their bycatch in the lobster fishery cod and cusk in the ......cusk are distributed across the north...

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North American Journal of Fisheries Management

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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

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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.


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


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


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.


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.

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their bycatch in the lobster fishery cod and cusk in the ......cusk are distributed across the north...

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