed in any other areas, except for five INPFC areas covered
by this assessment (these five INPFC areas included US Vancouver,
Columbia, Eureka, Monterey and Conception). Overall combined-skate
landings between 1950 and 2006 are shown in Figures 6.

In recent years, the Oregon and Washington Department of Fish & Wildlife
(ODFW and WDFW) have started to collect species compositions of the
"unspecified skates" market category. From ODFW and WDFW we obtained
data for species compositions of skate catches landed in Oregon in
1995-2006 and in Washington in 2004-2006 respectively. No
species-specific information was available for California landings.

To estimate the proportion of longnose skates within the "unspecified
skates" market category between 1950 and 2006, we used data from ODFW
and WDFW for years when skate species compositions were available. For
other relatively recent (since 1981) years/areas, species-composition
data from the NMFS shelf (triennial) survey, conducted principally by
the Alaska Fisheries Science Center (AFSC), were used to represent
species proportions in the fisheries. This survey was conducted every
third year from 1980 to 2004. For each of these years, the survey's
proportion of total skate catch comprised by longnose skates was
calculated for the area off each state. These proportions were applied
directly to the commercial landings data from the same year. For years
in which the survey was not conducted, the proportions of longnose skate
were estimated using a linear function connecting the two closest
available data points. The final percentages of longnose skate that were
applied to generic skate landings since 1981, by year and state, are
shown in Table 3. For the period between 1950 and 1980, when we did not
have any survey catches available, we applied the overall average
percentage of the longnose skate within the "unspecified skates" market
category (62%) for the last 25 years. The resultant time series of
longnose skate landed catch for the years 1950-2006 are shown in Figure
7. These time series show the increase in landings in the mid-1990's,
which corresponds to the time of increased demand from the Asian skate
market.

***Gear***

As a bycatch species, skates have been caught on the West Coast by a
variety of gears. The vast majority (almost 97%), however, are caught in
trawl gear (Figure 4). Consequently, this assessment focuses on the
catch of longnose skate by the trawl fishery. Other fisheries are
assumed to have the same fishery characteristics and selectivity.

***Condition code***

As described above, most skates have been landed as either "wings" or
"round". PacFIN records indicate that skates were landed as wings,
round, alive, dressed (head on), dressed (general), dressed (head off),
and dressed (head and tail off). To be able to convert landed weight
into round weight correctly, we discussed the ways in which skates were
landed with representatives of the State agencies, who helped us refine
the use of condition code information. For example, we discovered that
in Oregon, the condition code "dressed" was used for "wings" because, at
the time when differentiating skate wings was initiated, there were no
available new codes to be used. For Washington, PacFIN data also
included "dressed" records which were actually "wings." In California,
prior to 1995, the only condition code used to describe how skates were
landed was "wings" (Gerry Kobylinski, California PacFIN Coordinator,
pers. com.) although PacFIN data contain several condition codes for
this period. 

***Conversion factor***

Since "wings" comprise only a portion of total skate body, state
agencies use a conversion factor to convert landed weight into round
weight. Based on research conducted by ODFW a conversion factor of 2.6
is used for Oregon (Johnson and Hosie 1996). Other states relied upon
literature reviews to determine their conversion factors. Currently,
Washington uses conversion factor of 3, and California 3.1 (prior to
this year, California was using the value of 4.3).

#### Discard

***Discard rate***

For this assessment, we used three sources of information to
characterize fishery discards. The first source was a discard study in
Oregon and Washington in 1986 and 1987 (Rogers and Pikitch 1992). This
study found that 93% of the trawl fishery longnose skate catch (by
weight) was discarded. Marketing problems were indicated as the main
reason for the skate discard. The second source of discard data was the
Enhanced Data Collected Project (EDCP), conducted by ODFW between 1996
and 1998 in the waters off Oregon. The discard rate for skates was 53%
on trips included in this project, although most observed trips were
directed at deep-water species. The third source of discard data is the
NMFS West Coast Groundfish Observer Program (WCGOP), which provided
discard rate data for 2005. As in the EDCP observations, analysis of
WCGOP data indicates that the discard rate for the skates in 2005 was
53%. None of the sources collected size-specific discard information.

Since the rate of skate discard is highly dependent on market acceptance
(Rogers and Pikitch 1992), we modeled discard mortality for two time
periods -- one is before 1995, and the second is from 1995 till present
time, when skate market demands increased. In the base model, for the
first period we assumed the discard rate of 93% estimated in Rogers and
Pikitch (1992); for the second period we used the discard rate of 53%
estimated from EDCP and WCGOP data.

***Discard mortality***

To date, no studies have been conducted to estimate the mortality of
discarded longnose skate or any other skate. In tagging studies
conducted in Canada (Gordon McFarlane, pers. com.), tagged skates were
recovered several times in trawl surveys, indicating that skates can
survive trawl capture and on-deck sorting time. Anecdotal evidence from
commercial fisheries also indicates that skates are generally durable,
and can handle capture and release well. However, many factors, such as
trawl time, handling techniques, and time spent on the deck certainly
affect skate survival. For the base model in this assessment, we assumed
that 50% of discarded skates die, and performed a sensitivity analyses
on this assumption.

#### Biological data

Very limited biological data on longnose skate have been collected over
the years. For this assessment, biological information was provided
primarily by ODFW and WDFD.

***Size***

Size-composition data was provided by ODFW for Oregon catches landed
between 1995 and 2006 and by WDFW for Washington catches landed between
2004 and 2006. No size-composition data were available for California
landings. In the assessment we combined the data from Oregon and
Washington and used it to represent the size compositions of the
longnose skate caught in coast-wide commercial fishery. Sizes of
longnose skates were recorded as total length (TL) from the tip of the
snout to the end of the tail. TL of longnose skates in fishery catches
ranged from 40 to 140 cm, except for two fish with recorded TLs of 165
and 180 cm. These two lengths are considerably larger than any recorded
longnose skates in the area, and were subsequently excluded from our
analysis, due to the likelihood that they represent data entry errors.
Size data were aggregated into 5-cm length bins. Fishery skate size
compositions for longnose skate, by year, are shown in Figure 8.

***Age***

No fishery age-composition data are available for longnose skate.
Thompson (2006) conducted a study on age and growth of longnose skate as
a part of her MS research. For this study, she drew two small samples of
longnose skate from catches landed in Oregon (one in 2003 and one in
2004). Since elasmobranches do not have otoliths, the most common
structure used to age cartilaginous species is vertebrae (Cailliet and
Goldman 2004). The ages of longnose skates collected in these samples
were identified through the analysis of annual rings, or "annuli," on
the vertebra centra. Since the sample sizes of Thompson's data were
small (N=38 for 2003 and N=102 for 2004) and represented only a small
portion of the study area of the assessment, we used these data only to
calculate mean size-at-age in the model and not to describe age
composition of fisheries data.

### Fishery independent data

In this assessment we used four surveys conducted by NMFS as
fishery-independent data sources. These surveys are the NWFSC slope and
shelf-slope surveys, and the AFSC shelf (triennial) and slope surveys.
Details on latitudinal and depth ranges of these surveys, by year, are
presented in Table 4. Below we give an overview of each survey and
describe data that were used in our assessment.

[]{#__RefHeading___Toc167637172 .anchor}**NWFS slope survey**

The NWFSC slope survey was conducted annually from 1999 to 2002. Survey
methods are described in Keller et al. (2006). This survey was conducted
between 35^o^ and 48^o^07' N. Lat., encompassing all of the US
Vancouver, Columbia, Eureka, Monterey INPFC areas, and a portion of the
Conception area. The survey covered depths from 183 to 1280 m (100-700
fathoms).

***Biological information***

No biological data on longnose skate was collected during this survey.

#### NWFSC shelf-slope survey

The NWFSC shelf-slope survey was conducted annually from 2003 to 2006.
Survey methods are described in Keller et al. (2007). This survey ranged
from 32^o^34' to 48^o^22' N.Lat., encompassing all five INPFC areas
included in the scope of this assessment (US Vancouver, Columbia,
Eureka, Monterey, Conception). The survey covered depths between 55 and
1280 m (30-700 fathoms), which is almost the entire depth distribution
of longnose skate.

***Biological information***

*Size*

Size data were collected in all years. In 2003, 2004, and 2005, longnose
skates were measured in total length (TL), while in 2006 in disc width
(DW), which is the distance across pectoral fins. To convert DW data to
TL, we used the conversion equation, derived from the AFSC slope survey
in 1999, when a sample of 457 longnose skates was measured in both TL
and DW. Figure 9 shows the relationship between TL and DW for longnose
skate obtained from that study
($\text{TL} = 7\text{.}\text{36} + 1\text{.}\text{41} \cdot \text{DW}$,
*r^2^*=0.99). Size of longnose skates collected in this survey ranged
from 15 to 140 cm.

*Age*

A limited-sample of longnose skate age structures (vertebra) was
collected from 2003 NWFSC shelf-slope survey and processed by Thompson
(2006) as a part of her MS research. The ages of longnose skates were
identified through the analysis of annuli on the vertebra centra of
skates. The degree of age-reader agreement was explored through
comparing the readings of the same age structures by two other readers
(Thompson 2006). Although this provides some information regarding the
precision of the age determinations, they have not been validated with
regard to potential bias.

[]{#__RefHeading___Toc167637174 .anchor}**AFSC shelf (triennial)
survey**

The AFSC shelf (triennial) survey was conducted every third year between
1977 and 2004 (in 2004 this survey was conducted by the NWFSC). Survey
methods are described in Weinberg et al. (1994), Zimmermann et al.
(1994), Wilkins et al. (1998) and Winberg et al. (2002). Over this
period, the survey area varied in depth and latitudinal range (Table 4).
In order to utilize as many years as possible, we used data only from
the common depth and latitude range for analysis. Our analysis included
data from four INPFC areas (Monterey, Eureka, Columbia and U.S.
Vancouver) and depths between 55 and 366 meters.

***Biological information***

Longnose skate size data were collected in 1998, 2001 and 2004. In 1998,
sample size was very small and was not included in our analysis. In 2001
and 2004, individuals were measured in total length (TL). Size of
longnose skates collected in this survey ranged from 15 to 145 cm. No
age data for longnose skate was available for this assessment.

[]{#__RefHeading___Toc167637175 .anchor}**AFSC slope survey**

The AFSC slope survey was initiated in 1984. The survey methods are
described in Lauth (1999, 2000). Prior to 1997, this survey was
conducted in different latitudinal ranges in each year (Table 4).
Therefore, in this assessment we used data from surveys conducted in
1997, 1999, 2000 and 2001, which were consistent in latitudinal range
(from 34^o^30' to the U.S.-Canadian border) and depth (183-1280 m;
100-700 fathoms).

***Biological information***

Longnose skate size data were collected in 1997, 1999, 2000 and 2001. In
1997, longnose skates were measured in disc width (DW), while all other
years (1999, 2000 and 2001) were measured in total length (TL). In 1999,
longnose skates (457 individuals) were measured in both TL and DW. These
data were used as the basis for converting 1997 DW data to TL. Figure 9
shows the relationship between TL and DW for longnose skate that we used
($\text{TL} = 7\text{.}\text{36} + 1\text{.}\text{41} \cdot \text{DW}$,
*r^2^*=0.99). Size of longnose skates collected in this survey ranged
from 15 to 140 cm.

#### Survey biomass indices and length compositions

For each survey, a biomass index was estimated for areas included in the
analysis (Weinberg et al. 1994, Zimmermann et al. 1994, Wilkins et al.
1998, Winberg et al. 2002, Lauth 1999, 2000, Keller et al. 2006, Keller
et al. 2007).

Survey biomass indices (mt) and standard deviation of log (index),
calculated as $\sqrt{\text{ln}\left( 1 + \text{CV}^{2} \right)}$are
presented in Table 5. Biomass indices are also shown in Figures 10-13.

