Trends in the biomass, distribution, size composition and model-based estimates

Trends in the biomass, distribution, size composition and model-based estimates
Canadian Science Advisory Secretariat (CSAS)
Research Document 2015/084
Gulf Region
Trends in the biomass, distribution, size composition and model-based estimates
of commercial abundance of snow crab (Chionoecetes opilio) based on the multispecies bottom trawl survey of the southern Gulf of St. Lawrence, 1980-2014.
H.P. Benoît1 and N. Cadigan2
1
Fisheries and Oceans Canada
Gulf Fisheries Centre
343 avenue Université, P.O. Box 5030
Moncton (NB) E1C 9B6
2
Centre for Fisheries Ecosystem Research
Fisheries and Marine Institute of Memorial University of Newfoundland
P.O. Box 4920
St. John's (NL) A1C 5R3
February 2016
Foreword
This series documents the scientific basis for the evaluation of aquatic resources and
ecosystems in Canada. As such, it addresses the issues of the day in the time frames required
and the documents it contains are not intended as definitive statements on the subjects
addressed but rather as progress reports on ongoing investigations.
Research documents are produced in the official language in which they are provided to the
Secretariat.
Published by:
Fisheries and Oceans Canada
Canadian Science Advisory Secretariat
200 Kent Street
Ottawa ON K1A 0E6
http://www.dfo-mpo.gc.ca/csas-sccs/
csas-sccs@dfo-mpo.gc.ca
© Her Majesty the Queen in Right of Canada, 2016
ISSN 1919-5044
Correct citation for this publication:
Benoît, H.P., and Cadigan, N. 2016. Trends in the biomass, distribution, size composition and
model-based estimates of commercial abundance of snow crab (Chionoecetes opilio)
based on the multi-species bottom trawl survey of the southern Gulf of St. Lawrence,
1980-2014. DFO Can. Sci. Advis. Sec. Res. Doc. 2015/084. v + 25 p.
TABLE OF CONTENTS
ABSTRACT ..................................................................................................................................IV
RÉSUMÉ .......................................................................................................................................V
1. INTRODUCTION ...................................................................................................................... 1
2. METHODS ................................................................................................................................ 1
BACKGROUND AND DATA ........................................................................................... 1
2.1
2.1.1
The September multi-species RV survey ................................................................ 1
2.1.2
The snow crab survey ............................................................................................. 3
2.2
ANALYSIS ...................................................................................................................... 3
2.2.1
Multi-species RV survey indices .............................................................................. 3
2.2.2
Integrated abundance index estimation model ........................................................ 5
3. RESULTS AND DISCUSSION ................................................................................................. 6
3.1
MULTI-SPECIES RV SURVEY INDICES ....................................................................... 6
3.2
INTEGRATED ABUNDANCE INDEX ESTIMATION MODEL ........................................ 7
REFERENCES CITED .................................................................................................................. 8
TABLES ...................................................................................................................................... 10
FIGURES .................................................................................................................................... 12
iii
ABSTRACT
The research vessel bottom-trawl survey of the southern Gulf of St. Lawrence undertaken each
September (RV survey) has been shown to provide reliable standardized indices of biomass,
spatial distribution and habitat use of commercial-sized male snow crab (Chionoecetes opilio)
for 2001-present and of all snow crab (aggregated index) for 1980-present. Furthermore, results
from that survey have successfully been combined with data from a dedicated snow crab survey
as part of model-based estimation of the abundance of commercial male snow crab. This
document provides an update for biomass indices, spatial distribution, and size composition
based on the results of the 2014 RV survey. Furthermore, the document provides an update of
the model-based estimates of commercial crab abundance, as well as a presentation and
discussion of a few changes that were made for that estimation since 2014. This information
was provided in support of the regional snow crab assessment process that took place in
Moncton, NB on January 27-29, 2015. Of particular note, the RV survey confirmed continued
high biomasses of commercial-sized adult male snow crab since 2011 which were also
estimated by the dedicated snow crab survey. Model-based estimates of commercial crab
abundance in 2013 and 2014 were above the long-term average. The 2014 RV survey captured
an unusually high number of small crabs (≤15 mm) in several areas of the southern Gulf of St.
Lawrence. This is seemingly part of a general increase in small crab abundance since the early
2000s.
iv
Tendances de la biomasse, de la distribution, de la composition des tailles et des
estimations selon les modèles de l’abondance de crabe des neiges
(Chionoecetes opilio) de taille commerciale basé sur le relevé au chalut de fond
du crabe du neige et du relevé multi-espèces au chalut de fond du sud du Golfe
du St.-Laurent, 1980 à 2014
RÉSUMÉ
Le relevé annuel au chalut de fond effectué en septembre par un navire de recherche (NR)
dans le sud du golfe du Saint-Laurent (ci-après nommé relevé par NR) produit des indices
normalisés fiables de biomasse, de répartition et d'utilisation de l'habitat pour le crabe des
neiges (Chionoecetes opilio) mâle de taille commerciale depuis 2001, et pour tous les crabes
des neiges (indice agrégé) depuis 1980. De plus, les résultats provenant de ce relevé ont été
intégrés avec succès aux résultats provenant d’un relevé visant principalement le crabe des
neiges dans le cadre d’une estimation basée sur un modèle de l’abondance de crabes
commerciaux. Dans le présent document de recherche, une mise-à-jour des indices de
biomasse, de distribution et de répartition des tailles du relevé par NR sont présentés basés sur
les résultats du relevé de 2014. De plus, une mise-à-jour est présentée pour l’estimation basée
sur un modèle de l’abondance de crabes commerciaux. Ces informations sont fournies en appui
au processus d'évaluation régionale du crabe des neiges de 2015, lequel a eu à Moncton, au
N.-B., du 27 au 29 janvier. En particulier, le relevé par NR confirme l’existence soutenue d’une
biomasse élevée de crabes adultes de taille commerciale, qui a aussi été observée dans le
cadre du relevé dédié au crabe des neiges. L’estimation de l’abondance de crabes
commerciaux basée sur un modèle suggère que l’abondance se trouvait au delas de la
moyenne à long terme en 2013 et 2014. En 2014, le relevé par NR a capturé un nombre
anormalement élevé de petits crabs (≤15 mm) à plusieurs endroits dans le sud du golfe du
Saint-Laurent. Ceci fait partie d’une tendance générale à la hausse qui a débutée au début des
années 2000.
