Full Terms & Conditions of access and use can be found athttp://www.tandfonline.com/action/journalInformation?journalCode=ujfm20
Download by: [University of Maine - Orono] Date: 20 August 2016, At: 14:30
North American Journal of Fisheries Management
ISSN: 0275-5947 (Print) 1548-8675 (Online) Journal homepage: http://www.tandfonline.com/loi/ujfm20
Development of Abundance Indices for AtlanticCod and Cusk in the Coastal Gulf of Maine fromtheir Bycatch in the Lobster Fishery
Chongliang Zhang & Yong Chen
To cite this article: Chongliang Zhang & Yong Chen (2015) Development of AbundanceIndices for Atlantic Cod and Cusk in the Coastal Gulf of Maine from their Bycatch in theLobster Fishery, North American Journal of Fisheries Management, 35:4, 708-719, DOI:10.1080/02755947.2015.1043413
To link to this article: http://dx.doi.org/10.1080/02755947.2015.1043413
Published online: 13 Jul 2015.
Submit your article to this journal
Article views: 105
View related articles
View Crossmark data
http://www.tandfonline.com/action/journalInformation?journalCode=ujfm20http://www.tandfonline.com/loi/ujfm20http://www.tandfonline.com/action/showCitFormats?doi=10.1080/02755947.2015.1043413http://dx.doi.org/10.1080/02755947.2015.1043413http://www.tandfonline.com/action/authorSubmission?journalCode=ujfm20&show=instructionshttp://www.tandfonline.com/action/authorSubmission?journalCode=ujfm20&show=instructionshttp://www.tandfonline.com/doi/mlt/10.1080/02755947.2015.1043413http://www.tandfonline.com/doi/mlt/10.1080/02755947.2015.1043413http://crossmark.crossref.org/dialog/?doi=10.1080/02755947.2015.1043413&domain=pdf&date_stamp=2015-07-13http://crossmark.crossref.org/dialog/?doi=10.1080/02755947.2015.1043413&domain=pdf&date_stamp=2015-07-13
ARTICLE
Development of Abundance Indices for Atlantic Codand Cusk in the Coastal Gulf of Maine from theirBycatch in the Lobster Fishery
Chongliang ZhangCollege of Fisheries, Ocean University of China, 5 Yushan Road, Qingdao 266003, China;
and School of Marine Sciences, University of Maine, 225 Libby Hall, Orono, Maine 04469, USA
Yong Chen*School of Marine Sciences, University of Maine, 216 Libby Hall, Orono, Maine 04469, USA
AbstractLimited information is available about the abundance of Atlantic Cod Gadus morhua and Cusk Brosme brosme in
the coastal Gulf of Maine because the presence of lobster traps limits commercial fishing and surveys for thesespecies. We developed abundance indices for Atlantic Cod and Cusk from bycatch data obtained in a lobster seasampling program. We applied generalized linear models (GLMs) to standardize Atlantic Cod and Cusk bycatchrates. The CPUE data, measured as the count of Atlantic Cod and Cusk observed per trap haul, are characterizedby an extremely skewed distribution with a high percentage of zero observations. Two general approaches wereapplied to tackle the zero-dominated data: modeling with different error distributions and aggregating data overspatial scales. We evaluated eight models: binomial, Poisson, negative binomial, Tweedie model, hurdle model (alsoreferred to as the delta approach) with Poisson and negative binomial distribution, and zero-inflated model withPoisson and negative binomial distribution. The data were aggregated using six grids ranging from 0.01 to 0.5geological degrees (0.6–30 nautical miles). The standardized CPUE showed a gradual decline from 2006 to 2011,except for 2009 when a slight increase occurred for Atlantic Cod, and a general decline from 2006 to 2010 followedby an increase in 2011 for Cusk. The standardized CPUEs were consistent, in general, among the models andamong different spatial aggregation scenarios, suggesting that the CPUE standardization is robust with respect tochoices of data aggregation and statistical models. This study highlights the feasibility of developing abundanceindices based on bycatch data for monitoring fish stock dynamics in data-limited regions.
Fisheries management is generally based on a stock assess-
ment, which often requires inputs of various sources of data
collected from fishery-dependent and fishery-independent
monitoring programs (Hilborn and Walters 1992; Maunder
and Punt 2004). An abundance index, usually derived from
fishery-independent survey programs and in some cases also
from commercial or recreational fisheries, is required in
almost all formal stock assessments (Pennington 1985;
Pennington and Strømme 1998; Carlson and Brusher 1999;Lorance and Dupouy 2001; Campbell 2004).
Abundance indices derived from a fishery-independent pro-
gram are often considered more reliable in capturing temporal
and/or spatial variability of targeted fish stocks because their
designs follow statistical principles (Chen et al. 2006). How-
ever, a fishery-independent monitoring program tends to be
expensive and may not be available for all fish stocks. This is
particularly true for fish stocks distributed in areas for which it
is logistically difficult (e.g., complex bottom, a high density of
fixed gears) and/or too expensive (e.g., open ocean) for sur-
veys (Campbell 2004; Maunder and Punt 2004; Rotherham
*Corresponding author: [email protected] September 17, 2014; accepted April 16, 2015
708
North American Journal of Fisheries Management 35:708–719, 2015
� American Fisheries Society 2015ISSN: 0275-5947 print / 1548-8675 online
DOI: 10.1080/02755947.2015.1043413
et al. 2007; Rudershausen et al. 2010). Thus, many exploited
species are either not monitored at all or not monitored com-
prehensively with a fishery-independent survey program
(Lynch et al. 2012). Fishery-dependent monitoring, on the
other hand, is available for many commercial fisheries and
tends to generate a large quantity of data with a wide spatial
and temporal coverage and fine resolution (Bertrand et al.
2004). However, because maximized catch efficiency is the
goal for commercial fisheries and because fishers tend to target
the areas that are perceived to yield high catch, fishery-depen-
dent data are often considered less reliable in representing
temporal and spatial variability of fish stock abundances
(Campbell 2004; Maunder and Punt 2004).
Regardless of potential issues related to data collected in a
fishery-dependent program, CPUE has traditionally been used as
a relative abundance index for monitoring and assessment of fish
stocks (Richards and Schnute 1992; Harley et al. 2001; Good-
year et al. 2003;Maunder and Punt 2004). This approach implic-
itly assumes that CPUE is proportional to stock abundance,
which has often been debated (Beverton and Holt 1957; Peter-
man and Steer 1981; Rose and Leggett 1991; Harley et al.