The size data were aggregated into 27 size bins, with 5-cm bin length.
Size compositions were calculated as described in Weinberg et al.
(1994), Zimmermann et al. (1994), Wilkins et al. (1998), Winberg et al.
(2002), Lauth (1999, 2000), Keller et al. (2006), Keller et al. (2007)
and Hamel (2005). The size compositions for each survey, by year, are
presented in Figures14-16. Age composition for 2003 NWFSC shelf-slope
survey from Thompson (2006) are shown in Figure 17. The size-at-age data
plotted for fishery and NWFSC shelf-slope survey are presented in
Figures 18-19. Sample sizes of organisms measured in all length and age
samples by year are given in Tables 6-7.

#### Biological Parameters

Using the data described above, biological parameters, such as somatic
growth of individual fish, maturity-at-length, and the length-weight
relationship were estimated. There were no apparent differences found
between females and males in any of these parameters.

***Growth***

Several studies of longnose skate growth (Zeiner and Wolf 1993, Thompson
2006, McFarlane and King 2006, Gburski 2007) showed that growth of
longnose skate is best described by von Bertalanffy growth model
(Bertalanffy 1938). Growth parameters of von Bertalanffy model estimated
in different studies are summarized in Table 8.

SS2 uses the following version of the von Bertalanffy growth model:

$$L_{A} = L_{\infty} + \left( L_{1} - L_{\infty} \right)e^{- K(1 - A)}$$

Where asymptotic length, *L*~∝~, is calculated as:

$$L_{\infty} = L_{1} + \frac{L_{2} - L_{1}}{1 - e^{- K(\text{17} - 1)}}$$

In these equations, *L~A\ ~*is length (cm) at age *A*, *K* is growth
coefficient, *L*~∝~ is asymptotic length, and *L*~1~ and *L*~2~ are the
sizes associated with a reference ages near the youngest and the oldest
ages that are well represented in the data. For longnose skate, this
reference ages were 1 and 17 correspondingly.

***Maturity***

To estimate the relationship between size and maturity, SS2 employs the
logistic function:

$$M\text{\%} = \frac{1}{(1 + e^{\left( \beta(L - L\text{50}\text{\%}) \right)}}$$

Where *M*% is the proportion mature, *β* is coefficient used as a
constant, and *L*50% is the length at 50% maturity. For longnose skate,
*β* was estimated as -0.0986, and *L*50% as 120 cm (Thompson 2006).

McFarlane and King (2006), while studying maturity of longnose skate in
the British Columbia waters, estimated *β* for maturity logistic
function as -0.078, and *L*50% as 83cm, which is significantly lower
than estimated by Thompson (2006). Criteria to distinguish mature
individuals from immature differed between Thompson's and McFarlane and
King's studies. Neither approach, however, could be considered superior
to the other. For the base model, we used Thompson's data, which is more
likely to underestimate the proportion of mature skates. However, we
explored the uncertainly of this estimation through the sensitivity
analysis, as described later in this report.

***Length-weight relationships***

To establish the relationship between length and weight, the following
equation was used:

$$W = \alpha(L)^{\beta}$$

Where *W* is weight (kg), *L* is length (cm) and *α* and *β* are
coefficients used as constants. For longnose skate *α* was estimated as
0.00000428 and *β* as 3.05975.

## MODEL DESCRIPTION

This report describes the latest version of the assessment model for the
longnose skate, which includes changes made according to STAR Panel
requests. The list of STAR Panel requests is presented in Appendix 1.

### Overview

This assessment uses the Stock Synthesis 2 (SS2) modeling program
developed by Richard Methot at the NWFSC. We used the most recent
version of the program (version 2.00e) distributed on April 18, 2007
(Methot 2007).

In this assessment, it was assumed that one stock of longnose skate
occupies the waters off the continental West Coast area, from the
US-Canadian border in the north to US-Mexican border in the south. The
vast majority of longnose skates (97%) were caught in trawl fisheries;
therefore this stock was modeled with a single fishery. Since there were
no apparent differences between females and males in their biological
parameters or fishery and survey length and age frequencies, the
assessment uses a single sex model.

The likelihood components of the model included (1) survey abundance
indices, (2) fishery and survey length compositions, (3) NWFSC
shelf-slope survey age compositions, and (4) fishery and NWFSC
shelf-slope survey mean size-at-age. In the model, likelihood estimates
for the various data components were obtained by comparing expected
values from the model with the actual observations from sample data
based on "goodness of fit" procedures for log (*L*). Emphasis levels
were set to 1.0 for each likelihood component listed above.

The earliest record of skate catches in the US west coast is dated at
1916 (Martin and Zorzi 1993, Bonfil 1994). Therefore, the modeling
period of our assessment begins in 1916, assuming that in 1915 the
population was in an unfished equilibrium condition. To fill the
historical catches between unfished equilibrium in 1915 and the time
when longnose skate catch data were available (1950-2006), we linearly
ramped data from zero in 1915 up to the average catch level for the
period of 1950-1980 in 1949 (we assumed catch in 1949 to be the average
for the period between 1950-1980).

In the assessment, we reconstructed a time series of total catch for the
longnose skate outside of SS2 and then entered these time series in the
SS2 data file. The total catch time series included both landed catch
and discard mortality. For the base model, we assumed a 93% discard rate
prior to 1995 and 53% from 1995 forward to reflect skate market changes.
We also assumed 50% discard mortality for the entire time series. Figure
20 shows longnose skate total catch over time as used in the base model.
The uncertainties associated with discard and discard mortality
assumptions were explored in the sensitivity analysis, the results of
which are presented later in this report.

### Model parameters

The model utilizes 32 parameters. No prior assumptions were made
regarding the estimated parameters (the emphasis level "lambda" on all
prior distributions was set to 0). However, bounds were established on
all parameters, including life history, stock-recruitment, and
selectivity. Based on the information about survey coverage and behavior
of longnose skate in the natural environment, the catchability
coefficient *Q* for the NWFSC shelf-slope survey was fixed at the level
of 0.83. The determination of this value is described later in the
report. Values of *Q* for other surveys were estimated within the model.
Ageing error was input as data to the model and was not estimated. Input
variance factors were adjusted for length sample sizes in fishery and
surveys as well as AFSC shelf (triennial) survey CV.

All the explicit parameters used for the base model and their values are
given in Table 9. If parameters were estimated, initial values as well
as parameters bounds are also given. The phases in which estimated
parameters were calculated by the model are indicated in parentheses.

#### Natural mortality

To estimate natural mortality *M*, we explored several methods that
relate *M* with different life history parameters, including time of
sexual maturation and longevity (Charnov 1993, Frisk et al. 2001, Hoenig
1983, Rikhter and Efanov 1976, Roff 1986).

Based on published life-history parameters of skates, sharks and rays
over a wide geographic range, Frisk et al. (2001) developed models that
relate natural mortality of elasmobranch fishes with maximum age and age
of maturity. Based on both of these models, the natural mortality of
longnose skate was estimated at 0.2. Hoenig (1983) developed a model
that related total mortality to the maximum age of fish. Since Hoenig's
analysis was based largely on unexploited fish stocks, total mortality
in his model is often assumed to be natural mortality. Based on Hoenig's
model, longnose skate natural mortality was also estimated as 0.2. In
our model, natural mortality was thus fixed at the level of 0.2.

#### Growth and maturity parameters 

The von Bertalanffy growth parameters (*K*), length at age 1 (*L*~1~)
and length at age 17 (*L*~2~) were estimated within the model. Age 1 and
age 17 were chosen for *L*~1~ and *L*~2~ because they are extreme points
that are still well represented in the data. All three von Bertalanffy
parameters were estimated within the model. Other growth and maturity
parameters, such as CVs for *L*~1~ and *L*~2~, weight-at-length,
maturity-at-length and fecundity-at-weight, were fixed at the levels
estimated outside of SS2.

#### Stock-recruitment relationship

A Beverton-Holt model was used to describe the stock-recruitment
relationship for longnose skate. The level of virgin recruitment
(*R*~0~) was estimated using this relationship, in order to estimate the
magnitude of the initial spawning biomass. In the assessment model,
recruits were taken deterministically from the stock-recruit curve,
largely due to extremely limited age data and in order to avoid fitting
noise. Steepness *h* was fixed at a value of 0.4, to reflect the
*K*-type reproductive strategy of this species.

#### Selectivity

Selectivity parameters used in this assessment are specified as
functions of size. Separate size-based selectivity curves were fit to
the fishery and each survey, except for the NWFSC slope survey, which
was assumed to have the same selectivity as the NWFSC shelf-slope survey
and, therefore, was set to mirror it. To depict selectivity for the
fishery and the three surveys (except for the NWFSC slope survey), we
used a double-normal function, which has six parameters, including (1)
peak, which is the length at which selectivity is fully selected; (2)
width of plateau on the top; (3) width of the ascending part of the
curve (4) width of the descending part of the curve; (5) selectivity at
first size bin; and (6) selectivity at last size bin.

In all cases, we fixed the selectivity of the first size bin (parameter
5), based on the examination of size-composition data. Also, the size
selectivity of NWFSC shelf-slope survey (and, therefore, NWFSC slope
survey) and AFSC slope survey were assumed to be asymptotic. Figure 21
shows frequency of occurrence of longnose skate in the AFSC slope survey
catches by depth. In the last depth stratum of the survey (between 1098
and 1280 m), longnose skate was not found, which indicates that the
survey went deep enough and can be assumed to be asymptotic. NWFSC
shelf-slope and slope surveys extended to the same depth as the AFSC
slope survey (Table 4). We fixed the selectivity at last size bin
(parameter 6) and width of the descending part of the curve (parameter
4) at their maximum values to allow selectivity of these surveys to be
asymptotic. All other size selectivity parameters were estimated in the
model. Since we had limited age information, age-based selectivity was
set to 1.0 for all ages beginning at age 1.

#### NWFSC shelf-slope survey catchability *Q*

The value of the NWFSC shelf-slope survey catchability *Q* used for the
base model was calculated during the STAR Panel. First, a prior for *Q*
was developed following the methodology presented by Patrick Cordue.
Catchability depends on several factors such as latitudinal, vertical
and depth availabilities of fish to the survey gear and the probability
of spatially "available" fish being caught and retained by the gear. To
develop a prior on *Q*, the potential range in the proportion of
vulnerable skates for each factor was specified and "best guesses" for
each range were assumed. Latitudinal and depth availability was
specified based on the survey coverage of the assessment area. Vertical
availability and probability of catch was specified based on the known
behavior of the longnose skate.

The NWFSC shelf-slope survey covers the entire latitudinal range of the
assessment (Table 4); therefore latitudinal availability was assumed to
be 1. The survey appears to exceed the maximum depth distribution of
longnose skate (Figure 21) but may not fully cover the shallow end of
the skate distribution. Therefore, the range for the depth availability
was assumed between 0.95 and 1. Longnose skates are known to bury in the
sand to escape predators, which might cause a portion of skates be
unavailable to the bottom trawl gear. Therefore a range for vertical
availability was assumed between 0.75 and 0.95. Finally, the probability
of spatially available skates being captured and retained was assumed to
be between 0.75 and 1.5, since it is possible that longnose skate might
either avoid trawl nets or (similar to some flatfish) be herded by trawl
gear. "Best guess" estimates were set at the mid-point of the range for
individual factors and the overall best guess for the survey *Q* was
0.83. The minimum, maximum and mid-point values for each category used
to develop prior on *Q* is summarized in Table 10.

We did not use an informative prior on *Q* for the base model, but fixed
*Q* at 0.83, the value of *Q*, estimated as described above. The normal
prior on log(*Q*) was used to provide "low" and "high" *Q*s for
different states of nature used to address uncertainty in survey
catchability.

#### Age-determination error

To establish the level of accuracy of age determination, we used age
readings of the same age structures made by three different readers and
calculated standard deviations of age determination for each true age
(assumed as read by reader 1).