v
1. INTRODUCTION
There are two fishery-independent bottom-trawl surveys that provide relative abundance indices
for snow crab in the southern Gulf of St. Lawrence (sGSL). One of the surveys is principally
directed at snow crab and has been conducted annually since 1988 (henceforth called the crab
survey, CS) (Hébert et al. 2014). The second is a multi-species research vessel bottom-trawl
survey conducted annually since 1971 (henceforth called the research vessel survey, RVS),
which was initially focused on demersal fish but which has provided information on snow crab in
the catches since 1980 (Benoît 2014). Both surveys provide a coherent picture of the
abundance, distribution, habitat preferences and demographic structure of sGSL snow crab
(Benoît 2012).
This document provides an update for biomass indices, spatial distribution, and size
composition of sGSL snow crab based on the results of the 2014 RVS. The document also
provides an update for commercial snow crab abundance estimates derived from a model that
integrates the data from the RVS and CS (Benoît and Cadigan 2014). This model addresses a
number of shortcomings in the respective surveys to provide a standardized index of abundance
for 1980-2014. These shortcomings include past changes in the sampling frame for the CS,
uncalibrated changes in survey vessel and gear in the CS, and failure to disaggregate catches
of snow crab in the RVS by sex and size prior to 2001 (details in Benoît and Cadigan 2013,
2014). Slight changes to the modelling approach made after the 2014 assessment for the stock
are described in this document. Furthermore, the software used to fit the model changed. The
consequences of these two changes are presented and discussed.
The information presented in this document was provided in support of the regional snow crab
assessment process that took place in Moncton, NB from January 27-29, 2015.
2. METHODS
2.1
BACKGROUND AND DATA
2.1.1
The September multi-species RV survey
The RVS has been undertaken each September since 1971. It follows a random-stratified
design, with strata defined on the basis of depth and area (Fig. 1) (see Hurlbut and Clay 1990
for details on the survey methodology). A common group of strata has been sampled annually
since 1971, covering most of the southern Gulf of St. Lawrence (Northwest Atlantic Fishery
Organization area 4T). Three inshore strata (strata 401, 402, and 403) were added to the survey
in 1984. There are very few snow crab caught in these strata (Benoît and Cadigan 2013) and
these strata and data are excluded from analyses that include years prior to 1984 so that the
same set of strata are used in the time series analyzed. The target fishing procedure at each
station during the survey is a 30-min. tow at a speed of 3.5 knots. The number of valid fishing
sets completed annually has varied from approximately 70 during the early 1980s to 175 or
more during much of the 1990s and 2000s. In 2014, 156 valid sets were completed (Table 1).
Catches of snow crab (numbers and mass per tow) have consistently been recorded in the
survey since 1980 (Tremblay 1997). Prior to 1992, there was a small number of sets for which
catch numbers were recorded but mass was not when the mass was <1 kg (Table 1). This was
the consequence of the precision of the spring scales used at that time to weigh catches, and
these cases were generally when catch per tow was ≤ 0.5 kg; amounts were generally rounded
up to the nearest kg otherwise. For the calculation of an aggregated biomass index (kg/tow) the
mass was assumed to be 0.5 kg in these cases, producing a very comparable result to that
1
obtained using an estimated mean mass of crabs multiplied by the observed number in a set to
estimate catch mass. For the model based estimates, such cases were assumed to reflect the
absence of large snow crab (≥95 mm) in the catch (for an explanation see Benoît and Cadigan
2013). In most years prior to 2001 there was a small proportion of sets for which snow crab
catch mass was recorded, but not catch numbers (Table 1). In these instances, the number
caught was inferred using the stratum and year specific average catch mass per crab derived
from sets with both catch and mass observations.
Since 2001, captured crabs have also been measured (carapace width) and sexed. Since 2012
all individual crabs were meant to be sexed, measured, weighed and their maturity determined
based on the shape of the abdomen for females and based on measurements of chela height
using the method of Conan and Comeau (1986) for males. In addition, any missing or
regenerated appendages were meant to be noted. However, problems with the survey data
entry system arising mid-way through the 2014 survey prevented the recording of chela height
and appendage data. Consequently, the maturity of males could not be determined for the last
49 sets that caught males in 2014.
Fishing during the RV survey was carried out by the E.E. Prince from 1971 to 1985 using a
Yankee-36 trawl. Since then, a number of different vessels have been used, each fishing a
Western IIA trawl: the Lady Hammond (1985-1991), the CCGS Alfred Needler (1992-2002 and
2004-2005), the CCGS Wilfred Templeman (2003), and the CCGS Teleost (2004-present).