2001). Although stock abundance is critical in determining
CPUE in a commercial fishery, many other factors, such as spa-
tial dispersion of resources, fishing strategy, and abiotic–biotic
environmental variables, can also greatly influence fishing effi-
ciency, making nominal CPUE a poor representation of stock
abundance (Murawski and Finn 1988; Lange 1991; Perry and
Smith 1994). Nominal CPUE may provide misleading informa-
tion on the variability of a fish stock, and it is necessary to
remove the influence of factors other than stock abundance
before a set of CPUEs can be used as an index of stock abun-
dance (Goodyear et al. 2003; Hinton and Maunder 2003). This
process is often referred to as CPUE standardization and many
approaches to this have been developed (Hinton and Maunder
2003; Maunder and Punt 2004). The generalized linear model
(GLM) (Nelder andWedderburn 1972) and the generalized addi-
tive model (GAM) (Hastie and Tibshirani 1990) are two of the
most commonly used (Punt et al. 2000; Campbell 2004;
Maunder and Punt 2004; Shono 2005).
If the targeted stock is too small to sustain a commercial
fishery or stock habitat cannot be accessed as a result of gear
conflicts, complex environment, or regulations, neither fishery-
independent nor commercial fishery-dependent data are suffi-
cient or even available for assessing the dynamics of targeted
fish stocks. Atlantic Cod Gadus morhua and Cusk Brosme
brosme are in low abundance in the Gulf of Maine (GOM)
(Frank et al. 2005; Hare et al. 2012; NEFSC 2013). Although
survey and fishery data are available for the GOM, this infor-
mation is limited in the coastal GOM, which plays an impor-
tant role as nursery grounds for many fish species (Bigelow
and Schroeder 1953; Ames 2004), because the high density of
fixed gear for the lobster fishery has priority in this region and
would become entangled with trawls. However, Atlantic Cod
and Cusk are two bycatch species found in the lobster fishery.
Since 2006, Maine Department of Marine Resources (DMR)
has conducted a sea sampling program for which scientific
observers collect bycatch data onboard lobster fishing boats.
Like other bycatch species, the catch rates of Atlantic Cod and
Cusk are low (Kathleen Reardon, Maine DMR, West Boot-
hbay Harbor, unpublished data). Nevertheless, these bycatch
data provide valuable information for assessing temporal vari-
ability of stock abundances for these two fish species in the
coastal GOM.
Bycatch data are commonly characterized by skewed distri-
butions with a high percentage of zero observations, and
modeling methods such as those based on lognormal or log-
gamma distributions may not be suitable (Maunder and Punt
2004; Ortiz and Arocha 2004; Minami et al. 2007). Several
statistical methods have been developed for count data with
many zeroes, including (1) an ad hoc method (Robson 1966),
(2) Poisson or quasi-Poisson and negative-binomial regression,
which models catch rather than CPUE with fishing efforts used
as an offset (Reed 1986), and (3) two-stage models, including
the delta approach (often referred to as a hurdle model) (Lo
et al. 1992) and the zero-inflation model (Lambert 1992).
These methods have been applied and compared in several
studies (Hinton and Maunder 2003; Maunder and Punt 2004;
Shono 2008).
Spatial and/or temporal aggregation of data can also reduce
or eliminate the problem of a high proportion of zero observa-
tions. In addition, fisheries data are often required to be aggre-
gated before they can be used to protect the confidentiality of
exact fishing locations. However, this approach is seldom
applied in data analyses because aggregated data often result
in a loss of information (Maunder and Punt 2004) that may
fundamentally influence model fitting (Campbell 2004; Tian
et al. 2010, 2013). Spatial and temporal scale is a central ques-
tion for most ecological studies (Levin 1992), and in many
cases conclusions are essentially dependent on scale (Ciannelli
et al. 2008). This highlights the importance of exploring data
in different scales and of testing the influence of data aggrega-
tion (Tian et al. 2010).
The objective of this study was to develop abundance indi-
ces for Atlantic Cod and Cusk in the coastal GOM by using
bycatch data collected in the lobster fishery. Two general
approaches described above, modeling with an appropriate
distributional function and aggregating data, were explored for
dealing with the zero-dominated bycatch data. The modeling
approaches considered in this study are (1) one-stage models
including binomial, Poisson, negative-binomial, and Tweedie
model and (2) two-stage models including the hurdle model
with Poisson distribution (HDP, also referred to as the delta-
approach), hurdle model with negative binomial distribution
(HDNB), zero-inflated model with Poisson distribution (ZIP),
and zero-inflated model with negative binomial distribution
(ZINB). We also aggregated data on six different spatial
scales. The results derived from these methods were com-
pared. We examined the impacts of error distributional
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 709
functions and spatial scale of data aggregation on model fitting
and subsequently the robustness of developing standardized
CPUEs from the bycatch data for the coastal GOM Atlantic
Cod and Cusk. The proposed approach is also applicable to
data of a similar nature with large number of zero catches,
which is common in fisheries.
METHODS
Background and Collection of Atlantic Cod andCusk Bycatch Data in the Lobster Fishery
Atlantic Cod were subject to heavy fishing throughout its
range, resulting in overfished stocks in the United States and
Canada during the early 1990s. Cod biomass was reduced to
less than 5% of its maximum historical level and its population
has failed to recover even though the directed fishery has
ceased and fishing mortality has been reduced (Frank et al.
2005). Cusk are distributed across the North Atlantic from the
Northeast U.S. Continental Shelf to the European Shelf
(Knutsen et al. 2009) and have experienced a dramatic
decrease in abundance over the past 40 years in the Gulf of
Maine–Georges Bank–Scotian Shelf region (Hare et al. 2012).
Cusk are currently listed as a Species of Concern in the United
States and assessed as threatened and under consideration for
addition to Canada’s Species at Risk (Harris and Hanke 2010;
Hare et al. 2012).
Limited information is available for these two species in
the near-shore areas due to the limited coverage of surveys
by the Northeast Fisheries Science Center (NEFSC) and
Maine DMR as a result of the lobster fisheries (see details
in Discussion). While Atlantic Cod is assessed and managed
under the New England Fishery Management Council’s
Northeast Multispecies Fishery Management Plan, the Cusk
fishery in the United States is currently not under any man-
agement plan (Hare et al. 2012). Because of low catchabil-
ity, low abundance, and lack of coverage of main habitats
by the bottom trawl survey gear, few of these two species
were caught in the relevant trawl survey programs. For
example, the NEFSC survey mainly covers offshore areas
and may not represent inshore habitats, which cannot be
trawled as a result of the complex bottom and the existence
of a large number of fixed gears (NEFSC 2013).