## MODEL SELECTION AND EVALUATION

### Alternative model configurations

We explored many alternative model configurations of varying levels of
complexity in order to realistically describe the population dynamics of
the longnose skate with a parsimonious model and the best available
data. We evaluated the alternative models based on overall model fit and
convergence criteria. The alternative configurations included two-sex
versus single sex models; models that estimates recruitment deviations
versus treating recruits deterministically; and configurations starting
in 1980 in a non-zero equilibrium state versus starting in 1915 with
unfished equilibrium. We explored asymptotic versus dome-shaped size
selectivities, as well as fixed versus estimated von Bertalanffy growth
parameters.

The base run model reflects the best aspects from these exploratory
analyses. It appears to be parameterized enough to fit the observed
data, while maintaining reasonable parameter values and parsimonious
explanations for the underlying model processes. A summary of likelihood
components for the base model is presented in Table 11.

### Conversion criteria

We assessed convergence of the base run model according to the model's
ability to recover similar likelihood estimates when initialized from
dispersed starting points. Results from a set of 15 convergence tests
showed minor variability in the objective function and current
depletion. The Hessian matrix was positive definite for all tests and
the maximum gradient component for the base run was 0.000201095.

### Likelihood profile analysis

The chosen base model included several key parameters for which
assumptions had to be made in the absence of data. These parameters were
fixed based on general information about the species. The key model
parameters that were fixed included natural mortality *M*, steepness of
stock-recruitment curve *h*, and catchability coefficient *Q* of NWFS
shelf-slope survey and discard mortality. Uncertainties in NWFS
shelf-slope survey *Q* and discard mortality were addressed through
sensitivity analyses described later in this report. To explore how
informative the data were with regard to natural mortality and steepness
of the stock-recruitment curve, we performed likelihood profile analyses
where we varied the values of *M* and *h* and recorded the overall fit
of the model. We also looked at how sensitive model outcome was to these
variations.

Likelihood profiles of *M* and *h* along with subsequent changes in the
stock depletion are presented in Figures 22 and 23. For natural
mortality, the best fit of the model was achieved with *M* values of
0.18 and 0.2 (in the base model *M* is fixed at 0.2). For these values
of *M*, the levels of spawning biomass depletion are essentially the
same (65% and 66% respectively). Likelihood profiles on steepness
(values from 0.3-1) showed better fit for the model with high values of
*h*. However, all available information about elasmobranches suggests
that the longnose skate is not likely to be a highly productive species.
The depletion rates for various levels of *h* ranged between 61% and 74
% (Figure 23). Since little is known about longnose skate productivity,
in the base model we selected a value for *h* (0.4) that is towards the
low end of the examined range. This value is precautionary, relative to
values with better fits, but it is also more consistent with the
productivity of other elasmobranches.

## BASE RUN RESULTS

### Model fit

Comparisons between observed and estimated survey biomasses are shown in
Figures 24-27. The model was able to capture general trends for indices
in all surveys except for the AFSC shelf (triennial). The estimated
biomass in the 2004 AFSC shelf (triennial) appeared to be twice as high
as any other estimates in the survey time series. Other surveys
conducted around this time did not detect an increases in stock biomass.
In 2004, the shelf (triennia) survey was conducted by the NWFSC, not by
the AFSC, as in all previous years. Although an effort was made to
replicate AFSC protocols as closely as possible, this change may have
contributed to the substantial increase in the longnose skate biomass
index. Based on similar observed increases in the indices for several
flatfish stocks during the 2005 assessment cycle, a review of 2004
survey implementation was conducted by the NWFSC. However, that review
did not find any obvious implementational reasons for the increases in
flatfish CPUE. We will explore this issue in the future.

Fit to length- and age-frequency data are shown in Figures 28-32. Fits
to length compositions was good. However, the estimated age compositions
did not exhibit a very good fit, which could be explained by the
combination of deterministic recruitment and variations in catch
history. Fit to size-at-age data is presented in Figures 33-34.

### Model estimates

Figures 35-37 show growth and maturity curves, as well as length-weight
relationship estimated by the model. Table 12 and Figures 38-43 show the
total, summary, and spawning biomass, as well as depletion rate relative
to *B*~0~, recruitment and harvest rate time-series, as estimated by the
base model. Population numbers-at-age by year are given in Table 13. The
stock-recruitment relationship is presented in Figure 44. Selectivity
estimates for the fishery and surveys are shown in Figures 45-49.

### State of the stock

The summary of the recent trends in longnose skate exploitation and
estimated population levels are presented in Table 14. Currently, the
stock of the longnose skate in the US West Coast is not overfished
(Figure 50). Historically, the exploitation rate for the longnose skate
has been low. It reached its maximum level of 4.02 % in 1981. Currently,
the stock is at 66% of its unfished level. Since the longnose skate
stock is estimated to be above the overfished level, no rebuilding is
required.

## UNCERTAINTY AND SENSITIVITY ANALYSIS

This assessment reflects a data-moderate to data-poor circumstance with
respect to several influential model elements. The major uncertainties
for the assessment include the longnose skate catch history, Northwest
Fishery Science Center (NWFSC) shelf-slope survey catchability *Q* and
the female maturity schedule.

### Catch history

The catch history of longnose skate reflects retained catch (catch that
was retained and landed), discard and discard mortality. In addition to
uncertainty in those estimates, uncertainty is involved in estimating
the proportion of longnose skate in combined-skate landings, since
historically landings were recorded within the "unspecified skates"
market category. For recent years, the data on longnose skate landings
and discards are reasonably good, however since the discard rate is high
and discard mortality is essentially unknown, there is still
considerable uncertainty about the level of fishing mortality. To
address uncertainties related to longnose skate catch, alternative catch
histories, which reflect variations in the proportion of longnose skate
in combined-skate landings, as well as discard and discard mortality
rates, were developed. In addition to catch history used for the base
model, two alternative catch history scenarios were developed by the
STAR Panel. These alternative catch histories include "low" and "high"
histories, compared with the base model scenario, which was
reconstructed based on the best information about longnose skate catch
history available. Figures 51-53 show base, "low" and "high" longnose
skate catch histories respectively.

The "low" and "high" catch histories were constructed from the landings
estimates presented earlier in this report, but used different
assumptions regarding the proportion of longnose skate in the total
skate landings, the discard, and discard mortality rates. As catch
history in base model, the "low" and "high" catch histories were
constructed outside the model and were entered into an SS2 data file as
total catch. The following formula, developed by STAR Panel, was used to
translate combined-skate landings into longnose skate total catch
(*TC*):

$$\text{TC} = e\frac{p}{b}\left\lbrack 1 + \frac{\text{dm}}{1 - d} \right\rbrack$$

Where *TC* is total catch of longnose skate; *e* is estimated longnose
skate landing, *b* is the proportion of longnose skate in the combined-
skate landing, used to get *e* from a combined-skate landings; *p* is
proportion of longnose skate in the total skate landing to be applied to
construct "low" and high" catch histories, *d* is discard rate to be
applied to construct "low" and high" catch histories, and *m* is discard
mortality rate to be applied to construct "low" and high" catch
histories.

Based on the quality of landed catch records (prior to 1981 records were
less detailed and involved more uncertainty that after 1981) and changes
in skate markets (skate market increased in 1995), three time periods
were defined for the catch history of longnose skate: years up through
1980, 1981-1994, and 1995-present.

In the base model, for the first time period, a constant value (*b* =
0.62) for proportion of longnose skate in the combined-skate landing had
been used. Since 1981 annual values for *b* were estimated from fishery
species compositions and survey catches (as described earlier in this
report). Prior to 1995 (when the skate market changed) discard rate *d*
was assumed to be equal 93% based on Rogers and Pikitch's study (1992),
while since 1995 forward *d* was equal to 53%, based on the data from
ODCP and WCGOP. Discard mortality rate for the entire time of the
assessment was assumed to be 50%. For the "low" and "high" catch
histories, alternative values of *b*, *d* and *m*, calculated by STAR
Panel and shown in Table 15, were used.

Using the parameter values presented in the Table15 for corresponding
time periods, we reconstructed time series for "low" and "high" catch
histories, and conducted alternative runs for each of these scenarios,
tiering off the base model specification. Depletion was estimated to be
75% and 46% for the "low" and "high" catch histories, respectively
(depletion for the base model was estimated as 66%). We used the
alternative catch histories (along with different values of NWFSC
shelf-slope survey catchability *Q*) to define three different states of
nature and to develop decision table (Table 19).

### NWFSC shelf-slope survey catchability *Q*

To address uncertainty in NWFSC shelf-slope survey *Q*, model runs were
performed under base, "low", and "high" levels of *Q*. The value of *Q*
used for the base model was 0.83. For the "low" and "high" levels, we
used values of *Q* calculated by STAR Panel based on the normal prior on
log(*Q*). A random sample of size 10,000 was generated from the normal
distribution and the mean of the samples below the 25th percentile of
the normal distribution was exponentiated to provide the "low" *Q* (low
Q=0.654). The mean of the samples above the 75th percentile was
exponentiated to provide the "high" *Q* (high Q=1.046). Alternative
values of NWFSC shelf-slope survey catchability *Q* (along with
alternative catch histories) were used to define three different states
of nature and to develop the decision table (Table 19).

### Maturity

Uncertainty in female maturity was also explored. A maturity study of
the longnose skate, conducted by McFarlane and King (2006) in the
British Columbia waters, reported that parameters of the maturity curve
were significantly lower than those used in our assessment, as estimated
by Thompson (2006). McFarlane and King (2006) estimated slope of the
maturity function *β* as -0.078, and length at 50% maturity (*L*50%) as
83 cm, while Thomson (2006) estimated *β* as -0.098 and *L*50% as 120
cm. Criteria to distinguish mature individuals from immature differed
between Thompson's and McFarlane and King's studies, but neither
approach could be considered superior to the other. We ran our model
with the values of the maturity function estimated by Thompson (2006)
and then with the values estimated by McFarlane and King (2006). The
depletion of longnose skate in these two runs was 66% and 78%
respectively. For the base model, we used Thompson's data, which is more
likely to undereste the proportion of mature skates. However, we
recommend conducting an additional study of longnose skate maturity to
clarify this issue.

# REFERENCE POINTS

The summary of reference points for the longnose skate is presented in
Table 16. []{#__RefHeading___Toc167637200 .anchor}For the longnose
skate, the management target is defined as 40% of the unfished spawning
stock biomass (SB~40%~), which is estimated to be 2,814 mt (95%
Confidence Interval: 2,608-3,019 mt) in the base model. The stock is
declared overfished if the current spawning biomass is estimated to be
below 25% of unfished level. The MSY-proxy harvest rate for longnose
skate is SPR=F45%, which corresponds to an exploitation rate of 0.043.
This harvest rate provides an equilibrium yield of 1,264 mt (95%
Confidence Interval: 1,194-1,334 mt) at SB~40%~. The model estimate of
maximum sustainable yield (MSY) is 1,268 mt (95% Confidence Interval:
1,198-1,338). The estimated spawning stock biomass at MSY is 2,626 mt
(95% Confidence Interval: 2,433-2,819 mt). The exploitation rate
corresponding to the estimated SPRmsy of F61% is 0.027.

Reference point results are calculated on both a per-recruit and
total-recruits basis. The total-recruits results take into account the
spawner-recruitment relationship with the steepness as defined in the
base model (*h*=0.4). Because of this low steepness and other
reproductive characteristics of the stock, fishing at the target SPR of
45% is expected to reduce the spawning biomass to less than 12% of the
unfished level over the long term. Conversely, fishing at a rate that
would maintain spawning biomass near 40% of the unfished level would
require a target SPR much higher than 45%. The Council's Scientific and
Statistical Committee should consider the appropriateness of using the
current proxy harvest rate for setting the Allowable Biological Catch
for longnose skate.

# HARVEST PROJECTIONS

Tables 17 and 18 shows projections of future catches, summary biomass,
spawning biomass and stock depletion were made based on the current rate
of fishing mortality, as well as F45%. The projected spawning depletion
based on the current level of fishing and F 45% is shown in Figures 54
and 55. The projected spawning biomass was greater than 40% of unfished
level in both cases; therefore no 40:10 harvest control rule adjustment
was made. Optimum yield catch values were equivalent to the values of
ABC.