Parameters for the trawls and vessels used in the RV survey are provided in Tables 2 and 3,
respectively. Note that both trawls used in the survey are meant for fishing groundfish, though a
liner is used in the codend to retain small animals.
Prior to the gear change and all but one of the vessel changes in the RVS (CCGS Wilfred
Templeman used in 2003), paired tows involving the two vessels/gears at common sites were
undertaken to estimate their relative catchabilities (Benoît and Swain 2003a; Benoît 2006).
Based on these comparative fishing experiments, the E.E. Prince fishing the Yankee-36 was
found to be less efficient at capturing snow crab compared to the Lady Hammond and CCGS
Alfred Needler, and as a result corrections are applied to the E.E. Prince data prior to the
calculation of indices for the RVS (Benoît and Swain 2003a; Benoît 2006). No corrections are
applied for the CCGS Teleost (Benoît 2014). Note that in contrast to the approach used for the
RVS indices, adjustments for differences in relative catchability between vessels are estimated
and implemented directly in the model-based estimations (details below; Benoît and Cadigan
2014).
The absence of comparative fishing with the CCGS Wilfred Templeman used in 2003 precludes
the direct estimation of catchability relative to other RVS vessels. Though the model of Benoît
and Cadigan (2013, 2014) does provide an estimate for commercial-sized crabs (details below),
it does not provide an estimate for size-aggregated catches and still needs to be validated with
simulation testing. Consequently, results of the indices based exclusively on the RVS for 2003
are not presented in this report.
From 1971 to 1984, fishing in the RVS survey was restricted to daylight hours (07:00-19:00).
Since 1985, fishing has been conducted 24 hours per day. Because fishing efficiency can vary
by time of day, survey catches were standardized post-hoc for the calculation of indices from
the RVS, based on the results of analyses of survey catches and comparative fishing over the
diel cycle (Benoît and Swain 2003b; details in Benoît 2014). Note again that in contrast to the
approach used for the RVS indices, adjustments for diel differences in relative catchability are
estimated and implemented directly in the model-based estimations (details below; Benoît and
Cadigan 2014).
2
The estimation model of Benoît and Cadigan (2014) is based in part on the abundance of
commercial sized crabs (males ≥95 mm) in the RVS. Those values are directly available since
2001 but not for the 1980-2000 period. For the 1980-2000 time period, an empirical relationship
between the mean mass of crabs in a survey set and the proportion of large males (PLM) in that
set is used to predict the catches of commercial sized males based on length aggregated
catches (details in Benoît and Cadigan 2013, 2014). In the past that estimation step was done
externally to the model and was applied as part of an offset term during model fitting. In this
document we provide results from a new version of the model in which this estimation is
integrated into the model fitting (details below). This was done so that this source of uncertainty
is included in uncertainty estimates for snow crab abundance.
2.1.2
The snow crab survey
The snow crab survey has been conducted annually since 1988, though survey coverage was
very limited in 1996; details are available in Moriyasu et al. (2008). The survey has generally
been conducted following the commercial fishery, generally beginning in July and ending in late
September or early October, though the start and duration have varied between years. The
survey follows a systematic random sampling design in which, for most years, stations were
largely fixed once chosen. The survey gear is a Nephrops trawl (20 m Bigouden trawl net) and
the target fishing procedure at each site is a 4-6 minute tow at an average speed of
approximately 2 knots. Trawl mounted sensors are used to quantify the swept area of tows,
which is used to standardize the catches. Each individual crab captured in the snow crab survey
is sampled with respect to their biological characteristics. Here we consider only the catches of
commercial sized-males. For 2014, there were 353 valid CS sets included in the analyses
(Table 1).
Four chartered vessels have been used to conduct the survey since 1988: the side trawler EmySerge (1988-1998), and the stern trawlers, Den C Martin (1999-2002), Marco-Michel (20032012) and Jean-Mathieu (2013-2014). There has not been any comparative fishing between
these vessels to estimate their relative fishing efficiency. In addition to the change in vessels,
the survey gear was modified after 1990. Specifically, a chain that had been attached to the
trawl footgear was subsequently wrapped around the footgear to increase gear-handling safety
and fishing efficiency, based on the advice of experienced harvesters. There has been no
comparative fishing with respect to the gear modification.
The snow crab survey sampling frame has changed considerably from 1988 to 2014 (Moriyasu
et al. 2008; Benoît and Cadigan 2013). With the notable exception of 1996, the area covered
generally increased over time though the area was largely constant from 1997-2005 and from
2006 to present. Survey data for 1988-1996 are not used in the stock assessment because of
gaps in survey coverage with respect to the target sGSL snow crab assessment area (DFO
2012).
The approach of Benoît and Cadigan (2013; 2014) models the survey catches of commercial
snow crab as a function of the RVS strata (Fig. 1). Stratum 417 was modified slightly to include
a small area consistently sampled by the CS. Sets from the snow crab survey were attributed to
the strata based on their respective geographic positions using the ‘point.in.polygon’ function in
the ‘sp’ package for R (Bivand et al. 2008). The estimation domain for the model was strata 415439, including the adjustment to stratum 417.