The Maine DMR conducts a sea sampling program in
which onboard observers have been collecting lobster and
bycatch data since the 1980s. However, finfish bycatch data
of good quality were not collected until 2006. The sea sam-
pling program covers seven management zones for the lob-
ster fishery along the coast of Maine (i.e., Management
Zones A to G; Figure 1). Throughout each trip covered, sam-
plers recorded geographical position, depth, sediment types,
and catch information for each lobster trap. There were a
total of 210,997 traps recorded from 2006 to 2011 in the
area. This lobster bycatch data set provided an opportunity to
develop abundance indices quantifying the temporal variabil-
ity of Atlantic Cod and Cusk in the coastal GOM, which
serves as critical nursery grounds for many groundfish
species.
Environmental Variables
Four categories of explanatory variables that might affect
the spatiotemporal distribution of Atlantic Cod and Cusk and
subsequently their catch rates in the lobster fishery were
considered: (1) temporal factors, including year and month
(Damalas et al. 2007; Shono 2008); (2) spatial factors, includ-
ing latitude, longitude, and fishing zones (A–G) (Goodyear
2003; Damalas et al. 2007); (3) habitat variables, including
depth of sampling sites ranging from 0 to 226 ft (68.9 m), and
sediment types, measured in grain size and classified into
seven types (gravel, gravel–sand, sand, sand–silt/clay, sand–
clay/silt, clay–silt/sand, and sand/silt/clay (Somers 1987,
1994); and (4) the number of lobsters caught per trap. We con-
sidered the number of lobsters caught per trap (ranging from 0
to 46 individuals/trap) in modeling (Punt et al. 2001), and a
preliminary analysis showed that the presence of lobsters in a
trap had a significant nonlinear influence on the catch rate of
Atlantic Cod and Cusk. Instead of using a nonlinear model
that deals with the relationship, we changed the lobster catch
into a categorical variable, which, although resulting in a loss
of information, can avoid the nonlinearity problem. The catch
of lobster was classified into three categories: “absence,”
“low” (1–4 individuals), and “high” (5–46 individuals). This
grouping criterion is arbitrary, but we found the results were
robust to changes in the grouping criterion. Fishing efforts
were unequally distributed by month, depth, sediment type,
and spatial coordinates, suggesting bycatch is not spatially and
temporally random (Figure 1), which confirms the need for
the CPUE standardization.
Spatial Aggregation
The data were aggregated into six different spatial grids
ranging in size from 0.01 to 0.50 geological degrees (i.e.,
roughly an area of 0.36 to 900 squarenautical miles). For each
grid we calculated (1) the average of latitude, longitude, and
depth, (2) the sum catch of Atlantic Cod and Cusk and the
number of traps, (3) the dominating sediment type and man-
agement zone, and (4) the average catch of lobster per trap
and the subsequent catch-level classification described above.
The total numbers of cells in grid data were 13,702, 8,656,
4,120, 2,522, 1,757, and 1,243, respectively, from the finest to
the coarsest grids. The aggregated data of different scales
were referred to as “grid01,” “grid02,” . . . to “grid50,” i.e.,from the finest to the coarsest, so that the numbers, 01, 02, . . .and 50, correspond to a grid according to its size in geological
degrees.
710 ZHANG AND CHEN
Modeling Approaches
Eight models, which can be categorized as one-stage or
two-stage modeling approaches, were used. These methods
are only briefly summarized below as they have been
described in previous studies (Maunder and Punt 2004; Zeileis
et al. 2008).
GLM with binomial, Poisson, and negative-binomial distri-
butions.—A GLM with binomial, Poisson, and negative-
binomial distributions are commonly used for count data and
model count of catch instead of a nominal CPUE. For binomial
distribution, the count of catch and noncatch is used as a
response variable; for other models, catch is the response vari-
able and fishing effort is treated as an offset; thus, the differ-
ence in the number of traps among observations can be
handled (Reed 1986; Maunder and Punt 2004). The original
data set included a count of the bycatch in an individual trap,
and fishing effort was set to 1.
Tweedie model.—The Tweedie model, which is an exten-
sion of a compound Poisson model, is derived from the
stochastic process where the weight of counted objects has a
gamma distribution and has an advantage of handling the
zero-catch data in a unified way by expressing normal, Pois-
son, Gamma, and inverse Gaussian distribution with a power
parameter, p, altering within 0–3. Specifically, a p-value rang-
ing between 1 and 2 indicates a compound Poisson distribution
with mass zeroes (Candy 2004; Shono 2008).
Delta approach or hurdle model.—The delta approach, or
hurdle model, describes the probability of zero catch sepa-
rately from the probability of positive catch. Typically, the
probability of no catch is assumed to follow a logistic distribu-
tion, and positive catches are assumed to follow a truncated
Poisson or negative binomial distribution (Cragg 1971; Welsh
et al. 1996; O’Neill and Faddy 2003).
Zero-inflation model.—The zero-inflation model is also
expressed in two parts: the probability of being in a “perfect
state” (i.e., no catch), and the probability of being in an
“imperfect state” (i.e., catch may occur). The perfect state is
typically described with a logistic model, and the imperfect
FIGURE 1. Sampling area for Atlantic Cod and Cusk in the lobster fishery in the Gulf of Maine. The frequency distribution of eight variables in sea sampling
included year (2006–2011), month (12 months) , fishing zones (A to E), sediment type (measured in grain size and the composition of clay, silt, sand, and gravel),
depth (feet), longitude (70�400W to 67�W), latitude (43�N to 45�N), and the number of lobsters caught in each trap; x- and y-axes are longitude and latitude,respectively.
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 711
state is assumed to follow a complete Poisson or negative
binomial distribution, which are referred to as zero-inflated
Poisson (ZIP) and zero-inflated negative binomial (ZINB)
models, respectively (Lambert 1992; Hall 2000; Agarwal et al.
2002; Minami et al. 2007). The zero-inflated models perform
well when the processes that lead to zero observations are not
the same as those that lead to nonzero catches (Lambert 1992;
Hall 2000).
These models with different error distributional functions
were fitted to the data aggregated according to different spatial
scales, and the results were compared among the models as
well as among different spatial aggregations for evaluating the
impacts of distributional functions and data aggregation. The
performance of the models were compared with information
criteria, Akaike’s information criterion (AIC) and Bayesian
information criterion (BIC), and the percentage of deviance
explained (Zeileis et al. 2008). Although AIC, BIC, or any
other method based on likelihood functions are not exactly
comparable across different error assumptions, this study
adopted the approximate approach, as previous studies sug-
gested that AIC values for larger sample sizes typically gave
strong support to model selection across error distributions
(Dick 2004), which is the case for our data set (210,997 obser-
vations for unaggregated data). The CPUE, measured as the
number of Atlantic Cod and Cusk observed per trap haul, was
extracted from the fitted models as abundance indices (Maun-
der and Punt 2004), and the abundance index in 2011 was set
as the reference year to which the year effects of different
models were compared.