For this assessment, three states of nature were defined based on the
alternative longnose skate catch history and NWFSC shelf-slope survey
*Q*. The base scenario uses the base catch history and base *Q*
(*Q*=0.83), the "low" scenario uses the low catch history and low *Q*
(*Q*=0.654), and the "high" scenario uses the high catch history and
high *Q* (*Q*=1.046). Ten-year forecasts for each state of nature were
calculated based on F45% for the base scenario. Ten-year forecasts were
also produced with future catch fixed at the average amount (using the
base catch history) for last three years (2004-2006) and at 150% of that
three-year average. Under the "high" scenario, the F45% harvest rate is
projected to reduce the spawning stock biomass below 40% of the unfished
level within two years. In all other scenarios covered by the decision
table, the spawning biomass remains above the target level throughout
the 10-year projection period. The current rate of fishing mortality is
significantly lower than F45% (current exploitation rate is 1.25%).
Therefore, it is very unlikely that the stock, even under the "high"
scenario will fall below 40% of its virgin state in the next 10 years.

# RESEARCH AND DATA NEEDS

This assessment reflects a data-moderate to data-poor circumstance with
respect to several influential model elements, including catch history,
survey catchability, and some life history characteristics.
Consequently, some critical assumptions were based on very limited
supporting data and research. There are several data and research needs
which, if satisfied, could improve the assessment.

Data needs:

4)  Continue species-specific identification in fishery to improve the
    accuracy of fishery catch data;

5)  Continue monitoring discard of the longnose skate;

6)  Resume collecting and processing of vertebra samples for age
    determination to improve the accuracy of growth model parameters and
    size-at-age relationships.

Research needs:

5)  Conduct studies to determine survival rates of discarded longnose
    skate, especially with trawl gear, so that total fishing mortality
    can be estimated more precisely;

6)  Conduct studies on life history characteristics, especially those
    related to maturity and reproduction;

7)  Conduct age-validation studies;

8)  Conduct studies of longnose skate catchability by survey gear types.

# ACKNOWLEDGMENTS

The authors would like wholeheartedly thank everyone who contributed to
the development of this assessment. Rick Methot (NWFSC) for his
constructive suggestions on model design and prompt help with model
files, Beth Horness (NWFSC) and Mark Wilkins (AFSC) for providing survey
data, William Daspit (PacFIN) for providing fishery data, Mark Karnowski
(ODFW) for supplying Oregon fishery and ODCP data, Theresa Tsou (WDFW)
and Gerry Kobylinski (CaDFG) for providing Washington and California
fishery data, Jim Hastie (NWFSC) for supplying WCGOP discard data,
editing this assessment and useful suggestions, Peter Leipzig
(Fishermen\'s Marketing Association) for skate market information, Jean
Rogers for helpful advice and Sean Matson (OSU) for proofreading this
manuscript. Special thanks goes to STAR Panel members Martin Dorn,
Vivian Haist and Patrick Cordue, who significantly improved this
assessment model.

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# 

# 

# 

# 

# 

# 

# 

# 

# 

# TABLES AND FIGURES

## LIST OF TABLES

[Table 1. Summary of fishery-dependent data
42](#__RefHeading___Toc167695639)

[Table 2. Summary of fishery-independent data
43](#__RefHeading___Toc167695640)

[Table 3. Estimated percentage of longnose skate in combined-skate
landings 44](#__RefHeading___Toc167695641)

[Table 4. Surveys used in the assessment by year, latitudinal and depth
ranges 45](#__RefHeading___Toc167695642)

[Table 5. Survey biomass indices (mt) and standard deviation of log
(index) 46](#__RefHeading___Toc167695643)

[Table 6. Sample size for size composition data by source.
47](#__RefHeading___Toc167695644)

[Table 7. Sample size for age data by source.
47](#__RefHeading___Toc167695645)

[Table 8. von Bertalanffy growth parameters estimated in different
studies. 47](#__RefHeading___Toc167695646)

[Table 9. Parameters used for the base model
48](#__RefHeading___Toc167695647)

[Table 10. Minimum, maximum and mid-point values of different factors
affecting survey catchability used to estimate prior of NWFSC
shelf-slope survey log (Q) 49](#__RefHeading___Toc167695648)

[Table 11. The summary of likelihood components for the base model.
50](#__RefHeading___Toc167695649)

[Table 12. Estimated time-series for total, summary and spawning
biomass, recruitment harvest rate and depletion.
51](#__RefHeading___Toc167695650)

[Table 13. Numbers of longnose skate at age, estimated by the base model
53](#__RefHeading___Toc167695651)

[Table 14. Summary of recent trends in longnose skate exploitation and
estimated population levels. 55](#__RefHeading___Toc167695652)

[Table 15. Longnose skate proportion, discard and discard mortality
rates used to reconstruct alternative catch histories.
56](#__RefHeading___Toc167695653)

[Table 16. Summary of reference points for the longnose skate.
57](#__RefHeading___Toc167695654)

[Table 17. 10-year forecast of longnose skate catch, summary biomass,
spawning biomass and stock depletion estimated based on current rate of
fishing mortality. 58](#__RefHeading___Toc167695655)

[Table 18. 10-year forecast of longnose skate catch, summary biomass,
spawning biomass and stock depletion estimated based on F45%.
58](#__RefHeading___Toc167695656)

[Table 19. Decision table based on alternative states of nature
59](#__RefHeading___Toc167695657)

## 

## 

## 

## 

## 

## 

## 

## 

## 

## 

## TABLES

[]{#__RefHeading___Toc167695639 .anchor}Table 1. Summary of
fishery-dependent data used in the assessment by source and year since
1980.

![](media/image14.wmf){width="9.065972222222221in"
height="4.7243055555555555in"}

[]{#__RefHeading___Toc167695640 .anchor}Table 2. Summary of
fishery-independent data used in the assessment by source and year.

![](media/image15.wmf){width="9.0in" height="3.3868055555555556in"}

[]{#__RefHeading___Toc167695641 .anchor}Table 3. Estimated percentage of
longnose skate in combined-skate landings by state and year (for the
pre-1981, percentage of longnose skate in combined-skate landings is
assumed as 62%).

![](media/image16.wmf){width="3.5368055555555555in"
height="4.664583333333334in"}

[]{#__RefHeading___Toc167695642 .anchor}Table 4. Surveys used in the
assessment by year, latitudinal and depth ranges.

![](media/image17.wmf){width="4.675in" height="5.824305555555555in"}

[]{#__RefHeading___Toc167695643 .anchor}Table 5. Survey biomass indices
(mt) and standard deviation of log (index), calculated
as$\sqrt{\text{ln}\left( 1 + \text{CV}^{2} \right)}$.

![](media/image18.wmf){width="7.455555555555556in"
height="3.321527777777778in"}

[]{#__RefHeading___Toc167695644 .anchor}Table 6. Sample size for size
composition data (both sexes combined) by source.

![](media/image19.wmf){width="6.1in" height="2.4347222222222222in"}

[]{#__RefHeading___Toc167695645 .anchor}Table 7. Sample size for age
data (both sexes combined) by source.

![](media/image20.wmf){width="3.2041666666666666in"
height="0.7194444444444444in"}

[]{#__RefHeading___Toc167695646 .anchor}Table 8. von Bertalanffy growth
parameters estimated in different studies.

![](media/image21.wmf){width="4.988888888888889in"
height="0.9472222222222222in"}

[]{#__RefHeading___Toc167695647 .anchor}Table 9. Parameters used for the
base model.

![](media/image22.wmf){width="5.999305555555556in"
height="8.635416666666666in"}

[]{#__RefHeading___Toc167695648 .anchor}Table 10. Minimum, maximum and
mid-point values of different factors affecting survey catchability used
to estimate prior of NWFSC shelf-slope survey log (Q).

![](media/image23.wmf){width="4.269444444444445in" height="1.0625in"}

[]{#__RefHeading___Toc167695649 .anchor}Table 11. The summary of
likelihood components for the base model.

![](media/image24.wmf){width="2.767361111111111in"
height="2.4145833333333333in"}

![](media/image25.wmf){width="9.243055555555555in"
height="0.9409722222222222in"}

Fleet1=fishery

Fleet 2=NWFSC shelf-slope survey

Fleet 3=NWFSC slope survey

Fleet 4=AFSC shelf (triennial) survey

Fleet 5=AFSC slope survey

[]{#__RefHeading___Toc167695650 .anchor}Table 12. Estimated time-series
for total, summary and spawning biomass, recruitment harvest rate and
depletion (continued on the next page).

![](media/image26.wmf){width="6.197222222222222in"
height="6.800694444444445in"}

Table 12 (continuation). Estimated time-series for total, summary and
spawning biomass, recruitment harvest rate and depletion.

![](media/image27.wmf){width="6.268055555555556in"
height="6.725694444444445in"}

[]{#__RefHeading___Toc167695651 .anchor}Table 13. Numbers of longnose
skate at age, estimated by the base model (continued on the next page).

![](media/image28.wmf){width="9.359722222222222in"
height="5.072222222222222in"}

Table 13 (continuation). Numbers of longnose skate at age, estimated by
the base model.

![](media/image29.wmf){width="9.597916666666666in"
height="5.115277777777778in"}

[]{#__RefHeading___Toc167695652 .anchor}Table 14. Summary of recent
trends in longnose skate exploitation and estimated population levels.

![](media/image30.wmf){width="9.234027777777778in"
height="1.9729166666666667in"}

\* indicates values calculated as the average for the last three years
(2004-2006)

[]{#__RefHeading___Toc167695653 .anchor}Table 15. Longnose skate
proportion, discard and discard mortality rates used to reconstruct
alternative catch histories.

![](media/image31.wmf){width="5.661111111111111in"
height="1.320138888888889in"}

[]{#__RefHeading___Toc167695654 .anchor}Table 16. Summary of reference
points for the longnose skate.

![](media/image32.wmf){width="5.928472222222222in"
height="3.6618055555555555in"}

[]{#__RefHeading___Toc167695655 .anchor}Table 17. 10-year forecast of
longnose skate catch, summary biomass, spawning biomass and stock
depletion estimated based on current rate of fishing mortality.

![](media/image33.wmf){width="6.215277777777778in"
height="1.9131944444444444in"}

[]{#__RefHeading___Toc167695656 .anchor}Table 18. 10-year forecast of
longnose skate catch, summary biomass, spawning biomass and stock
depletion estimated based on F45%.

![](media/image34.wmf){width="6.215277777777778in"
height="1.9131944444444444in"}

[]{#__RefHeading___Toc167695657 .anchor}Table 19. Decision table based
on alternative states of nature, defined based on

alternative catch histories and different levels of NWFSC shelf-slope
survey catchability *Q*.