2.2
ANALYSIS
2.2.1
Multi-species RV survey indices
Trawlable biomass (kg) of commercial male snow crab in year t (RVt), was calculated as:
3
n
U l ,t J
RVt = Padultt ∑ l ∑ ∑ yi , j ,t a j β
l =1 nl ,t i =1 j =95
L
(1)
for t = 2001 to 2014 (excluding 2003),
where Padultt is the proportion of snow crab ≥95mm that were adults in year t,
Ul is the number of trawlable units in stratum l (i.e., surface area / area swept by a standard
tow),
nl,t is the number of survey tows in stratum l and year t,
yi,j,t is the standardized number of male crab of carapace width j caught in tow i in year t, and
a = 2.665E-7 and β = 3.089 are parameters for the relationship between carapace width (in mm)
and mass (in g) (Hébert et al. 2014).
The values for Padultt were taken from the dedicated snow crab survey for all years for reasons
of consistency (Hébert et al. 2014; Hébert pers. comm. for 2014 value). Confidence intervals
were calculated using the standard estimator for standard error based on stratified random
sampling (Krebs 1989) and using a Satterthwaite approximation for the degrees of freedom for
the t-value.
An aggregated biomass index for snow crab per standard 1.75 NM tow (mean kg/tow, Bt ; all
sizes and sexes) was calculated as:
U l nl ,t
Bt = ∑
∑ bi,t
l =1 U ⋅ nl ,t i =1
L
(2)
for t = 1980 to 2014 (excluding 2003),
where U is the total number of trawlable units in the survey domain and
bi,t is the observed biomass (kg) of snow crab in set i of year t.
Analyses for Bt were undertaken for two geographic areas of inference: the current snow crab
assessment area representing 57,840 km2, and the RV survey area for strata 415-439 (Fig. 1)
representing 70,061 km2. To approximate the snow crab assessment area, strata 401-403, 420,
421, 428, 432, and 435 were excluded from the analysis. Analyses for RVt were only
undertaken for the geographic area equivalent to the current snow crab assessment area
because the values of Padultt are pertinent to this area.
Annual survey-weighted proportions (Pj,s,t) of sGSL crab as a function of each mm carapace
diameter j, and each sex (for 2001-2011) or sex and maturity stage (2012-2014) s, were
calculated as:
Pj , s ,t =
∑ (w
i ,t
⋅ y i , j , s ,t )
i
∑∑∑ (w
i ,t
s
Where wi ,t =
js
i
⋅ y i , j s , s ,t
)
(3)
Ul
.
U ⋅ n l ,t
These values were used to produce annual histograms for the RV survey catches.
4
Catch rates as numbers per tow of commercial-sized adult male snow crab in the RV survey
were mapped using inverse distance weighted gradient interpolation. The contour levels for
plotting were defined as the 10th, 25th, 50th, 75th, and 90th percentiles of non-zero catches
over the period of interest, 2001-2014 (excluding 2003). Catch rates of small crab (≤15 mm)
were likewise mapped to illustrate their spatial distribution given an observed high relative
abundance since 2012.
2.2.2
Integrated abundance index estimation model
Here we provide a summary of the estimation model (see Benoît and Cadigan (2014) for
additional details).
The basic model assumes that crab density is stochastically constant within strata, i.e., density
varies randomly within a stratum with a constant mean. Density is assumed to be independent
from site to site within strata, and crab densities are modeled separately for each stratum and
for each year. The index of stock size is based on the strata size-weighted average of the strata
densities. Trawl catches are basically assumed to Negative Binomial (NB) random variables,
which is considered suitable for modeling trawl catches (Cadigan 2011). Trawl catches are
assumed to be a function of the underlying density, catchability of commercial snow crab to the
surveys, and the area swept by survey tows.
The model contains parameters that account for factors that affect the catchability of crab within
and between surveys. First, there is a parameter that accounts for different catchability between
day (7:00-19:00) and night tows in the RVS. Information to estimate this parameter comes from
the contrasts between day and night catches in the RVS within common strata and years and
for repeated (paired) tows conducted day and night at the same sites, typically within 24 hrs. No
diel adjustment is required for the CS (Benoît and Cadigan 2013).
Second, there is a suite of parameters to account for catchability differences between vessels
used for the surveys (qv; see Figure 2 for a summary of which vessels were used in each year):
v = Teleost ,
1,
2004 − 2014,


qWT →T ,
v = Wilfred Templeman,
2003,

q AN →T ,
v = Alfred Needler ,
1992 − 2005, not 2003,


v = Lady Hammond ,
1985 − 1992,
 qLH →T = qLH → AN q AN →T ,
q
v = EE Prince,
1980 − 1985,
= qEP→ LH qLH → AN q AN →T ,
qv =  EP→T
qSCS 1→T ,
gear used in SCS1,
1988 − 1990,


qSCS 2→T ,
gear used in SCS 2,
1991 − 1998,

qSCS 3→T ,
v in SCS 3,
1999 − 2002,


qSCS 4→T ,
v in SCS 4,
2003 − 2012.

qSCS 5→T ,
v in SCS 5,
2013, 2014

The notation qa→b indicates the catchability of vessel a relative to vessel b. The catchability of
the CCGS Teleost was fixed at one and CCGS Teleost was the reference vessel. Information to
estimate the catchabilities for all RVS vessels except the Wilfred Templeman comes almost
exclusively from the paired-tow comparative fishing data (within-pair catch contrast). Because
there was no direct comparative fishing between the EE Prince or the Lady Hammond and the
CCGS Teleost, these conversions were inferred stepwise, e.g. q EP →T = q EP → LH q LH → AN q AN →T .
Information to estimate the catchabilities for the remaining vessels (Wilfred Templeman and the
5
five CS vessels, SCS1-SCS5) comes from contrasts in catches between surveys, within strata
and years.