RESULTS
Distribution of Atlantic Cod and Cusk Bycatch Data
The CPUEs for the bycatch of Atlantic Cod and Cusk that
were calculated based on the sampled traps from the lobster
fishery sea sampling program were low; the average was two
fish per 1,000 traps for each species. Zero catch dominated the
sampled trap hauls in 99.8% of the observations for Atlantic
Cod and 99.9% for Cusk. The percentage of zero observations
decreased gradually in an increased spatial scale of data aggre-
gation and thus changed the data distribution (Figure 2). The
percentage of zero observations was reduced to 81.4% and
91.5% for Atlantic Cod and Cusk, respectively, when the
coarsest scale was used for data aggregation.
Model Comparison for Atlantic Cod
For original data without aggregation, only one-stage mod-
els were informative because HDP, HDNB, ZIP, and ZINB
were found to be not significant in their second stage (i.e.,
count-model stage), which essentially reduced them to the
binomial models. The binomial model had the least AIC and
BIC values, followed by the Poisson and negative binomial
models (Table 1). The Tweedie model provided no AIC and
BIC as this model used quasi-likelihood in its algorithm
(Candy 2004), but explained most of the deviance (18.4%).
All the variables except for depth were significant in the four
models (Table 2).
FIGURE 2. Frequency distribution of bycatch data of Atlantic Cod and Cusk (log10 scale) under different spatial scales. Spatial grids range from 0.01� to 0.50�
for data aggregations.
712 ZHANG AND CHEN
Six models were performed on “grid01” (i.e., aggregated
data with a grid scale of 0.01 degree) except unsolvable ZIP
and ZINB. The negative binomial model showed advantages
over all other models for AIC, BIC, and deviance explanation.
The binomial and Poisson models had the similar AIC and
BIC values, and explained low proportion of deviance. Two-
stage models, the HDP model and the HDNB model, explained
similar deviance but involved more parameters. The largest
proportion of deviance explained was 20.8%, which was
slightly higher than for the original data (i.e., 18.4%). The
models on “grid02” showed similar results, for which the neg-
ative binomial model was superior to the others for AIC and
BIC, followed by the ZIP model. The HDP model explained
the most deviation (i.e., 24.4%). For “grid05” and “grid10”
the negative binomial models were the best for AIC and devi-
ance explained, and ZIP had the lowest BIC value. The highest
proportion of explained deviance for these two data sets
increased to 29.7% and 33.3%, respectively. For the coarsest
aggregation “grid20” and “grid50” the negative binomial mod-
els had the lowest values for AIC and BIC, while the HDP
model had the largest deviance explained, 38.0% and 40.5%,
respectively (Table 1).
All variables except for depth had a significant effect on
most models (Table 2). For different aggregation scenarios,
deviance explained improved from 18.4% to 40.5%. The nega-
tive binomial model outperformed other models for most sce-
narios considered in this study, followed by the ZIP and HDP
models.
Model Comparison for Cusk
For the original data without aggregation, all the two-stage
models only showed the first stage (i.e., the binomial model
for presence and absence) to be significant. The negative bino-
mial model explained the highest percentage of deviance (i.e.,
38.1%), and the binomial model had the lowest values for AIC
TABLE 1. Model comparisons among different error distributions and spatial aggregation scenarios for Atlantic Cod using degree of freedom (df) of the model,
AIC, BIC, and deviance explained (PDE). The best model for each term is indicated in bold. The AIC and BIC values for the Tweedie distribution were not avail-
able as the model used a quasi-likelihood algorithm. An asterisk indicates models unavailable for computational singularity; a dash indicates models unlisted for
lack of significance; Neg-bin D negative binary.
Data set Terms Binomial Poisson Neg-bin Tweedie HDP HDNB ZIP ZINB
Original df 32 33 34 34 * * * *
AIC 5,097.2 5,192.0 5,188.0
BIC 5,446.0 5,540.8 5,547.1
PDE 0.131 0.150 0.165 0.184
Grid01 df 32 33 34 34 47 41 — —
AIC 3,259.2 3,252.3 3,212.6 3,226.8 3,241.1BIC 3,500.0 3,500.6 3,468.5 3,580.5 3,549.6
PDE 0.165 0.183 0.208 0.200 0.200 0.202
Grid02 df 32 33 34 34 53 41 35 —
AIC 2,890.3 2,887.3 2,833.8 2,854.5 2,876.0 2,846.6
BIC 3,116.5 3,120.5 3,074.0 3,229.0 3,165.7 3,093.9
PDE 0.186 0.217 0.240 0.227 0.244 0.226 0.233
Grid05 df 32 33 34 34 42 36 29 —
AIC 2,342.0 2,338.2 2,265.9 2,332.3 2,302.2 2,292.4BIC 2,544.3 2,546.9 2,480.9 2,597.9 2,529.9 2,475.8
PDE 0.228 0.274 0.297 0.279 0.284 0.277 0.291
Grid10 df 32 33 34 34 41 42 23 34
AIC 1,994.2 1,993.4 1,922.6 2,003.3 1,990.5 1,982.1 1,944.1
BIC 2,180.8 2,185.9 2,120.9 2,242.4 2,235.4 2,116.2 2,142.4
PDE 0.261 0.327 0.333 0.324 0.330 0.296 0.323 0.318
Grid20 df 32 33 34 34 48 52 40 41
AIC 1,798.0 1,797.5 1,706.4 1,763.4 1,738.1 1,755.4 1,709.6BIC 1,973.1 1,978.1 1,892.5 2,026.1 2,022.6 1,974.2 1,933.9
PDE 0.279 0.344 0.346 0.338 0.380 0.350 0.375 0.355
Grid50 df 32 33 33 34 58 56 39 *
AIC 1,638.1 1,637.9 1,544.2 1,593.5 1,581.7 1,601.2
BIC 1,802.1 1,807.1 1,713.3 1,890.7 1,868.7 1,801.1
PDE 0.299 0.346 0.332 0.333 0.405 0.341 0.376
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 713
and BIC. For “grid01,” “grid05,” and “grid10,” the ZINB
model had the lowest AIC value and explained the most devi-
ance, while the negative binomial model performed better for
BIC. For “grid02” the ZINB model had the highest proportion
of deviance explained while the ZIP model had the lowest
AIC value, and the HDP model had the lowest BIC value. For
the coarsest aggregations, “grid20” and “grid50,” the negative
binomial model had the lowest BIC value and the ZIP model
had the most explained deviance. The lowest AIC value was
produced by the negative binomial model for “grid20” and by
the ZINB model for “grid50” (Table 3).
