sm80n1-4205

Stock assessment for the western winter-spring cohort of neon flying squid (Ommastrephes bartramii) using environmentally dependent surplus production models

Jintao Wang 1,5, Wei Yu 1,5, Xinjun Chen 1,2,3,5, Yong Chen 4,5

1 College of Marine Sciences, Shanghai Ocean University, 999 Hucheng Ring Road, Lingang New City, Shanghai 201306, China. E-mail: xjchen@shou.edu.cn
2 National Engineering Research Centre for Oceanic Fisheries, Shanghai Ocean University, 999 Hucheng Ring Road, Lingang New City, Shanghai 201306, China.
3 Key Laboratory of Sustainable Exploitation of Oceanic Fisheries Resources, Ministry of Education, Shanghai Ocean University, 999 Hucheng Ring Road, Lingang New City, Shanghai 201306, China.
4 School of Marine Sciences, University of Maine, Orono, Maine 04469, USA.
5 Collaborative Innovation Centre for National Distant-water Fisheries, 999 Hucheng Ring Road, Lingang New City, Shanghai 201306, China.

Summary: The western winter-spring cohort of neon flying squid, Ommastrephes bartramii, is targeted by Chinese squid-jigging fisheries in the northwest Pacific from August to November. Because this squid has a short lifespan and is an ecological opportunist, the dynamics of its stock is greatly influenced by the environmental conditions, which need to be considered in its assessment and management. In this study, an environmentally dependent surplus production (EDSP) model was developed to evaluate the stock dynamics of O. bartramii. Temporal variability of favourable spawning habitat with sea surface temperature (SST) of 21-25°C (Ps) was assumed to influence carrying capacity (K), while temporal variability in favourable feeding habitat areas with different SST ranges in different months (Pf) wa s assumed to influence intrinsic growth rate (r). The parameters K and r in the EDSP model were thus assumed to be linked to temporal variability in the proportion of Ps and Pf, respectively. According to Deviance Information Criterion values, the estimated EDSP model with Ps was considered to be better than the conventional surplus production model or other EDSP models. For this model, the maximum sustainable yield (MSY) varied from 210000 to 262500 t and biomass at MSY level varied from 360000 to 450000 t. The fishing mortality rates of O. bartramii from 2003 to 2013 were much lower than the fishing mortality at target level and MSY level (Ftar and FMSY) and stock biomass was higher than BMSY, suggesting that this squid was not in the status of overfishing and stock was not overfished. The management reference points in the EDSP model for O. bartramii were more conservative than those in the conventional model. This study suggests that the environmental conditions on the spawning grounds should be considered in squid stock assessment and management in the northwest Pacific Ocean.

Keywords: Ommartrephes bartramii; stock assessment; surplus production model; environmental factors; Northwest Pacific Ocean.

Evaluación de la cohorte occidental de invierno-primavera del calamar volador neon (Ommastrephes bartramii) utilizando modelos de producción excedente dependientes del medio ambiente

Palabras clave: Ommartrephes bartramii; evaluación de stock; modelo de producción excedente; factores ambientales; Océano Pacifico Noroeste.

Citation/Como citar este artículo: Wang J., Yu W., Chen X., Chen Y. 2016. Stock assessment for the western winter-spring cohort of neon flying squid (Ommastrephes bartramii) using environmentally dependent surplus production models. Sci. Mar. 80(1): 69-78. doi: http://dx.doi.org/10.3989/scimar.04205.11A

Editor: W. Norbis.

Received: January 7, 2015. Accepted: October 14, 2015. Published:

Contents

INTRODUCTIONTop

The neon flying squid, Ommastrephes bartramii, is an economically important oceanic species widely distributed in the northwest Pacific Ocean (, ). This squid has been commercially exploited by Japanese squid-jigging fleets since 1974, and later by South Korea and Taiwan province of China. In 1993, the Chinese mainland squid-jigging fleets began exploratory fishing to investigate the abundance of O. bartramii in waters bounded by 38-42°N and 140-150°E. In 1999, several efforts further extended the fishing grounds eastward to 175°W (, ). In general, Chinese squid-jigging vessels mainly fish in the regions between 170°W and 175°W in June and July, and then shift to waters west of 165°E from August to November (). The total annual production of squid caught by Chinese mainland ranged from 36764 to 113200 t from 2003 to 2013.