Third there are two parameters that determine the NB over-dispersion; one for between-site
variability of crab density (k) and one for within pair over-dispersion (kp).
The model was originally implemented in AD Model Builder (ADMB; Fournier et al. 2012). The
model has recently also been implemented in Template Model Builder (TMB; Kristensen 2013),
a new model fitting environment that provides considerably more efficient and rapid estimation
of random effects, as are used here to model the NB over-dispersion and to address within pair
correlations. Though the estimates obtained using both modelling environments are expected to
be very similar, they are nonetheless compared here to confirm that this is the case.
A second change to the model compared to the 2014 assessment concerns the estimation of
the proportion of large males (PLM) for RVS catches for 1980-2000. Whereas PLM was
estimated outside the model for the 2013 and 2014 assessment documents (Benoît and
Cadigan 2013; 2014), for the present analyses the estimation was integrated directly in the
model fitting. In this manner, the uncertainty inherent in the PLM estimation is integrated in the
uncertainty of annual abundance estimates. We compare the results obtained using both
approaches.
The comparisons of model results between model fitting environments and for internal versus
external estimation of PLM were completed before the 2014 survey results were available.
Those comparisons were therefore based on the data for 1980 to 2013.
3. RESULTS AND DISCUSSION
3.1
MULTI-SPECIES RV SURVEY INDICES
The biomass of commercial-sized adult male snow crab increased from a relatively low level in
2001, to a relatively high level mid-decade, declining to the lowest levels of the 2000s in 2010
(Fig. 3). Since then, the index has increased, reaching a level in 2013 and 2014 that is
comparable to that of the mid-2000s.
The RV survey aggregated biomass index (all sizes, both sexes) provides a longer-term
perspective of snow crab population dynamics in the sGSL (Fig. 4). Trends in this index during
the 2000s generally match those observed for large male crab (Fig. 3) because the large males
typically comprise the bulk of the biomass in the catches. The exception was in 2013, when the
aggregated index reached its highest value since the early 1990s (Fig. 4). The value for 2014
was above the long-term average of 6.0 kg/tow.
The size-frequency distributions of crabs in the RV survey are shown in Figure 5. Generally, the
late 2000s were characterized by a higher proportion of snow crab <30 mm, relative to the early
2000s. In particular, a very high proportion of small crab (≤15 mm) was observed in the 20122014 surveys. Crabs of this size were captured at higher abundances and in more locations in
2013 and 2014 compared to surveys in 2001-2011 (Fig. 6). In fact, high densities of small crabs
were caught throughout most of the survey area. These crabs may represent a very early signal
of strong incoming recruitment that will hopefully be tracked over the coming years. Higher
proportions of such small crabs are expected in the RV survey compared to the dedicated crab
survey because of a smaller mesh size in the RV survey trawl codend (19 mm in RV survey
compared to 40 mm in the snow crab survey). This may explain why abundance of crabs
≤15 mm has not appeared particularly elevated in the dedicated crab survey in 2012 and 2013.
6
The relative composition of commercial-sized adult male crab in 2014 was comparable to the
levels seen in 2007, 2008 and 2011-2013 (Fig. 5). As in 2012 and 2013, the proportion of crab
larger than 110 mm remained small and at a level comparable to that observed during the
relatively low abundance years of 2001 and 2009. Densities of commercial-sized adult male
snow crab over the Magdalen shallows and the west of Cape Breton Island in the 2014 RV
survey were similar to those observed in 2012-2013 (Fig. 7).
3.2
INTEGRATED ABUNDANCE INDEX ESTIMATION MODEL
Very similar trends in estimated snow crab abundance were obtained from the models with
external versus internal estimation of the proportion of large males, PLM (Fig. 8). Internal
estimation resulted in slightly greater uncertainty for the abundance estimates for the 1980 to
2000 period (Fig. 9B) compared to results from the model with external estimation (Fig. 9A).
This result was expected given that uncertainty in the PLM estimation is desirably reflected in
the overall uncertainty of model parameter estimates when that estimation is done internally.
This is also evident in the slightly larger confidence intervals for the vessel/gear catchability
parameters (Fig 10). Though the estimates for those parameters did differ a little between
internal and external PLM estimation, particularly for vessels that were in service prior to 2001,
the respective confidence intervals obtained for external versus internal estimation overlapped
for each of the parameters.
There were very few differences in the results obtained for the model with internal estimation of
PLM, whether it was estimated in ADMB or TMB (Fig. 11 and 12). There were a few instances
of larger residuals from the model fit in ADMB compared to TMB (Fig. 13). This is the result of a
difference in the treatment of random effects between environments. In TMB, the Laplace
approximation was used directly to obtain the marginal likelihood by integrating out the random
effects for replicate tows at a site. In ADMB, the Laplace approximation approach was very slow
and the integration had to be coded and then implemented with a special function (adromb
function).
Based on the advantages of TMB over ADMB and the pertinence of including the PLM
estimation directly in the model, these two changes were made for the model estimation for the
1980 to 2014 period. The 2014 CS was the second year in which the vessel Jean-Matthieu
(SCS5) was used to complete the survey. The estimated catchability coefficient for that vessel
increased relative to last year’s estimate, resulting in a value that was closer to those for the
other CS vessels (Fig. 14). The confidence intervals for that estimate were also narrower. The
parameter attenuation and increased precision with an additional year of data are expected
statistically and were predicted in 2014 based on a quick retrospective analysis of the data for
the SCS4 vessel, Marco Michel (see Table 5 in Benoît and Cadigan 2014). Further additional
years of data are likely to result in smaller changes in the estimated parameter and more
modest improvements in precision.