All the selected environmental variables except for sedi-
ment types and longitude had a significant effect on most mod-
els (Table 2). The proportion of deviance explained was
improved from 38.1% to 66.1% by data aggregation. The
ZINB model outperformed other models for most scenarios
for AIC and deviance explained, while the negative binomial
model tended to be better for BIC.
Relative Abundance Indices
For Atlantic Cod, the standardized CPUE tended to
decrease from 2006 to 2011 (Figure 3a). The abundance index
of Cusk also tended to decrease from 2006 to 2010, but
increased in 2011 (Figure 3b). The patterns were consistent
across all models for Atlantic Cod (Figure 3a), but had more
variations in the zero-inflated models for Cusk (Figure 3b).
One-stage models—the binomial, Poisson, negative binomial,
and Tweedie models—showed similar results, while there
were more variations among the two-stage models when data
were aggregated on large spatial scales.
DISCUSSION
This study evaluated various methods of developing abun-
dance indices for Atlantic Cod and Cusk in the coastal GOM
based on their bycatch data in the lobster fishery from 2006 to
2011. The standardized CPUE was consistent across most
models with different error distributions for a given set of spa-
tial aggregation scenarios, suggesting a decreasing trend for
Atlantic Cod and a decreasing–recovering trend for Cusk in
the coastal GOM (Figure 3).
There were limited spatial overlaps between trawl surveys
and the sea sampling program from which the bycatch data
were collected (Figure 4). We compared Atlantic Cod abun-
dance derived from our bycatch data in the coastal GOM with
the abundance indices derived from the NEFSC and Maine–
New Hampshire trawl surveys in fall and spring from 2006 to
2011. The standardized bycatch CPUE had a temporal trend
similar to that of the Maine–New Hampshire fall survey, but
differed greatly from the other surveys (Figure 5). The differ-
ence might be attributed to the seasonal migration of Atlantic
Cod, as well as the limited spatial overlaps of Atlantic Cod
between surveys areas (Figure 4). The temporal trend of the
standardized CPUE for Cusk was partially consistent with the
spring bottom-trawl survey abundance index of NEFCS (Hare
et al. 2012; NEFSC, unpublished data available at http://nefsc.
noaa.gov/epd/ocean/MainPage/ioos.html); however, the trawl
TABLE 2. The frequency of variables that were significant in the models. The values in bold indicate the remarkable low frequency of depth in the model for
Atlantic Cod and longitude and sediment type in the model for Cusk.
Variables
Data set Year Month Longitude Latitude Zone Sediment Depth Presence of lobster
Atlantic Cod
Original 1.00 1.00 1.00 1.00 1.00 1.00 0.00 1.00
Grid01 1.00 1.00 1.00 1.00 1.00 1.00 0.00 1.00
Grid02 1.00 1.00 0.86 1.00 1.00 1.00 0.29 1.00Grid05 1.00 1.00 1.00 1.00 1.00 0.71 0.14 1.00
Grid10 1.00 1.00 0.88 1.00 0.63 0.50 0.00 1.00
Grid20 1.00 1.00 1.00 0.88 1.00 1.00 0.00 1.00
Grid50 1.00 1.00 0.29 0.86 0.86 1.00 0.00 1.00
Cusk
Original 1.00 1.00 0.00 1.00 1.00 1.00 1.00 1.00
Grid01 1.00 1.00 0.00 0.75 1.00 0.25 1.00 1.00
Grid02 1.00 1.00 0.25 1.00 1.00 0.63 1.00 1.00Grid05 1.00 1.00 0.25 1.00 1.00 0.13 1.00 1.00
Grid10 1.00 1.00 0.13 1.00 1.00 0.00 1.00 1.00
Grid20 1.00 1.00 0.00 1.00 1.00 0.00 1.00 1.00
Grid50 1.00 1.00 0.00 1.00 1.00 0.00 1.00 1.00
714 ZHANG AND CHEN
surveys caught a very small number of Cusk, which prevents a
meaningful comparison. These differences among surveys
suggested that it was necessary to consider standardized
CPUE data from the sea sampling program, which covers an
area not well covered by the existing sampling programs. In
general, the results demonstrated that CPUE standardization
was robust for model choices and data aggregations, highlight-
ing the potential of developing an abundance index from
bycatch data for this data-limited area.
Generalized linear models have been well developed and
were commonly used in CPUE standardization to remove fac-
tors other than stock abundance in influencing catch rates
(Hinton and Maunder 2003; Maunder and Punt 2004; Lynch
et al. 2012). In developing GLMs, a selection of appropriate
error distribution is often important for an adequate descrip-
tion of the variability of data because it reflects the assump-
tions associated with the model. Bycatch data are typically
characterized by a large proportion of zeroes (Ortiz and
Arocha 2004), which may violate the assumptions of most
commonly used statistical analyses such as normality and con-
stant variance. In addition, if the data are treated as a lognor-
mal distribution that commonly occurs in biological surveys,
computational issues arise because of the invalid natural loga-
rithm of zero. Although often used in fisheries models, the “ad
hoc” method with lognormal or log-gamma distribution was
not desirable here because of the high sensitivity to the value
added (Punt et al. 2000), particularly given the high proportion
of zero observations in this study. Modeling count data instead
of using a continuous model of CPUE is more appropriate for
data with a large proportion of zeroes, if the problem of over-
dispersion can be handled properly (Maunder and Punt 2004;
Zeileis et al. 2008).
Neither the residuals diagnostic plot nor the cumulative
residual plot were informative for comparing the performance
of various models for this study, and cross validation easily
failed for generating a subset containing all-zero observations.
TABLE 3. Model comparisons for Cusk among error distribution and spatial aggregation scenarios using degree of freedom (df) of the model, AIC, BIC, and
the percentage of deviance explained (PDE). The best model for each term is indicated in bold. The AIC and BIC values for the Tweedie distribution were not
available as the model used quasi-likelihood algorithm; a dash indicates models unlisted for lack of significance; Neg-bin D negative binary.