![](media/image35.wmf){width="9.243055555555555in"
height="5.233333333333333in"}

[]{#__RefHeading___Toc167637207 .anchor}**LIST OF FIGURES:**

[Figure1. Photograph of longnose skate, Raja rhina.
63](#__RefHeading___Toc167697386)

[Figure 2. Size distribution of longnose skate by depth.
64](#__RefHeading___Toc167697387)

[Figure 3. Area map for longnose skate assessment
65](#__RefHeading___Toc167697388)

[Figure 4. PacFIN skate landings by gear
66](#__RefHeading___Toc167697389)

[Figure 5. The number of boat trips when skates were landed by state and
by year. 67](#__RefHeading___Toc167697390)

[Figure 6. Time-series of combined-skate landings by year and state
68](#__RefHeading___Toc167697391)

[Figure 7. Estimated longnose skate landings by year.
69](#__RefHeading___Toc167697392)

[Figure 8. Length composition of longnose skate caught in fishery.
70](#__RefHeading___Toc167697393)

[Figure 9. Relationship between total length and disk width
71](#__RefHeading___Toc167697394)

[Figure 10. Estimated biomass of the longnose skate from NWFSC slope
survey. 72](#__RefHeading___Toc167697395)

[Figure 11. Estimated biomass of the longnose skate from NWFSC
shelf-slope survey. 73](#__RefHeading___Toc167697396)

[Figure 12. Estimated biomass of the longnose skate from AFSC shelf
(triennial) survey. 74](#__RefHeading___Toc167697397)

[Figure 13. Estimated biomass of the longnose skate from AFSC slope
survey. 75](#__RefHeading___Toc167697398)

[Figure 14. Length composition of longnose skate caught in the NWFSC
shelf-slope survey. 76](#__RefHeading___Toc167697399)

[Figure 15. Length composition of longnose skate caught in the AFSC
shelf (triennial) survey. 77](#__RefHeading___Toc167697400)

[Figure 16. Length composition of longnose skate caught in the AFSC
slope survey. 78](#__RefHeading___Toc167697401)

[Figure 17. Age composition of longnose skate caught in the NWFSC
shelf-slope survey. 79](#__RefHeading___Toc167697402)

[Figure 18. Size-at-age data of longnose skate caught in fishery.
80](#__RefHeading___Toc167697403)

[Figure 19. Size-at-age data of longnose skate collected in the NWFSC
shelf-slope survey. 81](#__RefHeading___Toc167697404)

[Figure 20. Time-series of estimated longnose skate total catch.
82](#__RefHeading___Toc167697405)

[Figure 21. Longnose skate frequency of occurrence in AFSC slope survey
by depth. 83](#__RefHeading___Toc167697406)

[Figure 22. Likelihood profile analysis for natural mortality
84](#__RefHeading___Toc167697407)

[Figure 23. Likelihood profile analysis for stock-recruitment curve
steepness. 84](#__RefHeading___Toc167697408)

[Figure 24. Observed and expected values of biomass index (mt) for the
NWFSC shelf-slope survey. 85](#__RefHeading___Toc167697409)

[Figure 25. Observed and expected values of biomass index (mt) for the
NWFSC slope survey. 86](#__RefHeading___Toc167697410)

[Figure 26. Observed and expected values of biomass index (mt) for the
AFSC triennial shelf survey. 87](#__RefHeading___Toc167697411)

[Figure 27. Observed and expected biomass index (mt) for the AFSC slope
survey. 88](#__RefHeading___Toc167697412)

[Figure 28. Fit to fishery length frequency of longnose skate .
89](#__RefHeading___Toc167697413)

[Figure 29. Fit to length frequency of longnose skate for NWFSC
shelf-slope survey. 90](#__RefHeading___Toc167697414)

[Figure 30. Fit to length frequency of longnose skate for AFSC shelf
(triennial) survey. 91](#__RefHeading___Toc167697415)

[Figure 31. Fit to length frequency of longnose skate for AFSC slope
survey. 92](#__RefHeading___Toc167697416)

[Figure 32. Fit to age frequency of longnose skate for NWFSC shelf-slope
survey. 93](#__RefHeading___Toc167697417)

[Figure 33.Fit to size-at-age data of longnose skate caught in fishery.
94](#__RefHeading___Toc167697418)

[Figure 34. Fit to size-at-age data of longnose skate caught in NWFSC
shelf-slope survey 95](#__RefHeading___Toc167697419)

[Figure 35. Growth curve of longnose skate estimated by the base model.
96](#__RefHeading___Toc167697420)

[Figure 36. Maturity curve of female longnose skate estimated by the
base model. 97](#__RefHeading___Toc167697421)

[Figure 37. Length-weight relationship for longnose skate estimated by
the base model. 98](#__RefHeading___Toc167697422)

[Figure 38. Time-series of total biomass, estimated by the base-run
model 99](#__RefHeading___Toc167697423)

[Figure 39. Time-series of summary biomass, estimated by the base-run
model 100](#__RefHeading___Toc167697424)

[Figure 40. Time-series of spawning biomass, estimated by the base-run
model 101](#__RefHeading___Toc167697425)

[Figure 41. Time-series of spawning depletion, estimated by the base-run
model 102](#__RefHeading___Toc167697426)

[Figure 42. Time-series of recruitment, estimated by the base-run model
103](#__RefHeading___Toc167697427)

[Figure 43. Time-series of harvest rate, estimated by the base-run model
104](#__RefHeading___Toc167697428)

[Figure 44. Stock recruitment relationship, estimated by the base-run
model 105](#__RefHeading___Toc167697429)

[Figure 45. Fishery selectivity, estimated by the base-run model
106](#__RefHeading___Toc167697430)

[Figure 46. Selectivity for NWFSC shelf-slope survey, estimated by the
base-run model 107](#__RefHeading___Toc167697431)

[Figure 47. Selectivity for NWFSC slope survey
108](#__RefHeading___Toc167697432)

[Figure 48. Selectivity for AFSC triennial shelf survey, estimated by
the base model 109](#__RefHeading___Toc167697433)

[Figure 49. Selectivity estimates for AFSC slope survey
110](#__RefHeading___Toc167697434)

[Figure 50. Exploitation rate and spawning biomass relative to their
target values 111](#__RefHeading___Toc167697435)

[Figure 51. Base catch history for longnose skate
112](#__RefHeading___Toc167697436)

[Figure 52. "Low" catch history for longnose skate
113](#__RefHeading___Toc167697437)

[Figure 53. "High" catch history for longnose skate
114](#__RefHeading___Toc167697438)

[Figure 54. Spawning depletion of longnose skate with future projection
calculated under current fishing mortality rate
115](#__RefHeading___Toc167697439)

[Figure 55. Spawning depletion of longnose skate with future projection
calculated under F 45% 116](#__RefHeading___Toc167697440)

## 

## 

## 

## 

## 

## 

## 

## 

## 

## 

## 

[]{#__RefHeading___Toc167637208 .anchor}**FIGURES**

![](media/image36.jpeg){width="5.277777777777778in"
height="3.638888888888889in"}

[]{#__RefHeading___Toc167697386 .anchor}Figure1. Photograph of longnose
skate, Raja rhina.

![](media/image37.wmf){width="5.992361111111111in"
height="4.010416666666667in"}

[]{#__RefHeading___Toc167697387 .anchor}Figure 2. Size distribution of
longnose skate by depth, calculated from AFSC triennial survey
(1980-2004) (x-axis represents upper threshold values of 100 m depth
intervals).

![](media/image38.png){width="5.208333333333333in"
height="6.489583333333333in"}

[]{#__RefHeading___Toc167697388 .anchor}Figure 3. Area map for longnose
skate assessment that includes International Northern Pacific Fisheries
Council (INPFC) fisheries management regions defined by latitude.

![](media/image39.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697389 .anchor}Figure 4. PacFIN skate landings
by gear averaged for the last 25 years, indicating that 97% of landed
catch was brought by trawl fishery.

![](media/image40.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697390 .anchor}Figure 5. The number of boat
trips when skates were landed by state and by year.

![](media/image41.wmf){width="6.499305555555556in"
height="4.254861111111111in"}

[]{#__RefHeading___Toc167697391 .anchor}Figure 6. Time-series of
combined-skate landings by year and state.

![](media/image42.wmf){width="6.247916666666667in"
height="4.090277777777778in"}

[]{#__RefHeading___Toc167697392 .anchor}Figure 7. Estimated longnose
skate landings by year.

![](media/image43.wmf){width="6.372916666666667in"
height="6.363888888888889in"}

[]{#__RefHeading___Toc167697393 .anchor}Figure 8. Length composition of
longnose skate (both sexes combined) caught in fishery.

![](media/image44.wmf){width="5.997222222222222in"
height="3.936111111111111in"}

[]{#__RefHeading___Toc167697394 .anchor}Figure 9. Relationship between
total length (TL) and disk width (DW) for the longnose skate received
from 1999 AFSC slope survey (
$\text{TL} = 7\text{.}\text{36} + 1\text{.}\text{41} \cdot \text{DW}$).

![](media/image45.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697395 .anchor}Figure 10. Estimated biomass of
the longnose skate from NWFSC slope survey.

![](media/image46.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697396 .anchor}Figure 11. Estimated biomass of
the longnose skate from NWFSC shelf-slope survey.

![](media/image47.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697397 .anchor}Figure 12. Estimated biomass of
the longnose skate from AFSC shelf (triennial) survey.

![](media/image48.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697398 .anchor}Figure 13. Estimated biomass of
the longnose skate from AFSC slope survey.

![](media/image49.wmf){width="6.250694444444444in"
height="6.241666666666666in"}

[]{#__RefHeading___Toc167697399 .anchor}Figure 14. Length composition of
longnose skate (both sexes combined) caught in the NWFSC shelf-slope
survey.

![](media/image50.wmf){width="6.121527777777778in" height="6.1125in"}

[]{#__RefHeading___Toc167697400 .anchor}Figure 15. Length composition of
longnose skate (both sexes combined) caught in the AFSC shelf
(triennial) survey.

![](media/image51.wmf){width="6.250694444444444in"
height="6.241666666666666in"}

[]{#__RefHeading___Toc167697401 .anchor}Figure 16. Length composition of
longnose skate (both sexes combined) caught in the AFSC slope survey.

![](media/image52.wmf){width="6.236805555555556in"
height="6.227777777777778in"}

[]{#__RefHeading___Toc167697402 .anchor}Figure 17. Age composition of
longnose skate (both sexes combined) caught in the NWFSC shelf-slope
survey (2003).

![](media/image53.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697403 .anchor}Figure 18. Size-at-age data of
longnose skate (both sexes combined) caught in fishery.

![](media/image54.wmf){width="5.992361111111111in"
height="3.9944444444444445in"}

[]{#__RefHeading___Toc167697404 .anchor}Figure 19. Size-at-age data of
longnose skate (both sexes combined) collected in the NWFSC shelf-slope
survey.

![](media/image55.wmf){width="6.499305555555556in"
height="4.254861111111111in"}

[]{#__RefHeading___Toc167697405 .anchor}Figure 20. Time-series of
estimated longnose skate total catch.

![](media/image56.wmf){width="5.884027777777778in"
height="6.631944444444445in"}

[]{#__RefHeading___Toc167697406 .anchor}Figure 21. Longnose skate
frequency of occurrence in AFSC slope survey by depth (1984-1996).

![](media/image57.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697407 .anchor}Figure 22. Likelihood profile
analysis for natural mortality

![](media/image58.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697408 .anchor}Figure 23. Likelihood profile
analysis for stock-recruitment curve steepness *h*.

![](media/image59.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697409 .anchor}Figure 24. Observed and expected
values of biomass index (mt) for the NWFSC shelf-slope survey.

![](media/image60.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697410 .anchor}Figure 25. Observed and expected
values of biomass index (mt) for the NWFSC slope survey.

![](media/image61.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697411 .anchor}Figure 26. Observed and expected
values of biomass index (mt) for the AFSC triennial shelf survey.

![](media/image62.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697412 .anchor}Figure 27. Observed and expected
biomass index (mt) for the AFSC slope survey.

![](media/image63.wmf){width="6.250694444444444in"
height="6.241666666666666in"}

[]{#__RefHeading___Toc167697413 .anchor}Figure 28. Fit to fishery length
frequency of longnose skate (both sexes combined).

![](media/image64.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697414 .anchor}Figure 29. Fit to length
frequency of longnose skate (both sexes combined) for NWFSC shelf-slope
survey.

![](media/image65.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697415 .anchor}Figure 30. Fit to length
frequency of longnose skate (both sexes combined) for AFSC shelf
(triennial) survey.

![](media/image66.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697416 .anchor}Figure 31. Fit to length
frequency of longnose skate (both sexes combined) for AFSC slope survey.

![](media/image67.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697417 .anchor}Figure 32. Fit to age frequency
of longnose skate (both sexes combined) for NWFSC shelf-slope survey.

![](media/image68.wmf){width="6.121527777777778in"
height="6.127083333333333in"}

[]{#__RefHeading___Toc167697418 .anchor}Figure 33.Fit to size-at-age
data of longnose skate caught in fishery.