The change in the qv value for SCS5 resulted in a decrease in the estimated abundance of
commercial snow crab for 2013 compared to estimates derived from the data series excluding
the 2014 surveys (Fig. 15). The estimated abundance for 2014 is slightly greater than the
estimate for 2013, both values are at an elevated level relative to estimates for years after 1995,
and both are above the long-term average of around 105 crabs/km2. The similar fits provided to
the model for the 1980-2013 versus 1980-2014 data were also reflected in very similar residual
patterns (Fig. 16).
As was found previously, the NB variance model provided a good description of the variance in
the raw residuals with respect to the mean (Fig. 17).
7
Overall, the conclusions of Benoît and Cadigan (2013; 2014) remain valid with the addition of
the 2014 values and the other slight changes to the model and model fitting. The model
provides a useful method for integrating the available data on snow crab abundance in the
sGSL, making the best use of available data. The model draws strength from both the RV and
crab surveys to estimate relative catchability parameters that would otherwise be difficult to
estimate (SCS1-SCS5 and
). Furthermore, the model provides a useful framework in
which to efficiently estimate relative catchability coefficients for the RV survey vessels and for a
diel effect by drawing simultaneously on information from samples that are grouped at the site
level and at the stratum level (S. Wang, N.G. Cadigan, and H.P. Benoît. Inference about
regression parameters using highly stratified survey count data with over-dispersion and
repeated measurements. Unpublished report submitted to Journal of Applied Statistics). By
estimating these parameters within a common modeling framework, their associated
uncertainties are reflected in the estimated abundance index, as was shown here by the
inclusion of the PLM estimation directly in the model.
The switch to TMB for estimation brought a considerable improvement in estimation speed. This
has effectively removed a barrier that restricted our ability to conduct simulation testing of the
model to ensure its statistical reliability.
REFERENCES CITED
Benoît, H.P. 2006. Standardizing the southern Gulf of St. Lawrence bottom-trawl survey time
series: results of the 2004-2005 comparative fishing experiments and other
recommendations for the analysis of the survey data. DFO Can. Sci. Advis. Sec. Res.
Doc. 2006/008.
Benoît, H.P. 2012. A comparison of the abundance, size composition, geographic distribution
and habitat associations of snow crab (Chionoecetes opilio) in two bottom trawl surveys in
the southern Gulf of St. Lawrence. DFO Can. Sci. Advis. Sec. Res. Doc. 2012/015. iv +
34 p.
Benoît, H.P. 2014. Update on trends in the abundance, distribution and size composition of
snow crab (Chionoecetes opilio) in the September multi-species bottom trawl survey of the
southern Gulf of St. Lawrence, 1980-2013.DFO Can. Sci. Advis. Sec. Res. Doc. 2014/081.
v + 12 p.
Benoît, H.P., and Cadigan, N.G. 2013. Model-based estimation of commercial-sized snow crab
(Chionoecetes opilio) abundance in the southern Gulf of St. Lawrence, 1980-2012, using
data from two bottom trawl surveys. DFO Can. Sci. Advis. Sec. Res. Doc. 2013/114. v +
47 p.
Benoît, H.P., and Cadigan, N. 2014. Model-based estimation of commercial-sized snow crab
(Chionoecetes opilio) abundance in the southern Gulf of St. Lawrence, 1980-2013, using
data from two bottom trawl surveys. DFO Can. Sci. Advis. Sec. Res. Doc. 2014/082. v +
24 p.
Benoît, H.P., and Swain, D.P. 2003a. Standardizing the southern Gulf of St. Lawrence bottomtrawl survey time series: adjusting for changes in research vessel, gear and survey
protocol. Can. Tech. Rep. Fish. Aquat. Sci. No. 2505: iv + 95 p.
Benoît, H.P., and Swain, D.P. 2003b. Accounting for length- and depth-dependent diel variation
in catchability of fish and invertebrates in an annual bottom-trawl survey. ICES J. Mar. Sci.
60: 1298-1317.
8
Bivand, R.S., Pebesma, E.J., and Gomez-Rubio, V. 2008. Applied spatial data analysis with R.
Springer, NY. 378 p.
Cadigan, N.G. 2011. Confidence intervals for trawlable abundance from stratified-random
bottom trawl surveys. Can. J. Fish. Aquat. Sci. 68: 781-794.
Conan, C.Y., and Comeau, M. 1986. Functional maturity and terminal molt of male snow crab,
Chionoecetes opilio. Can. J. Fish. Aquat. Sci. 43: 1710-1719.
DFO. 2012. Proceedings of the Gulf Region Science Peer Review Framework Meeting of
Assessment Methods for the Snow Crab Stock of the southern Gulf of St. Lawrence;
November 21 to 25, 2011. DFO Can. Sci. Advis. Sec. Proceed. Ser. 2012/023.
Fournier, D.A., Skaug, H.J., Ancheta, J., Ianelli, J.,Magnusson, A., Maunder, M., Nielsen, A.,
and Sibert, J. 2012. AD Model Builder: using automatic differentiation for statistical
inference of highly parameterized complex nonlinear models. Optimization Methods &
Software 27: 233–249.
Hébert, M., Wade, E., DeGrâce, P., Landry, J.-F., and Moriyasu, M. 2014. The 2013
assessment of the snow crab (Chionoecetes opilio) stock in the southern Gulf of St.