Data set Terms Binomial Poisson Neg-bin Tweedie HDP HDNB ZIP ZINB
Original df 32 33 34 34 — — — —
AIC 2,755.9 2,888.8 4,571.0
BIC 3,094.5 3,227.4 4,919.8
PDE 0.252 0.288 0.381 0.350
Grid01 df 26 27 28 28 34 36 45 55
AIC 1,731.9 1,727.1 1,681.6 1,719.1 1,680.8 1,680.0 1,612.3
BIC 1,927.5 1,930.3 1,892.3 1,975.0 1,951.7 2,018.6 2,026.2
PDE 0.378 0.406 0.446 0.430 0.416 0.456 0.445 0.467Grid02 df 26 33 34 34 36 31 48 43
AIC 1,595.2 1,592.5 1,547.0 1,577.5 1,544.4 1,522.3 1,525.4
BIC 1,778.9 1,825.7 1,787.2 1,831.9 1,763.4 1,861.5 1,829.2
PDE 0.402 0.415 0.454 0.438 0.426 0.451 0.467 0.479
Grid05 df 26 27 28 28 32 33 34 35
AIC 1,282.7 1,279.7 1,229.9 1,222.2 1,227.7 1,219.8 1,213.6
BIC 1,447.1 1,450.4 1,407.0 1,424.5 1,428.4 1,434.8 1,434.9
PDE 0.469 0.478 0.514 0.499 0.519 0.524 0.523 0.538Grid10 df 26 27 28 30 31 35 35
AIC 1,111.2 1,110.0 1,053.7 1,065.7 1,057.0 1,061.0 1,046.9
BIC 1,262.9 1,267.5 1,217.1 1,240.7 1,237.9 1,265.2 1,251.0
PDE 0.510 0.515 0.549 0.520 0.548 0.551 0.558 0.568
Grid20 df 26 27 28 28 36 31 45 34
AIC 968.9 964.0 901.0 1,116.0 1,078.8 1,158.7 1,078.8
BIC 1,111.1 1,111.7 1,054.2 1,116.0 1,078.8 1,158.7 1,078.8
PDE 0.543 0.574 0.590 0.571 0.616 0.588 0.633 0.610Grid50 df 26 27 28 28 29 30 33 33
AIC 840.7 839.9 797.4 829.4 807.4 793.9 788.8
BIC 973.9 978.3 940.9 978.1 961.1 963.0 957.9
PDE 0.583 0.619 0.615 0.608 0.629 0.608 0.661 0.635
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 715
The AIC, BIC, and the proportion of deviance explained were
used for model comparison, suggesting that the binomial and
Poisson models yielded similar results, which was reasonable
when sample size was large and probability was low (Feller
1968). The Tweedie model was better than the Poisson model
in explaining deviance, but worse than the negative binomial
model. In general, the Tweedie model showed limited ability
in estimating the power parameter p (the p-value can be
adjusted to express normal, Poisson, Gamma, and inverse
Gaussian distribution) on our data set with dominant zero
observations. The negative binomial models outperformed the
other one-stage models, and were better than some two-stage
models, suggesting it has more power for modeling count
data. The negative binomial models had the flexibility in han-
dling overdispersed data with an additional parameter u (Ortizand Arocha 2004); however, relevant studies showed that the
negative binomial model might overestimate model coeffi-
cients as well as the trend of year effect in CPUE
FIGURE 3. Standardized abundance indices of (a) Atlantic Cod and (b) Cusk extracted from the models with different error distribution and data with different
spatial aggregation. The year 2011 was used as the reference year.
716 ZHANG AND CHEN
standardization (Ortiz and Arocha 2004; Minami et al. 2007),
and the estimation of the dispersion parameter was empha-
sized for fitting a negative binomial regression model.
Two-stage models are supposed to be more appropriate for
describing data with many zero observations (Zeileis et al.
2008), and previous studies showed that the hurdle models
would outperform other models when fitting such data (Ortiz
and Arocha 2004; Minami et al. 2007). Although the biologi-
cal processes of lobster trap bycatch for Atlantic Cod and
Cusk have not been identified, it is assumed that the first stage
model captures the presence–absence of fish, and the second
stage describes the rate of catch given that fish are present.
However, in this study two-stage models were not superior to
the negative binomial model for Atlantic Cod and Cusk, prob-
ably resulting from statistical problems such as overfit.
Although the zero-inflated models showed the best perfor-
mance for AIC and deviance explanation for Cusk, they also
yielded contrasting temporal trends among different spatial
aggregation scenarios. Consistent with this study, the ZINB
models can perform poorly for data dominated by zero-value
observations (Minami et al. 2007). The results highlight the
risk of model selection based on information criteria and devi-
ance. The comparison among multiple approaches of modeling
would be helpful for model validation when true values are not
available, which is common in fishery and ecological studies.
Generally, modeling on unaggregated count data are pre-
ferred to avoid a loss of information (Maunder and Punt 2004).
However, in situations when models are focused on extracting
relative temporal trends rather than making precise predictions
such as CPUE standardizations, detailed and fine-scale
FIGURE 4. Spatial overlap of lobster sea sampling sites (grey zone) and the sampling sites of trawl surveys within the lobster zones from 2006 to 2011; x- and
y-axes are longitude and latitude, respectively.
FIGURE 5. Relative abundance indices from 2006 to 2011 of Atlantic Cod
from the NEFSC and Maine DMR Maine–New Hampshire trawl surveys in
fall and spring together with standardized CPUE from bycatch data. Values
were standardized for each index for comparison.
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 717
information may not be necessary. Moreover, the large varia-
tions resulting from sampling may result in undesirable perfor-
mance (Punt et al. 2000; Tian et al. 2010). As shown in this
study, the data aggregation changed the distribution of catch
data (Figure 2) and influenced the performance of models with
different error distributions (Tables 1, 3). With the spatial
aggregation in larger scales, the models were improved in devi-
ance explanation, AIC values, and BIC values, yet yielded sim-
ilar trends of abundance indices (Figure 3), suggesting the
CPUE standardization is robust regarding the loss of the infor-
mation resulting from spatial aggregation. However, a careful
consideration on data distribution is still necessary for selecting
models when a better performance is desired (Punt et al. 2000;
Maunder and Punt 2004; Ortiz and Arocha 2004).
Catch per unit effort is implicitly assumed to be propor-
tional to stock abundance in addition to other relevant varia-
bles that may influence bycatch rates in the process of CPUE
standardization (Marr 1951; Campbell 2004; Maunder and
Punt 2004). However, standardized values should be viewed
skeptically when the processes underlying data are not well
understood or potentially important covariables are not consid-
ered in the model (Minami et al. 2007). For this study, envi-
ronmental variables such as water temperature, salinity, and
pH were not used because they were not available from the
sea sampling program. Those environmental variables usually
exhibit high correlations with temporal or spatial variables
such as seasons and areas, and can be properly represented by
month and spatial coordination, the use of which may avoid
collinearity in regression analyses. However, collinearity
among explanatory variables is a critical issue for model fit-
ting, and caution should be taken in interpreting models if the
objective is to explore the relationship between catch and envi-
ronmental variables rather than standardize CPUE.