The North Pacific population of O. bartramii has been classified into four stocks: the central stock of the autumn cohort, the eastern stock of the autumn cohort, the western stock of the winter-spring cohort and the central-eastern stock of the winter-spring cohort (). Of the four stocks, the western winter-spring cohort of O. bartramii has become a traditional fishing target for the Chinese squid-jigging fleets in water between 150 and 165°E (). This cohort migrates from subtropical waters to the subarctic boundary during the first half of the summer and then moves northward into the subarctic domain from August to November. The squid mature gradually in autumn and are thought to begin their spawning migration in October and November (, ).

Fishery biology, abundance and fishing ground distribution of O. bartramii have been well studied over the last few decades (, , , , , ). Squid abundance and distribution are found to be significantly influenced by environmental conditions on the spawning and feeding grounds. For example, evaluated the sea surface temperature anomaly (SSTA) on the spawning and feeding grounds of O. bartramii, and concluded that high SSTA caused by La Niña events would lead to low recruitment, while the SSTA in an El Niño year tended to be normal and lead to high recruitment. Variability in the SST on the feeding ground could also result in different spatial distribution of the squid fishing ground. examined the variations in the proportion of thermal habitats with favourable sea surface temperature areas (PFSSTA) in 1995-2004, and suggested that PFSSTA in February on the spawning ground and from August to November on the feeding ground could explain about 60% of the variability in the abundance of O. bartramii. Additionally, developed a habitat suitability index (HSI) model to identify the optimal habitat in relation to the oceanographic conditions, including sea surface temperature (SST), sea surface salinity (SSS), sea surface height anomaly (SSHA) and chlorophyll-a (Chl-a) concentration. They found that the highest monthly catch and fishing effort occurring in the different waters were closely related to those variables.

Previous studies evaluated the annual stock size of the autumn cohort and winter-spring cohort of O. bartramii on the basis of catch data analyses (, ). Due to the unique life history of this species, traditional age- or length-structured models are not appropriate for evaluating the influences of intensive commercial jigging fleets on its stock dynamics. Many methods have been proposed for assessing short-lived species such as the squid. evaluated the annual biomass of the autumn cohort in 1982-1992 on driftnet fishing grounds using a stock production model incorporating covariates (ASPIC non-equilibrium dynamic model) () and the DeLury depletion model (). For the winter-spring cohort, fitted a modified depletion model to the Chinese squid-jigging fisheries data to estimate squid stock abundance in 2000-2005, and found that the annual maximum allowable catch ranged from 80000 to 100000 t, which was consistent with the estimation by for the annual sustainable catch of the western stock. However, as a short-lived ecological opportunist, O. bartramii is also typically subject to large fluctuations in abundance, responding rapidly to changes in environmental conditions (, , , , , , , ). Therefore, environmental variables are considered to play a critical role in regulating the dynamics of squid stocks and need to be considered in the squid stock assessment.

An environmentally dependent surplus production (EDSP) model has been developed from the traditional surplus production model. In surplus production models, fish population dynamics and fishing processes including natural mortality, growth, recruitment, and fishing mortality are assumed to be a function of a single aggregated measure of biomass (). This approach may be suitable for species with a short-life span and/or limited availability of age/size composition data (). Research has also shown that surplus production models, although simple, may provide more accurate and precise estimates of management-related quantities than complex models (, ). Therefore, a surplus production model incorporating environmental variables would be an appropriate approach for assessing the O. bartramii stock.

O. bartramii is a short-lived species with a lifespan of less than one year (), whose yearly biomass is almost dependent on the recruitment (). Thus, it is reasonable to consider the environmental indices in the assessment of the O. bartramii stock. However, the traditional surplus models treat the carrying capacity and intrinsic rate of growth as constant (), which is inconsistent with the facts that carrying capacity and population growth rate for squid may fluctuate greatly over time as a result of changes in environmental condition on the spawning ground and feeding ground. In this study, we developed two environmental indicators including the proportions of the areas with favourable SST on the spawning ground (Ps) and feeding ground (Pf), which were assumed to influence carrying capacity (K) and intrinsic growth rate (r), respectively. We evaluated the traditional production models and several EDSP models with both indices, Ps only or Pf only, being incorporated. These models were compared and an optimal model was selected for estimating the squid stock abundance and reference points. This study may provide a new insight into the assessment of O. bartramii stock.