![](media/image69.wmf){width="6.121527777777778in"
height="6.127083333333333in"}

[]{#__RefHeading___Toc167697419 .anchor}Figure 34. Fit to size-at-age
data of longnose skate caught in NWFSC shelf-slope survey.

![](media/image70.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697420 .anchor}Figure 35. Growth curve of
longnose skate (both sexes combined) estimated by the base model.

![](media/image71.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697421 .anchor}Figure 36. Maturity curve of
female longnose skate estimated by the base model.

![](media/image72.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697422 .anchor}Figure 37. Length-weight
relationship for longnose skate estimated by the base model.

![](media/image73.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697423 .anchor}Figure 38. Time-series of total
biomass, estimated by the base-run model.

![](media/image74.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697424 .anchor}Figure 39. Time-series of
summary biomass, estimated by the base-run model.

![](media/image75.wmf){width="5.999305555555556in"
height="4.041666666666667in"}

[]{#__RefHeading___Toc167697425 .anchor}Figure 40. Time-series of
spawning biomass, estimated by the base-run model.

![](media/image76.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697426 .anchor}Figure 41. Time-series of
spawning depletion, estimated by the base-run model.

![](media/image77.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697427 .anchor}Figure 42. Time-series of
recruitment, estimated by the base-run model.

![](media/image78.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697428 .anchor}Figure 43. Time-series of
harvest rate, estimated by the base-run model.

![](media/image79.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697429 .anchor}Figure 44. Stock recruitment
relationship, estimated by the base-run model.

![](media/image80.wmf){width="7.177083333333333in"
height="7.166666666666667in"}

[]{#__RefHeading___Toc167697430 .anchor}Figure 45. Fishery selectivity,
estimated by the base-run model.

![](media/image81.wmf){width="7.177083333333333in"
height="7.166666666666667in"}

[]{#__RefHeading___Toc167697431 .anchor}Figure 46. Selectivity for NWFSC
shelf-slope survey, estimated by the base-run model.

![](media/image82.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697432 .anchor}Figure 47. Selectivity for NWFSC
slope survey (mirrored to NWFSC shelf-slope survey).

![](media/image83.wmf){width="7.177083333333333in"
height="7.166666666666667in"}

[]{#__RefHeading___Toc167697433 .anchor}Figure 48. Selectivity for AFSC
triennial shelf survey, estimated by the base model.

![](media/image84.wmf){width="7.177083333333333in"
height="7.166666666666667in"}

[]{#__RefHeading___Toc167697434 .anchor}Figure 49. Selectivity estimates
for AFSC slope survey.

![](media/image8.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697435 .anchor}Figure 50. Exploitation rate and
spawning biomass relative to their target values (circle indicates the
point that corresponds to 2007).

![](media/image85.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697436 .anchor}Figure 51. Base catch history
for longnose skate, reconstructed based on the best information about
longnose skate catch available.

![](media/image86.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697437 .anchor}Figure 52. "Low" catch history
for longnose skate (see section Uncertainty and sensitivity analysis and
Table 15 for values used for proportion of longnose skate in
combined-skate catches, discard and discard mortality rates).

![](media/image87.wmf){width="5.996527777777778in"
height="3.9256944444444444in"}

[]{#__RefHeading___Toc167697438 .anchor}Figure 53. "High" catch history
for longnose skate (see section Uncertainty and sensitivity analysis and
Table 15 for values used for proportion of longnose skate in
combined-skate catches, discard and discard mortality rates).

![](media/image88.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697439 .anchor}Figure 54. Spawning depletion of
longnose skate with future projection calculated under current fishing
mortality rate.

![](media/image89.wmf){width="5.992361111111111in"
height="5.9840277777777775in"}

[]{#__RefHeading___Toc167697440 .anchor}Figure 55. Spawning depletion of
longnose skate with future projection calculated under F 45%.

[]{#__RefHeading___Toc167637209 .anchor}**APPENDIX 1:** List of STAR
Panel requests

During the STAR Panel review of the assessment, analysis and evaluation
of the base model were performed. These analyses and evaluations caused
changes in the base model specifications. These changes significantly
improved the assessment model. This appendix provides an overview of
changes to the base model that were implemented during the STAR panel
review, as well as requests by the STAR Panel for additional model runs
that were conducted during the review.

Prior to the STAR Panel, the base model had the following
characteristics:

-   The model began in 1980 and assumed non-zero equilibrium catch in
    1979;

-   Landed and discarded catch were entered separately in the SS2 data
    file;

-   Historical landed catch records (1951-1980) were used only to
    estimate initial equilibrium catch;

-   Model included two sexes;

-   Natural mortality *M* was fixed at 0.1

-   Two out of three parameters of von Bertalanffy growth model (*L*~1~
    and *L*~2~) were estimated, while the third parameter (*K*) was
    fixed;

-   From1984 forward, the model treated recruits stochastically and
    recruitment deviations were estimated;

-   NWFSC slope-shelf survey *Q* was fixed at 1;

-   Selectivities of slope surveys were not fixed asymptotic;

-   The model used a "data point" approach for iterative re-weighting.

After the STAR Panel, the base model for the longnose skate has the
following features:

-   The model begins in 1916 and assumes unfished equilibrium in 1915;

-   Landed catch and discard mortality are combined in the data file as
    total catch, estimated outside of SS2;

-   Historical records (1951-1980) are used to reconstruct time-series
    of longnose skate catches, with a linear increase in catches from
    1916 to 1951;

-   Model includes one sex;

-   Natural mortality *M* is fixed at 0.2;

-   All three parameters of von Bertalanffy growth parameters (*L*~1~,
    *L*~2~ and *K*) are estimated;

-   Recruits are treated deterministically, and are taken from the
    estimated stock-recruit curve;

-   NWFSC slope-shelf survey *Q* is fixed at 0.83;

-   Selectivities of slope surveys are fixed asymptotic;

-   Iterative re-weighting was conducted by applying the same adjustment
    to all points in each data series..

The STAR Panel requested model changes in five series. All of the STAR
Panel requests were reflected in new base model and current assessment
report.

**STAR panel requests for longnose skate analyses (Series 1)**

Modify base case (from current formulation):

-   One sex model

-   No recruitment deviations

-   Use F45% proxy for MSY

-   Do not assume discards on historical catch estimates, rather adjust
    the catch series to account for discarding, proportion of longnose
    skate in skate catch, discard mortality, etc.

A.  Do fits using the base case formulation as adjusted above, with the
    equilibrium non-zero catch initialization (in 1980) to:

    1.  The "best" historical catch (same as current)

    2.  The low historical catch (see below)

    3.  The high historical catch (see below)

For these three series we are interested to see the biomass trajectories
and a summary of the likelihood components.

B. Do a fit initializing the population at equilibrium conditions in
1915, with catches ramping up from 0 to the high historical catch
between 1915 and 1950 and constant at the high historical level from
1951 to 1980. Show a comparison of the estimated 1980 age structure from
this run and from run A3 above. This run is formulated the same as the
runs "A" above, other than in how the population is initialized.

C. Based on run A1 above: Modify selectivity for the two slope surveys
to be asymptotic. Do a profile on *q*.

D. AFSC triennial survey data. Jim Hastie is getting summary information
so that potential bias in catchability in the 2004 survey can be
investigated.

**STAR panel requests for longnose skate analyses (Series 2)**

> The updated base case continues from changes made under the Series 1
> requested changes (One sex model, no recruitment deviations).
> Additional changes to the new update base case will include:

-   Washington State 1950-1979 catches will be removed

-   *M*=0.2 (subject to evaluating basis for this)

-   Population to be initialized at equilibrium in 1916

-   Re-do the iterative re-weighting of fishery sample sizes using the
    output from SS2 (i.e., rescale a series, rather than individual
    samples)

-   Slope surveys selectivity parameters; asymptotic selectivity,
    estimate peak parameter, and no estimation of descending width
    parameters (because it had no influence on the fits)

> For this new base case:

A.  Fit to the "best" catch data series

B.  Separate fits to the "low catch" and "high catch" series

C.  Profile on *q* (NWFSC shelf-slope survey) for the "best" catch
    series run

D.  Do a fit using the B.C. estimates of maturity at length ("best"
    catch series)

E.  Provide supporting information for *M*=0.2

F.  For one run (e.g., base case with "best" catch series) try different
    techniques to see if you find alternative minima (jittering or other
    method to begin with different initial parameter estimates and
    different phases for the parameters).

**STAR panel requests for longnose skate analyses (Series 3)**

New base case:

-   fix one parameter (descending limb) of fishery selectivity

-   add priors for *q* and *M*

-   finish iterative re-weighting for sample sizes

-   keep the Thompson estimates of maturity for base case

-   add extra error to AFSC shelf survey (so that the RMSEs are similar
    to SEs)

1)  Run base case scenario with "best" catch series. Produce R graphics
    for this run.

2)  Run base case formulation with low catch series

3)  Run base case formulation with high catch series

4)  Run model with B.C. maturity estimates (otherwise same formulation
    as base case)

**STAR panel requests for longnose skate analyses (Series 4)**

Base case as defined in previous request:

1)  Run base case formulation using the low catch series but fixing the
    shelf-slope survey *q* at the value estimated for the base case run
    (using the "best" catch series)

2)  Run base case formulation using the high catch series but fixing the
    shelf-slope survey *q* at the value estimated for the base case run
    (using the "best" catch series)

**STAR panel requests for longnose skate analyses (Series 5)**

Base case as defined in previous request, except that M is fixed 0.2 and
the NWFSC shelf-slope survey *q* is fixed at 0.83. Three runs:

1)  Low *q* (0.654) and low catch history

2)  Mid *q* (0.83) and mid catch history

3)  High *q* (1.046) and high catch history

[]{#__RefHeading___Toc167637210 .anchor}**APPENDIX 2:** Codes for the
longnose skate assessment model

**SS2 data file**

1916 #\_styr

2008 #\_endyr

1 #\_nseas

12 #\_months/season

1 #\_spawn_seas

1 #\_Nfleet

4 #\_Nsurv

fishery1%survey1_NWFSC_shelf_slope%survey2_NWFSC_slope%survey3_Triennial%Survey4_AFSC_Slope

0.5 0.5 0.66 0.66 0.9 #\_surveytiming_in_season

1 #\_Ngenders

24 #\_Nages

#\_catch_biomass(mtons):\_columns_are_fisheries,\_rows_are_year\*season\"

0 #\_init_equil_catch_for_each_fishery (1915)

19.62103302 #1916

39.24206604 #1917

58.86309906 #1918

78.48413208 #1919

98.1051651 #1920

117.7261981 #1921

137.3472311 #1922

156.9682642 #1923

176.5892972 #1924

196.2103302 #1925

215.8313632 #1926

235.4523962 #1927

255.0734293 #1928

274.6944623 #1929

294.3154953 #1930

313.9365283 #1931

333.5575613 #1932

353.1785944 #1933

372.7996274 #1934

392.4206604 #1935

412.0416934 #1936

431.6627264 #1937

451.2837595 #1938

470.9047925 #1939

490.5258255 #1940

510.1468585 #1941

529.7678915 #1942

549.3889245 #1943

569.0099576 #1944

588.6309906 #1945

608.2520236 #1946

627.8730566 #1947

647.4940896 #1948

667.1151227 #1949

367.57568 #1950

264.31344 #1951

298.89208 #1952

913.72872 #1953

333.47072 #1954

948.78104 #1955

422.04888 #1956

365.20728 #1957

379.89136 #1958

517.25856 #1959

315.94456 #1960

1568.35448 #1961

878.6764 #1962

994.728 #1963

972.46504 #1964

553.25824 #1965

681.62552 #1966

677.3624 #1967

1191.77888 #1968

771.62472 #1969

428.20672 #1970

186.62992 #1971

287.99744 #1972

294.15528 #1973

287.52376 #1974

325.41816 #1975

891.93944 #1976

898.09728 #1977

1453.72392 #1978

1542.77576 #1979

998.51744 #1980

3212.684566 #1981

2165.499881 #1982

1676.587936 #1983

862.63616 #1984

1242.938008 #1985

1026.139441 #1986

1177.537321 #1987

759.7376229 #1988

838.3027082 #1989

661.0358749 #1990

563.9250269 #1991

334.0527082 #1992

523.0623677 #1993

735.481455 #1994

367.3896881 #1995

1474.014567 #1996

2685.460845 #1997

1220.16021 #1998

1835.376757 #1999

2108.321244 #2000

1342.347064 #2001

487.5559279 #2002

1323.043348 #2003

581.5133621 #2004

959.0928615 #2005

1157.063834 #2006

899.2233525 #2007

899.2233525 #2008

21 #\_N_cpue_and_surveyabundance_observations
#(2-NWFSC_shelf_slope,3-NWFSC_slope,4-Triennnial,5-AFSC_Slope)