The interaction among catches in a lobster trap can also
influence the CPUE standardization (Punt et al. 2001).
Although the bycatch efficiency of lobster traps has not been
well studied, the models in this study showed that the catch of
lobster had a significant correlation with the bycatch rate of
Atlantic Cod and Cusk in all models with different error func-
tions and spatial scales (Table 2). On average, the bycatch rate
of Cusk in traps without lobsters was 10 times that of traps
with lobsters present, and the ratio was higher for Atlantic
Cod (calculated from primary data). Thus, possible species
interactions within a trap may reduce the catch rate of the fish-
ing gear. This effect needs to be considered for further stock
assessment and fishery management.
ACKNOWLEDGMENTS
We thank Maine DMR and all the onboard observers of the
sea sampling program for collecting the data. We thank
Kathleen Reardon and Carl Wilson for their help in interpret-
ing the lobster sea sampling data. Financial support of this
study was provided by the Northeast Cooperative Research
Program at the NOAA Northeast Fisheries Science Center and
the NOAA Saltonstall–Kennedy Grant Program.
REFERENCESAgarwal, D. K., A. E. Gelfand, and S. Citron-Pousty. 2002. Zero-inflated mod-
els with application to spatial count data. Environmental and Ecological Sta-
tistics 9:341–355.
Ames, E. P. 2004. Atlantic Cod stock structure in the Gulf of Maine. Fisheries
29(1):10–28.
Bertrand, S., E. D�ıaz, and M. eNiquen. 2004. Interactions between fish and fish-
er’s spatial distribution and behaviour: an empirical study of the anchovy
(Engraulis ringens) fishery of Peru. ICES Journal of Marine Science
61:1127–1136.
Beverton, R. J. H., and S. J. Holt. 1957. On the dynamics of exploited fish pop-
ulations. UK Ministry of Agriculture, London.
Bigelow, H. B., and W. C. Schroeder. 1953. Fishes of the Gulf of Maine. U.S.
Government Printing Office, Washington, D.C.
Campbell, R. A. 2004. CPUE standardisation and the construction of indices of
stock abundance in a spatially varying fishery using general linear models.
Fisheries Research 70:209–227.
Candy, S. G. 2004. Modelling catch and effort data using generalised linear
models, the Tweedie distribution, random vessel effects and random stra-
tum-by-year effects. CCAMLR (Commission for the Conservation of Ant-
arctic Marine Living Resources) Science 11:59–80.
Carlson, J. K., and J. H. Brusher. 1999. An index of abundance for coastal spe-
cies of juvenile sharks from the northeast Gulf of Mexico. Marine Fisheries
Review 61:37–45.
Chen, Y., S. Sherman, C. Wilson, J. Sowles, and M. Kanaiwa. 2006. A compari-
son of two fishery-independent survey programs used to define the population
structure of American lobster (Homarus americanus) in the Gulf of Maine.
U.S. NationalMarine Fisheries Service Fishery Bulletin 104:247–255.
Ciannelli, L., P. Fauchald, K.-S. Chan, V. N. Agostini, and G. E. Dingsør.2008. Spatial fisheries ecology: recent progress and future prospects. Journal
of Marine Systems 71:223–236.
Cragg, J. G. 1971. Some statistical models for limited dependent variables
with application to the demand for durable goods. Econometrica 39:829–
844.
Damalas, D., P. Megalofonou, and M. Apostolopoulou. 2007. Environmental,
spatial, temporal and operational effects on Swordfish (Xiphias gladius)
catch rates of eastern Mediterranean Sea longline fisheries. Fisheries
Research 84:233–246.
Dick, E. J. 2004. Beyond ‘lognormal versus gamma’: discrimination among
error distributions for generalized linear models. Fisheries Research
70:351–366.
Feller, W. 1968. An introduction to probability theory and its applications.
Wiley, New York.
Frank, K. T., B. Petrie, J. S. Choi, and W. C. Leggett. 2005. Trophic cascades
in a formerly cod-dominated ecosystem. Science 308:1621–1623.
Goodyear, C. P. 2003. Spatio-temporal distribution of longline catch per unit
effort, sea surface temperature and Atlantic marlin. Marine and Freshwater
Research 54:409–417.
Goodyear, C. P., D. Die, D. W. Kerstetter, D. B. Olson, E. Prince, and G. P.
Scott. 2003. Habitat standardization of CPUE indices: research needs.
ICCAT Collective Volume of Scientific Papers 55:613–623.
Hall, D. B. 2000. Zero-inflated Poisson and binomial regression with random
effects: a case study. Biometrics 56:1030–1039.
Hare, J. A., J. P. Manderson, J. A. Nye, M. A. Alexander, P. J. Auster, D. L.
Borggaard, A. M. Capotondi, K. B. Damon-Randall, E. Heupel, I. Mateo, L.
O’Brien, D. E. Richardson, C. A. Stock, and S. T. Biegel. 2012. Cusk
(Brosme brosme) and climate change: assessing the threat to a candidate
marine fish species under the US Endangered Species Act. ICES Journal of
Marine Science 69:1753–1768.
718 ZHANG AND CHEN
Harley, S. J., R. A. Myers, and A. Dunn. 2001. Is catch-per-unit-effort propor-
tional to abundance? Canadian Journal of Fisheries and Aquatic Sciences
58:1760–1772.
Harris, L. E., and A. R. Hanke. 2010. Assessment of the status, threats and
recovery potential of Cusk (Brosme brosme). Canadian Science Advisory
Secretariat Research Document 2010/004.
Hastie, T. J., and R. J. Tibshirani. 1990. Generalized additive models. CRC
Press, Boca Raton, Florida.
Hilborn, R., and C. J. Walters. 1992. Quantitative fisheries stock assessment:
choice, dynamics and uncertainty. Reviews in Fish Biology and Fisheries
2:177–178.
Hinton, M. G., and M. N. Maunder. 2003. Methods for standardizing CPUE
and how to select among them. ICCAT Collective Volume of Scientific
Papers 56:169–177.
Knutsen, H., P. E. Jorde, H. Sannaes, A. Rus Hoelzel, O. A. Bergstad, S. Ste-
fanni, T. Johansen, and N. C. Stenseth. 2009. Bathymetric barriers promot-
ing genetic structure in the deepwater demersal fish Tusk (Brosme brosme).
Molecular Ecology 18:3151–3162.
Lambert, D. 1992. Zero-inflated Poisson regression, with an application to
defects in manufacturing. Technometrics 34:1–14.