Lawrence (Areas 12, 19, 12E and 12F). DFO Can. Sci. Advis. Sec. Res. Doc. 2014/084.
Hurlbut, T., and Clay, D. 1990. Protocols for research vessel cruises within the Gulf Region
(demersal fish) (1970-1987). Can. Manuscr. Rep. Fish. Aquat. Sci. 2082: 143 p.
Krebs, C.J. 1989. Ecological methodology. Harper Collins Publishers, N.Y.
Kristensen, K. 2013. TMB: General random effect model builder tool inspired by ADMB. R
package version 1.0.
Moriyasu, M., Wade, E., Hébert, M., and Biron, M. 2008. Review of the survey and analytical
protocols used for estimating abundance indices of southern Gulf of St. Lawrence snow
crab from 1988 to 2006. DFO Can. Sci. Advis. Sec. Res. Doc. 2008/069.
Tremblay, M.J. 1997. Snow crab (Chionoecetes opilio) distribution limits and abundance trends on
the Scotian shelf. J. Northw. Atl. Fish. Sci. 21: 7-22.
9
TABLES
Table 1. Annual summary of the number of sets from the research vessel (RVS) and snow crab (CS)
surveys used to estimate the abundance index. The summary for the RVS sets is further broken down to
indicate the number of sets for which both catch mass and numbers were recorded and sets for which
values of only one of the two variables was recorded.
Year
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
RVS
total valid
sets
70
70
65
67
102
209
164
152
147
166
141
188
162
183
154
175
194
202
192
180
182
141
173
78
212
231
165
163
177
148
137
126
142
122
156
RVS
sets with
numbers and
mass
47
57
47
48
85
162
156
128
121
143
134
184
154
176
150
168
189
185
145
175
181
141
173
78
212
231
165
163
177
148
137
126
142
122
156
RVS
sets with
numbers only
2
13
17
14
12
41
0
13
19
14
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
RVS
sets with mass
only
21
0
1
5
5
6
8
11
7
9
1
4
8
7
4
7
5
17
47
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
CS
valid sets
154
155
212
215
233
208
259
260
72
259
261
277
280
290
319
317
347
355
354
355
355
355
354
353
321
351
353
Table 2. Parameters for the two trawls used in the RV survey of the southern Gulf of St. Lawrence.
Characteristics
Years in operation
Footrope
Footrope length (ft)
Headline length (ft)
Headline height (ft)
Wingspread (ft)
Door type
Door weight (lbs)
Lengthening piece
liner (inches)
Codend liner (inches)
Yankee 36
1971-1984
7 inch (outer sections) and 14
inch (inner sections) rubber
disc spacers + 17 lb. iron
spacers
80
60
9
35
Steel bound wood
1,000
1.25
Western IIA
1985-present
21 inch (outer) and 18 inch
(inner) rubber bobbins and 6.75
inch diameter 7 inch long rubber
spacers
106
75
15
41
Portuguese (all steel)
1,800
1.25
0.25 inches
0.75 inches
Table 3. Parameters for the vessels used in the RV survey of the southern Gulf of St. Lawrence for the
years presented in this report.
Characteristics
Vessel type
Tonnage
Length (m)
E.E. Prince
Stern trawler
406
40
Lady Hammond
Stern trawler
897
58
11
CCGS Alfred Needler
Stern trawler
959
50
CCGS Teleost
Stern trawler
2,405
63
FIGURES
49°
415
416
425
417
426
424
418
48°
427
419
428
423
422
436
43
8
439
420
435
47°
429
421
40
437
431
434
1
433
402
46°
432
66°
65°
64°
63°
403
62°
61°
60°
Figure. 1. Stratum boundaries for the southern Gulf of St. Lawrence September RV survey.
Figure 2. Summary of the survey vessels used in the snow crab surveys (SC) and research vessel survey
(RVS) as a function of year for 1980-2014
12
Figure 3. Estimated trawlable biomass (tonnes; mean ± 95% confidence interval) of commercial-sized
adult male snow crab in the RV survey, 2001-2014, for a geographic area comparable to that used for the
current snow crab assessment.
13
Figure 4. Biomass index (kg/tow; mean ± 95% confidence interval) for all snow crab (male and female) in
the RV survey, 1980-2014, for a geographic area comparable to that used for the current snow crab
assessment (open blue diamond) and for the entire RV survey area (solid red circle).
14
Figure 5. Annual survey-weighted relative frequency distributions (expressed as proportions) of snow
crab by carapace width (mm) as a function of sex (for 2001-2011) or sex and maturity stage (2012-2014).
The numbers in each panel indicate the value of the annual abundance index (numbers per tow) for snow
crab (all sizes and sexes). The data for 2003 are not shown because that survey was incomplete.
15
49°
2001
2007
2012
2002
2008
2013
2004
2009
2014
2005
2010
48°
47°
46°
49°
48°
47°
46°
49°
48°
47°
46°
49°
66° 65° 64° 63° 62° 61° 60°
48°
47°
46°
49°
# / tow
2006
2011
48°
1
2
4
12.5
47°
34.4
46°
66° 65° 64° 63° 62° 61° 60°
66° 65° 64° 63° 62° 61° 60°
Figure 6. Annual geographic distribution of catch rates (number of crabs per tow) of small snow crab
(≤15 mm) in the September RV survey, 2001-2014 (excluding 2003). The small crosses indicate the set
locations. The contour levels represent the 10th, 25th, 50th, 75th and 90th percentiles of non-zero
catches for the entire period.