#\_year seas index obs se(log)

#NWFS Slope_shelf survey (30-700 fm)

2003 1 2 50768.03368 0.084145859 #\_orig_obs:

2004 1 2 55648.33897 0.073307751 #\_orig_obs:

2005 1 2 50762.1337 0.063176781 #\_orig_obs:

2006 1 2 55267.92954 0.083718657 #\_orig_obs:

#NWFS Slope survey (100-700 fm)

1999 1 3 28431.13646 0.128927013 #\_orig_obs:

2000 1 3 24002.32992 0.165365711 #\_orig_obs:

2001 1 3 24150.43873 0.143851631 #\_orig_obs:

2002 1 3 27022.31278 0.097986123 #\_orig_obs:

#Triennial (30-200 fm)

1980 1 4 968 0.218 #\_orig_obs:

1983 1 4 1453 0.149 #\_orig_obs:

1986 1 4 1552 0.162 #\_orig_obs:

1989 1 4 3049 0.179 #\_orig_obs:

1992 1 4 1672 0.162 #\_orig_obs:

1995 1 4 1635 0.156 #\_orig_obs:

1998 1 4 3733 0.159 #\_orig_obs:

2001 1 4 3180 0.084 #\_orig_obs:

2004 1 4 7827 0.093 #\_orig_obs:

#AFSC Slope (100-700 fm)

1997 1 5 17226 0.12389778 #\_orig_obs:

1999 1 5 14199 0.108038426 #\_orig_obs:

2000 1 5 13748 0.12580153 #\_orig_obs:

2001 1 5 14278 0.122041609 #\_orig_obs:

2 #\_discard_type(1=biomass;\_2=fraction)

0 #\_N_discard_obs

0 #\_N_meanbodywt_obs

#Yr Seas Type Part Value CV

#2006 1 1 1 2.58 0.95

0.0001 #\_comp_tail_compression

0.0001 #\_add_to_comp

#\_N_LengthBins

27

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120
125 130 135 140 145

22 #\_N_Length_obs

#Yr Seas Flt/Svy Gender Part Nsamp datavector(female-male)

#Fishery

1995 1 1 0 0 53 0 0 0 0 0 0 0 0 0 0 0.037735849 0.056603774 0.018867925
0.075471698 0.188679245 0.113207547 0.075471698 0.150943396 0.094339623
0.037735849 0.056603774 0.075471698 0.018867925 0 0 0 0

1996 1 1 0 0 99 0 0 0 0 0 0 0 0 0.01010101 0 0.02020202 0.050505051
0.101010101 0.151515152 0.181818182 0.111111111 0.111111111 0.111111111
0.050505051 0.04040404 0.03030303 0.01010101 0.01010101 0.01010101 0 0 0

1997 1 1 0 0 459 0 0 0 0 0 0.002178649 0 0.004357298 0.013071895
0.021786492 0.047930283 0.054466231 0.087145969 0.091503268 0.145969499
0.126361656 0.104575163 0.098039216 0.054466231 0.067538126 0.023965142
0.026143791 0.021786492 0.006535948 0.002178649 0 0

1998 1 1 0 0 84 0 0 0 0 0 0.011904762 0.047619048 0.023809524 0
0.047619048 0.011904762 0.071428571 0.083333333 0.178571429 0.142857143
0.119047619 0.130952381 0.035714286 0.035714286 0.023809524 0.011904762
0.023809524 0 0 0 0 0

1999 1 1 0 0 311 0 0 0 0 0 0 0.003215434 0 0.006430868 0.009646302
0.025723473 0.035369775 0.048231511 0.08681672 0.144694534 0.15755627
0.135048232 0.090032154 0.067524116 0.073954984 0.061093248 0.028938907
0.006430868 0.012861736 0.006430868 0 0

2000 1 1 0 0 299 0 0 0 0 0 0 0 0 0 0 0.013377926 0.040133779 0.053511706
0.110367893 0.127090301 0.143812709 0.123745819 0.120401338 0.080267559
0.063545151 0.043478261 0.046822742 0.023411371 0.006688963 0
0.003344482 0

2001 1 1 0 0 457 0 0 0 0 0 0 0 0.006564551 0.002188184 0.015317287
0.035010941 0.050328228 0.080962801 0.096280088 0.148796499 0.13785558
0.120350109 0.083150985 0.061269147 0.054704595 0.054704595 0.021881838
0.013129103 0.006564551 0.010940919 0 0

2002 1 1 0 0 235 0 0 0 0 0 0 0 0 0 0.004255319 0 0.034042553 0.063829787
0.131914894 0.165957447 0.157446809 0.157446809 0.085106383 0.068085106
0.029787234 0.063829787 0.034042553 0.004255319 0 0 0 0

2003 1 1 0 0 518 0 0 0 0 0 0 0 0.013513514 0.019305019 0.027027027
0.063706564 0.079150579 0.084942085 0.104247104 0.115830116 0.106177606
0.102316602 0.083011583 0.069498069 0.052123552 0.036679537 0.019305019
0.013513514 0.005791506 0.001930502 0.001930502 0

2004 1 1 0 0 149 0 0 0 0 0 0 0 0.006711409 0.013422819 0 0.006711409
0.013422819 0.046979866 0.087248322 0.11409396 0.167785235 0.073825503
0.093959732 0.11409396 0.080536913 0.053691275 0.060402685 0.046979866
0.013422819 0.006711409 0 0

2005 1 1 0 0 248 0 0 0 0 0 0 0 0 0 0 0 0.008064516 0.02016129
0.064516129 0.064516129 0.112903226 0.137096774 0.133064516 0.137096774
0.133064516 0.092741935 0.052419355 0.036290323 0.004032258 0.004032258
0 0

2006 1 1 0 0 603 0 0 0 0 0 0 0 0 0 0 0 0.011608624 0.03814262
0.081260365 0.107794362 0.135986733 0.096185738 0.099502488 0.114427861
0.109452736 0.07628524 0.058043118 0.039800995 0.024875622 0.006633499 0
0

#NWFS Shelf_slope survey

2003 1 2 0 0 2675 0.000153143 0.010446371 0.052865857 0.057020155
0.056969682 0.074003282 0.078485036 0.08485576 0.067196025 0.060574022
0.057080145 0.066755707 0.071773516 0.065475447 0.052347076 0.043758763
0.031927664 0.02670609 0.019021869 0.008626458 0.006355062 0.00300481
0.003249119 0.000818884 0 0.00053006 0

2004 1 2 0 0 2647 0.000749611 0.015337003 0.039522762 0.066109916
0.048693229 0.061780396 0.068493942 0.090977691 0.076685202 0.088616396
0.06833257 0.074510142 0.065118796 0.066820305 0.053379229 0.042423605
0.025787787 0.018419471 0.011893947 0.006418267 0.003456819 0.002238862
0.001775282 0.001106247 0.001015137 0.000337386 0

2005 1 2 0 0 3326 0 0.016755488 0.055840771 0.063564351 0.067027308
0.077055281 0.070944638 0.074542922 0.073580392 0.069575534 0.061129744
0.062941288 0.061324177 0.061409618 0.054730843 0.039891822 0.028213688
0.025276804 0.016186173 0.006979488 0.003907415 0.003051025 0.005005446
0.000759643 0.000306139 0 0

2006 1 2 0 0 3325 0 0 0.001416816 0.034348927 0.053760622 0.073713285
0.063959501 0.076317292 0.078679747 0.065346917 0.08617749 0.060220398
0.067448639 0.055182885 0.075019689 0.055820984 0.0480657 0.029674178
0.027260659 0.016960297 0.010884979 0.008460468 0.006897071 0.002685534
0.001302793 0.000395129 0

#Triennial

2001 1 4 0 0 796 0 0.018280364 0.033732258 0.069089355 0.053676643
0.05767752 0.061090051 0.075796257 0.074982001 0.0616435 0.060193756
0.081533398 0.070666441 0.049609647 0.080940154 0.060433135 0.028598769
0.016980002 0.020290904 0.015977181 0.002819286 0.003242945 0.002098088
0 0 0 0.000648344

2004 1 4 0 0 794 0 0.024273252 0.057540289 0.056475451 0.045736376
0.056825564 0.053425147 0.059794931 0.053619976 0.055329675 0.045571338
0.077470615 0.115810859 0.057692936 0.036163376 0.059355181 0.039309118
0.040189936 0.047703914 0.006091645 0.003863367 0.003663002 0.003261743
0.000832309 0 0 0

#AFSC Slope

1997 1 5 0 0 764 0 0 0.005347784 0.023488466 0.021111317 0.061647608
0.059301493 0.104640293 0.110245197 0.079598263 0.096338749 0.07456304
0.081054704 0.04050164 0.063165014 0.051421584 0.049336808 0.021410921
0.02075607 0.010713947 0.005848062 0.009237117 0.006154195 0.002582645
0.000865769 0.000669314 0

1999 1 5 0 0 731 0 0.009117414 0.039426599 0.061591825 0.083621386
0.092257061 0.103421937 0.099310388 0.083754789 0.078494886 0.052785373
0.050162803 0.049083344 0.043815061 0.038659965 0.027462902 0.031536278
0.018952251 0.015220695 0.010861494 0.005361119 0.003958062 0 0
0.001144365 0 0

2000 1 5 0 0 743 0.00211345 0.036186922 0.031756364 0.061243376
0.07867173 0.093999265 0.091674939 0.090969654 0.058462173 0.069604189
0.068993455 0.053546347 0.041490576 0.043178906 0.047777876 0.034642343
0.032378887 0.022268755 0.016922877 0.007506844 0.008654331 0.004020956
0.002950818 0.000984969 0 0 0

2001 1 5 0 0 681 0 0.014688929 0.009970098 0.019972499 0.068060303
0.118687433 0.127096269 0.096840372 0.089846499 0.078159363 0.054172957
0.052361879 0.044467393 0.041932806 0.043032848 0.040156899 0.03721173
0.023845346 0.016927802 0.011086603 0.003751119 0.006711379 0.001019472
0 0 0 0

#\_N_AgeBins

24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 1
#\_N_ageerror_definitions

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5
16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 25.5

0.3669 0.594088526 1.060660172 1.097517861 1.011299794 1.744739994
0.963624112 1.030776406 0.9397724035 0.866025404 0.564076075 1.026436276
1.064120736 1.095445115 0.353553391 1.541103501 1.620185175 1
1.111788648 1.111788648 1.111788648 3.16227766 1.111788648 1.1 1.1
#\_N_Agecomp_obs

1

#Yr Seas Flt/Svy Gender Part Ageerr Lbin_lo Lbin_hi Nsamp datavector

2003 1 2 0 0 1 -1 -1 258 0.042635659 0.062015504 0.050387597 0.069767442
0.050387597 0.058139535 0.069767442 0.093023256 0.07751938 0.046511628
0.03875969 0.081395349 0.073643411 0.058139535 0.034883721 0.042635659
0.027131783 0.011627907 0.007751938 0.003875969 0 0 0 0