MATERIALS AND METHODSTop

Fishery data

Data on daily catch (t), effort (days fished, d), fishing dates and fishing locations (longitude and latitude) were obtained from the Chinese mainland commercial jigging fleets operating in the areas between 35-45°N and 145-165°E in the northwest Pacific Ocean from July to December from 2003 to 2013. The western stock of the winter-spring cohort and the central-eastern stock of the winter-spring cohort are separated near 170°E (Bower and Ichii 2005). Thus, the Chinese commercial jigging fleet should target a unit stock. One unit of fishing area was defined as 0.5° latitude by 0.5° longitude.

We assumed no by-catches in the squid fishery (), and there would be little discard relative to annual catches. Chinese jigging vessels, about 200 in number from 2003 to 2013, were equipped with an engine of 120 KW×2, 112 KW squid attracting lights and 16 squid-jigging machines, and had almost identical fishing power and lighting operation. Therefore, catch per unit fishing day (CPUE, t d–1) of the squid-jigging vessels was a reliable indicator of stock abundance on the fishing ground (). The monthly nominal CPUE in one fishing unit of 0.5°×0.5° is calculated as follows:

 $CPUE y m i = C y m i F y m i$ (1)

where CPUEymi is monthly CPUE at i fishing unit in month m and year y; Cymi is monthly catch (t) at i fishing unit in month m and year y; and Fymi is number of fishing days at i fishing unit in month m and year y.

Because the annual catch of O. bartramii by Chinese mainland accounted for about 80% of the total catches of this species (), we modified the annual total catch of O. bartramii from 2003 to 2013 in the northwest Pacific for our estimation (Fig. 1). Although the total annual catch estimated using this approach may have some issues for some years, the focus of this study is to develop and demonstrate a modelling framework which incorporates critical habitat information in the stock assessment for environmentally-sensitive species, and this data set is sufficient to serve this purpose.

Environmental data

Environmental variables SST, SSH and Chl-a concentration were used to obtain the standardized yearly CPUE based on the generalized additive model (GAM). Monthly SST, SSH and Chl-a concentration data from 2003 to 2013 on the presumed spawning (20°-30°N, 130°-170°E) and fishing grounds (38°-46°N, 150°-165°E) were obtained from the Live Access Server of National Oceanic and Atmospheric Administration OceanWatch (http://oceanwatch.pifsc.noaa.gov/las/servlets/dataset). The spatial resolution of SST, SSH and Chl-a concentration data were 0.1°×0.1°, 0.25°×0.25°, and 0.05°×0.05°, respectively. All the environmental data were then converted to a 0.5°×0.5° grid by the method of averaging for each month in order to correspond to the spatial grid of CPUE. For instance, averaging 25 points of SST can convert to a 0.5°×0.5° grid.

Standardizing yearly CPUE by generalized additive model

CPUE is commonly assumed to be proportional to stock abundance. Therefore, it is usually considered as a relative abundance index in the monitoring and assessment of a fish stock (). The GAM model is previously employed to standardize yearly CPUEs, which represent the same proportional change in stock size of O. bartramii using data samples (). The CPUE is naturally ln-transformed with errors being assumed to be normally distributed in the GAM modelling. This assumption was evaluated using Q-Q plots. The functional relationships between CPUE and environmental variables are likely to be non-linear (). Thus, GAM was used for the CPUE standardization in this study, which can be written as:

 Ln(CPUE+c)=factor(year)+factor(month)+s(longitude)+s(latitude)+s(SST)+s(SSH)+s(Chl-a)+ε (2)

where s is a spline smoother function; and constant c is assumed to be 10% of mean CPUE (); var ε= σ2 and E(ε)=0.

Environmentally dependent surplus production models

The areas with the favourable SST (21-25°C) in the presumed spawning ground (20º-30ºN, 130º-170ºE) during the spawning season (January-April) play a critical role in determining the recruitment of O. bartramii (, , , ), and the areas with favourable SST (15ºC-19ºC in August, 14-18°C in September, 10-13°C in October and 12-15°C in November) on the feeding ground (38°-46°N, 150°-165°E) during the feeding season (August-November) influence the distribution of O. bartramii in feeding activity (, , ). Annual environmental indices were averaged from monthly Ps and Pf which were calculated by the number of fishing units with the optimal SST divided by the total number of the fishing units on the spawning and feeding ground, respectively.