16
49°
2001
2007
2012
2002
2008
2013
2004
2009
2014
2005
2010
48°
47°
46°
49°
48°
47°
46°
49°
48°
47°
46°
49°
66° 65° 64° 63° 62° 61° 60°
48°
47°
46°
49°
# / tow
2006
2011
48°
1
2
4.4
10.3
47°
20.4
46°
66° 65° 64° 63° 62° 61° 60°
66° 65° 64° 63° 62° 61° 60°
Figure 7. Annual geographic distribution of snow crab catch rates (number of crabs per tow; males
≥95 mm) in the September RV survey, 2001-2014 (excluding 2003). The small crosses indicate the set
locations. The contour levels represent the 10th, 25th, 50th, 75th and 90th percentiles of non-zero
catches for the entire period.
17
Figure 8. Annual estimated densities (number per km²) of southern Gulf commercial male snow crab,
1980 to 2013 for the model estimated in ADMB with the proportion of large males (PLM) estimation done
externally (black line) and internally (red line) to the model. The shaded region indicates the 95%
confidence interval range for the model with external estimation.
Figure 9. Annual estimated densities (number per km²) of southern Gulf commercial male snow crab,
1980 to 2013. The horizontal lines indicate the series average and the shaded regions indicates the 95%
confidence interval ranges. The results for the model for which the proportion of large males (PLM)
estimation was done externally to the model are shown in panel A (left) and the results for the model that
integrated the PLM estimation are shown in panel B (right).
18
Figure 10. Estimates (crosses) of survey vessel/gear relative catchabilities, log(qv), with 95% confidence
intervals (bars) for the model estimated in ADMB with the proportion of large males (PLM) estimation
done externally (black) and internally (red) to the model. The catchability comparisons are annotated as
follows: WT= CCGS Wilfred Templeman → CCGS Teleost, PR = EE Prince → Lady Hammond, LH =
Lady Hammond → CCGS Alfred Needler, and AN = CCGS Alfred Needler → CCGS Teleost. The entries
SCS are for the catchability of the snow crab survey vessel/gear, relative to the Teleost: SCS1 – Snow
crab survey gear for 1988-1990, SCS2 – vessel for 1991-1998, SCS3 – vessel for 1999-2002, SCS4 –
vessel for 2003-2012,and SCS5 – vessel for 2013-2014.
19
Figure 11. Annual densities (number per km²) of southern Gulf commercial male snow crab, 1980 to
2013, estimated in TMB (black line) and in ADMB (red line), in both cases with internal estimation of the
proportion of large males. The shaded region indicates the 95% confidence interval range for the model
estimated in TMB.
20
Figure 12. Estimates (crosses) of survey vessel/gear relative catchabilities, log(qv), with 95% confidence
intervals (bars), obtained from the model fit TMB (black) and in ADMB (red), in both cases with internal
estimation of the proportion of large males.The catchability comparisons are annotated as follows:
WT = CCGS Wilfred Templeman → CCGS Teleost, PR = EE Prince → Lady Hammond, LH = Lady
Hammond → CCGS Alfred Needler, and AN = CCGS Alfred Needler → CCGS Teleost. The entries SCS
are for the catchability of the snow crab survey vessel/gear, relative to the Teleost: SCS1 – Snow crab
survey gear for 1988-1990, SCS2 – vessel for 1991-1998, SCS3 – vessel for 1999-2002, SCS4 – vessel
for 2003-2012,and SCS5 – vessel for 2013-2014.
21
ADMB
TMB
Figure 13. Model residuals by year (x-axes) and vessel (panels),from the model fit in ADMB (left panel)
and in TMB (right panel), in both cases with internal estimation of the proportion of large males.Notable
differences in residuals between ADMB and TMB are indicated using red circles.
22
Figure 14. Estimates (crosses) of survey vessel/gear relative catchabilities, log(qv), with 95% confidence
intervals (bars), obtained from the model fit inTemplate Model Builder for 1980-2014 (black) and 19802013 (red), in both cases with internal estimation of the proportion of large males. The catchability
comparisons are annotated as follows: WT = CCGS Wilfred Templeman → CCGS Teleost, PR = EE
Prince → Lady Hammond, LH = Lady Hammond → CCGS Alfred Needler, and AN = CCGS Alfred
Needler → CCGS Teleost. The entries SCS are for the catchability of the snow crab survey vessel/gear,
relative to the Teleost: SCS1 – Snow crab survey gear for 1988-1990, SCS2 – vessel for 1991-1998,
SCS3 – vessel for 1999-2002, SCS4 – vessel for 2003-2012,and SCS5 – vessel for 2013-2014.
23
Figure 15. Annual densities (number per km²) of southern Gulf commercial male snow crab, 1980 to 2013
(red) or 1980 to 2014 (black), estimated in Template Model Builder with internal estimation of the
proportion of large males. The shaded region indicates the 95% confidence interval range for 1980-2014
estimation.
24
A)
B)
Figure 16. Model residuals by year (x-axes) and vessel (panels), for the model fit in TMB for A) 19802014 and B) 1980-2013.
Figure 17. Standard deviations (sd’s) of the binned raw residuals for the final model fit in TMB with
internal estimation of the proportion of large males. The solid line is the NB prediction of the raw residual
sd, sqrt (predicted + predicted2 /k). The right panel is the same as the left panel but using a narrower
range on both the x and y axes.
25
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