Lange, A. M. 1991. Alternative survey indices for predicting availability of
longfin squid to seasonal northwest Atlantic fisheries. North American Jour-
nal of Fisheries Management 11:443–450.
Levin, S. A. 1992. The problem of pattern and scale in ecology: the Robert H.
MacArthur award lecture. Ecology 73:1943–1967.
Lo, N. C.-H., L. D. Jacobson, and J. L. Squire. 1992. Indices of relative abun-
dance from fish spotter data based on delta-lognomal models. Canadian
Journal of Fisheries and Aquatic Sciences 49:2515–2526.
Lorance, P., and H. Dupouy. 2001. CPUE abundance indices of the main target
species of the French deep-water fishery in ICES sub-areas V–VII. Fisheries
Research 51:137–149.
Lynch, P. D., K. W. Shertzer, and R. J. Latour. 2012. Performance of methods
used to estimate indices of abundance for highly migratory species. Fisher-
ies Research 125–126:27–39.
Marr, J. C. 1951. On the use of the terms abundance, availability and apparent
abundance in fishery biology. Copeia 1951:163–169.
Maunder, M. N., and A. E. Punt. 2004. Standardizing catch and effort data: a
review of recent approaches. Fisheries Research 70:141–159.
Minami, M., C. E. Lennert-Cody, W. Gao, and M. Roman-Verdesoto. 2007.
Modeling shark bycatch: the zero-inflated negative binomial regression
model with smoothing. Fisheries Research 84:210–221.
Murawski, S., and J. Finn. 1988. Biological bases for mixed-species fisheries:
species co-distribution in relation to environmental and biotic variables.
Canadian Journal of Fisheries and Aquatic Sciences 45:1720–1735.
NEFSC (Northeast Fisheries Science Center). 2013. Gulf of Maine Atlan-
tic Cod (Gadus morhua) stock assessment for 2012. National Marine
Fisheries Service, NEFSC, Reference Document 13-01, Woods Hole,
Massachusetts.
Nelder, J. A., and R. W. M. Wedderburn. 1972. Generalized linear models.
Journal of the Royal Statistical Society Series A 135:370–384.
O’Neill, M. F., and M. J. Faddy. 2003. Use of binary and truncated negative
binomial modelling in the analysis of recreational catch data. Fisheries
Research 60:471–477.
Ortiz, M., and F. Arocha, 2004. Alternative error distribution models for stan-
dardization of catch rates of non-target species from a pelagic longline fish-
ery: billfish species in the Venezuelan tuna longline fishery. Fisheries
Research 70:275–297.
Pennington, M. 1985. Some statistical techniques for estimating abundance
indices from trawl surveys. U.S. National Marine Fisheries Service Fishery
Bulletin 84:519–526.
Pennington, M., and T. Strømme. 1998. Surveys as a research tool for manag-ing dynamic stocks. Fisheries Research 37:97–106.
Perry, R. I., and S. J. Smith. 1994. Identifying habitat associations of marine
fishes using survey data: an application to the northwest Atlantic. Canadian
Journal of Fisheries and Aquatic Sciences 51:589–602.
Peterman, R. M., and G. J. Steer. 1981. Relation between sport-fishing catch-
ability coefficients and salmon abundance. Transactions of the American
Fisheries Society 110:585–593.
Punt, A., D. Smith, R. Thomson, M. Haddon, X. He, and J. Lyle. 2001.
Stock assessment of the Blue Grenadier Macruronus novaezelandiae
resource off south-eastern Australia. Marine and Freshwater Research
52:701–717.
Punt, A. E., T. I. Walker, B. L. Taylor, and F. Pribac. 2000. Standardization of
catch and effort data in a spatially-structured shark fishery. Fisheries
Research 45:129–145.
Reed, W. J. 1986. Analyzing catch–effort data allowing for randomness in the
catching process. Canadian Journal of Fisheries and Aquatic Sciences
43:174–186.
Richards, L. J., and J. T. Schnute. 1992. Statistical models for estimating
CPUE from catch and effort data. Canadian Journal of Fisheries and Aquatic
Sciences 49:1315–1327.
Robson, D. 1966. Estimation of the relative fishing power of individual ships.
ICNAF (International Commission for the Northwest Atlantic Fisheries)
Research Bulletin 3:5–14.
Rose, G., and W. Leggett. 1991. Effects of biomass-range interactions on
catchability of migratory demersal fish by mobile fisheries: an example of
Atlantic Cod (Gadus morhua). Canadian Journal of Fisheries and Aquatic
Sciences 48:843–848.
Rotherham, D., A. Underwood, M. Chapman, and C. Gray. 2007. A strategy
for developing scientific sampling tools for fishery-independent surveys of
estuarine fish in New South Wales, Australia. ICES Journal of Marine Sci-
ence 64:1512–1516.
Rudershausen, P., W. Mitchell, J. Buckel, E. Williams, and E. Hazen.
2010. Developing a two-step fishery-independent design to estimate the
relative abundance of deepwater reef fish: application to a marine pro-
tected area off the southeastern United States coast. Fisheries Research
105:254–260.
Shono, H. 2005. Is model selection using Akaike’s information criterion
appropriate for catch per unit effort standardization in large samples? Fish-
eries Science 71:978–986.
Shono, H. 2008. Application of the Tweedie distribution to zero-catch data in
CPUE analysis. Fisheries Research 93:154–162.
Somers, I. 1987. Sediment type as a factor in the distribution of commercial
prawn species in the western Gulf of Carpentaria, Australia. Marine and
Freshwater Research 38:133–149.
Somers, I. F. 1994. Species composition and distribution of commercial
penaeid prawn catches in the Gulf of Carpentaria, Australia, in relation
to depth and sediment type. Marine and Freshwater Research 45:317–
335.
Tian, S., Y. Chen, X. Chen, L. Xu, and X. Dai. 2010. Impacts of spatial scales
of fisheries and environmental data on catch per unit effort standardisation.
Marine and Freshwater Research 60:1273–1284.
Tian, S., C. Han, Y. Chen, and X. Chen. 2013. Evaluating the impact of spatio-
temporal scale on CPUE standardization. Chinese Journal of Oceanology
and Limnology 31:935–948.
Welsh, A. H., R. B. Cunningham, C. Donnelly, and D. B. Lindenmayer. 1996.
Modelling the abundance of rare species: statistical models for counts with
extra zeros. Ecological Modelling 88:297–308.
Zeileis, A., C. Kleiber, and S. Jackman. 2008. Regression models for count
data in R. Journal of Statistical Software [online serial] 27(8).
ABUNDANCE INDICES FOR ATLANTIC COD AND CUSK 719
Top Related