#\_N_MeanSize-at-Age_obs

3

#Yr Seas Flt/Svy Gender Part Ageerr Ignore datavector

#samplesize

2003 1 2 0 0 1 10 22.32727273 26.21875 35.99230769 41 46.99230769
45.76666667 56.26666667 60.6625 68.1 76.02727273 72.01 80.92857143
85.00526316 89.62666667 98.93333333 97.53636364 105.9285714 104.7666667
121.2 124.2 0 0 0 0 11 16 13 18 13 15 18 24 20 12 10 21 19 15 9 11 7 3 2
0 0 0 0 2003 1 1 0 0 1 10 0 0 34 43.6 44.6 0 0 69.7 0 0 79.6 82.5 94.05
105.5 102.9166667 114.8 122.9 109.925 112.75 0 130 0 0 110.9 0 0 1 1 1 0
0 1 0 0 5 5 2 4 6 2 2 4 2 0 1 0 0 1

2004 1 1 0 0 1 10 18.8 30.9 0 0 45.4 58.65 56.5 64.06666667 73.425
78.075 80.21818182 92.775 92.26666667 94.9 99.2 105.8625 15.91666667
111.3111111 113.5666667 129.5 116.5 135 0 0 2 3 3 4 8 11 4 15 9 5 8 6 9
3 1 2 1 0 0

0 #\_N_environ_variables

0 #\_N_environ_obs

999

**Control file**

1 #\_N_Growth_Patterns

1 #\_N_submorphs

1 #\_N_areas

1 1 1 1 1 #\_area_assignments_for_each_fishery_and_survey

1 #\_recruit_design\_(G_Pattern_x_birthseas_x_area)\_X\_(0/1_flag)

0 #\_recr_distr_interaction

0 #\_Do_migration

0 0 0
#\_movement_pattern\_(season_x_source_x_destination)\_x\_(0/1_flag)\_minage_maxage

0 #\_Nblock_Designs

0.5 #\_fracfemale

1 #\_submorph_between/within

-1 #vector_submorphdist\_(-1_first_val_for_normal_approx)

1 #\_natM_amin

3 #\_natM_amax

1 #\_Growth_Age-at-L1

17 #\_Growth_Age-at-L2

0 #\_SD_add_to_LAA

0 #\_CV_Growth_Pattern

1 #\_maturity_option

8 #\_First_Mature_Age

3 #\_parameter_offset_approach

1 \# new flag For selection of env and block adjustment method

-1 #\_MGparm_Dev_Phase

#\_growth_parms

#\_LO HI NIT PRIOR PR_type SD PHASE env-var use_dev dev_minyr dev_maxyr
dev_stddev Block Block_Fxn

0.01 0.8 0.2 0.2 0 0.04 -3 0 0 0 0 0.5 0 0#\_Gpattern:\_1

-3 3 0 0 -1 99 -3 0 0 0 0 0.5 0 0#M1_natM_old_as

15 40 26.958 26.958 -1 99 4 0 0 0 0 0.5 0 0#M1_Lmin

70 130 109.74 109.74 -1 99 4 0 0 0 0 0.5 0 0#M1_Lmax

0.05 0.15 0.047 0.047 -1 99 4 0 0 0 0 0.5 0 0#M1_VBK

0.1 0.5 0.1394 0.1394 -1 99 -3 0 0 0 0 0.5 0 0#M1_CV-young

-1 1 -0.708 -0.708 -1 99 -3 0 0 0 0 0.5 0 0#M1_CV-old

-3 3 4.28e-006 4.28e-006 -1 99 -3 0 0 0 0 0.5 0 0#\_wt-len&maturity

2 4 3.05975 3.05975 -1 99 -3 0 0 0 0 0.5 0 0#Female wt-len-2

10 140 120.753 120.753 -1 99 -3 0 0 0 0 0.5 0 0#Female mat-len-1

-0.09 -0.05 -0.0985876 -0.0985876 -1 99 -3 0 0 0 0 0.5 0 0#Female
mat-len-2

-3 3 0.5 1 -1 99 -3 0 0 0 0 0.5 0 0#Female eggs/gm intercept

-3 3 0 0 -1 99 -3 0 0 0 0 0.5 0 0#Female eggs/gm slope

-4 4 0 0 -1 99 -3 0 0 0 0 0.5 0 0#\_recrdistribution_by_growth_pattern

-4 4 0 0 -1 99 -3 0 0 0 0 0.5 0 0#\_recrdistribution_by_area1

-4 4 4 0 -1 99 -3 0 0 0 0 0.5 0 0#\_recrdistribution_by_season 1

1 1 1 1 -1 99 -3 0 0 0 0 0.5 0 0#\_cohort_growth_deviation

0 #\_custom_MG-env_setup

0 #\_custom_MG-block_setup

#\_Spawner-Recruitment

1 #\_SR_function: 1=Beverton-Holt

#\_LO HI INIT PRIOR PR_type SD PHASE

5 15 13 11.1 -1 10 1 #Ln(R0)

0.2 1 0.4 0.6 -1 0.2 -1 #steepness

0 0.4 0.3 0.3 -1 0.8 -3 #SD_recruitments

0 0 0 0 -1 99 -3 #Env_link

-2 2 0 0 -1 99 -1 #init_eq

0 0 0 0 -1 0 -99 \# new parameter Line reserved For future use as
autocorrelation

0 #\_SR_env_link

3 #\_SR_env_target_1=devs;\_2=R0;\_3=steepness

0 #do_recr_dev: 0=none; 1=devvector; 2=simple deviations

1984 2008 -15 15 3 #\_recr_devs

1492 #\_first_yr_fullbias_adj_in_MPD

#\_initial_F_parms

#\_LO HI INIT PRIOR PR_type SD PHASE

0 1 0 0.03 -1 99 -1

#\_Q_setup

\# A=do power, B=env-var, C=extra SD, D=devtype(\<0=mirror, 0/1=none,
2=cons, 3=rand, 4=randwalk); E=0=num/1=bio, F=err_type

#\_A B C D E F

0 0 0 0 1 0 #Fishery

0 0 0 2 1 0 #Survey1_NWFSC_shelf_slope

0 0 0 2 1 0 #Survey2_NWFSC_slope

0 0 0 2 1 0 #Survey3_Trieannial

0 0 0 2 1 0 #Survey4_AFSC_Slope

#\_Q_parms(if_any)

\# LO HI INIT PRIOR PR_type SD PHASE

-7 5 -0.19 -0.19 0 0.187 -1

-7 0 -0.6 0 0 99 1

-7 0 -0.6 0 0 99 1

-7 0 -0.6 0 0 99 1

#\_size_selex_types

#\_Pattern Discard Male Special

24 0 0 0 \# 1

24 0 0 0 \# 2

5 0 0 2 \# 3

24 0 0 0 \# 4

24 0 0 0 \# 5

#\_age_selex_types

#\_Pattern Discard Male Special

10 0 0 0 \# 1

10 0 0 0 \# 2

10 0 0 0 \# 3

10 0 0 0 \# 4

10 0 0 0 \# 5

#\_selex_parms

#\_LO HI INIT PRIOR PR_type SD PHASE env-var use_dev dev_minyr dev_maxyr
dev_stddev Block Block_Fxn

#\_size_sel: 1_fishery

80 100 85 85 0 99 2 0 0 0 0 0.5 0 0 \# PEAK

-6 4 -6 -6 0 99 2 0 0 0 0 0.5 0 0 \# TOP:\_width of plateau

-1 9 5.8 5.8 0 99 2 0 0 0 0 0.5 0 0 \# Asc_width

-1 9 8.3 6.7 0 99 -2 0 0 0 0 0.5 0 0 \# Desc_width

-5 9 -5 -5 0 99 -2 0 0 0 0 0.5 0 0 \# INIT:\_selectivity_at_fist_bin

-5 9 9 9 0 99 2 0 0 0 0 0.5 0 0 \# FINAL:\_selectivity_at_last_bin

#\_size_sel: 2_NWFSC_shelf_slope

20 80 50 50 0 99 2 0 0 0 0 0.5 0 0 \# PEAK

-6 4 -1.5 -1.5 0 99 2 0 0 0 0 0.5 0 0 \# TOP:\_width of plateau

-1 9 9 9 0 99 2 0 0 0 0 0.5 0 0 \# Asc_width

-1 9 6 6 0 99 -2 0 0 0 0 0.5 0 0 \# Desc_width

-5 9 -4.8 -4.8 0 99 -2 0 0 0 0 0.5 0 0 \# INIT:\_selectivity_at_fist_bin

-5 9 9 9 0 99 -2 0 0 0 0 0.5 0 0 \# FINAL:\_selectivity_at_last_bin

#\_size_sel: 3_NWFSC_slope

-2 1 -1 1 0 99 -2 0 0 0 0 0.5 0 0 \# Min Bin Number in Survey 2

-2 27 -1 27 0 99 -2 0 0 0 0 0.5 0 0 \# Max Bin Number in Survey 2

#\_size_sel: 4_Triennial

50 75 75 75 0 99 2 0 0 0 0 0.5 0 0 \# PEAK

-6 4 -2.8 -2.8 0 99 2 0 0 0 0 0.5 0 0 \# TOP:\_width of plateau

-1 9 9 9 0 99 2 0 0 0 0 0.5 0 0 \# Asc_width

-1 9 7.2 7.2 0 99 2 0 0 0 0 0.5 0 0 \# Desc_width

-5 9 -5 -5 0 99 -2 0 0 0 0 0.5 0 0 \# INIT:\_selectivity_at_fist_bin

-5 9 9 9 0 99 2 0 0 0 0 0.5 0 0 \# FINAL:\_selectivity_at_last_bin

#\_size_sel: 5_Slope

50 60 45 45 0 99 2 0 0 0 0 0.5 0 0 \# PEAK

-6 4 -5.5 -5.5 0 99 2 0 0 0 0 0.5 0 0 \# TOP:\_width of plateau

-1 9 5 5 0 99 2 0 0 0 0 0.5 0 0 \# Asc_width

-1 9 7.7 7.7 0 99 -2 0 0 0 0 0.5 0 0 \# Desc_width

-5 9 -4 -4 0 99 -2 0 0 0 0 0.5 0 0 \# INIT:\_selectivity_at_fist_bin

-5 9 9 9 0 99 -2 0 0 0 0 0.5 0 0 \# FINAL:\_selectivity_at_last_bin

1 #\_new flag For environment and block adjustment method

0 #\_custom_sel-env_setup

0 #\_custom_sel-block_setup

-1 #\_selparmdev-phase

#\_Variance_adjustments_to_input_values

#\_1 2 3 4 5

0 0 0 0.211025 0 #\_add_to_survey_CV

0 0 0 0 0 #\_add_to_discard_CV

0 0 0 0 0 #\_add_to_bodywt_CV

0.783545 0.408719 0 0.460038 0.645069 #\_mult_by_lencomp_N

0 0.534747 0 0 0 #\_mult_by_agecomp_N

1 1 1 1 1 #\_mult_by_size-at-age_N

30 #\_DF_for_discard_like

30 #\_DF_for_meanbodywt_like

1 #\_maxlambdaphase

0 #\_sd_offset

#\_lambdas\_(columns_for_phases)

0 #\_CPUE/survey:\_1

1 #\_CPUE/survey:\_2

1 #\_CPUE/survey:\_3

1 #\_CPUE/survey:\_4

1 #\_CPUE/survey:\_5

1 #\_discard:\_1

1 #\_discard:\_2

1 #\_discard:\_3

1 #\_discard:\_4

1 #\_discard:\_5

1 #\_meanbodyweight

1 #\_lencomp:\_1

1 #\_lencomp:\_2

1 #\_lencomp:\_3

1 #\_lencomp:\_4

1 #\_lencomp:\_5

1 #\_agecomp:\_1

1 #\_agecomp:\_2

1 #\_agecomp:\_3

1 #\_agecomp:\_4

1 #\_agecomp:\_5

1 #\_size-age:\_1

1 #\_size-age:\_2

1 #\_size-age:\_3

1 #\_size-age:\_4

1 #\_size-age:\_5

1 #\_init_equ_catch

1 #\_recruitments

0 #\_parameter-priors

1 #\_parameter-dev-vectors

100 #\_crashPenLambda

0.7 #\_maximum allowed harvest rate

999

##