Schaefer’s surplus production model (referred to as SP) can be written as

 $log( B t )| K, σ 2 =log(K)+ u t log( B t )| B t−1 ,K,r, σ 2 =log{ B t−1 +r B t−1 ( 1− B t−1 K )− C t−1 }+ u t$ (3)
 $log( I t )| B t ,q, τ 2 =log(q)+log( B t )+ υ t$ (4)

where Bt is the biomass in t year; K is the carrying capacity; r is the intrinsic rate of stock growth; q is the catch ability coefficient; and It is the CPUE in t year. It is assumed to be proportional to Bt, and ut and υt are independent and identically distributed IID N (0, σ2) and IID N(0, τ2) random variables respectively.

We hypothesized that for a given year “effective” carrying capacity was in proportion to Ps and the “effective” intrinsic stock growth rate changed in proportion to Pf for O. bartramii. Therefore, the surplus production model with the parameter of Ps (referred to as Ps-EDSP) is given by:

 $log( B t )| K, σ 2 =log(K)+ u t log( B t )| B t−1 ,K,r, σ 2 =log{ B t−1 +r B t−1 ( 1− B t−1 P s t−1 K )− C t−1 }+ u t$ (5)

The surplus production model with the parameter of Pf (referred to as Pf-EDSP) is given by:

 $log( B t )| K, σ 2 =log(K)+ u t log( B t )| B t−1 ,K,r, σ 2 =log{ B t−1 +P f t−1 r B t−1 ( 1− B t−1 K )− C t−1 }+ u t$ (6)

The surplus production model with the parameters of both Ps and Pf (referred to as Ps-Pf-EDSP) is given by:

 $log( B t )| K, σ 2 =log(K)+ u t log( B t )| B t−1 ,K,r, σ 2 =log{ B t−1 +P f t−1 r B t−1 ( 1− B t−1 P s t−1 K )− C t−1 }+u$ (7)

Based on the results of and , we assumed that the initial biomass of O. bartramii B0 in 2003 was 400000 t. The likelihood function and prior distribution of the parameters in Bayesian inference were stated as follows:

- Likelihood function

We fitted Schaefer’s surplus production models by Bayesian inference in R using the R2WinBugs library (). A likelihood function was used to estimate the degree of fitting between the observation data and the data predicted by the surplus production models (). We assumed that the observation errors followed the ln-normal distribution, and the likelihood function is written as:

 $L(I|θ)= ∏ 2003 2013 1 I t σ 2π exp{ [log( I t )−log(q B t )] 2 2 σ 2 }$ (8)

The σ was estimated to be 0.12 in the CPUE stanardization.

- Setting prior distribution of model parameters

- Calculating posterior distribution of parameters

The initial guess values for the parameters of models in the likelihood estimation were set as follows: the intrinsic rate of growth was 0.8, carrying capacity was 400000 t and the catchability coefficient was 0.5×10–5. The posterior distribution of parameters of Schaefer models were calculated by the Markov Chain Monte Carlo (MCMC) method in R. Three MCMC chains were used and the number of MCMC iterations was 50000, and the first 10000 results of iterations were discarded. For the subsequent 40000 times, we saved the results every 40 times.

Fishery biological reference points, including maximum sustainable yield (MSY), fishing mortality at MSY level (FMSY), biomass at MSY level (BMSY), fishing mortality at target level (Ftar, fishing mortality at 0.1 level, F0.1), fishing mortality at MSY level (FMSY), and actual fishing mortality for year t (Ft) based on the SP and EDSP were estimated using mean values of posterior distribution of parameters of models (Table 1). The selection of models was based on the deviance information criterion (DIC), where the lowest DIC is selected to be the best model.

Table 1. – The fishery management reference points of O. bartramii in the northwest Pacific Ocean. BRP, biological reference point; SP, surplus production; EDSP, environmentally dependent surplus production models; Ps, proportion of favourable spawning habitat areas with sea surface temperature of 21-25°C; Pf, proportion of favourable feeding habitat areas with different sea surface temperature ranges in different months; MSY, maximum sustainable yield. Note: Ct is the catch in year t and Bt is the biomass in year t.

Management reference point Catch Fishing mortality coefficient (F) Biomass (B)
BRP in SP model MSY=rK/4 FMSY=r/2
F
0.1=0.45r
Ft=Ct/Bt
BMSY=K/2
BRP in Ps-EDSP, Pf-EDSP, Ps-Pf-EDSP models MSY=Pf rPs K/4 FMSY=Pf r/2
F0.1=0.45Pf r
Ft=Ct/Bt
BMSY=Ps K/2

RESULTSTop

Comparing the nominal CPUE with the GAM-standardized CPUE

The GAM model was constructed based on temporal (year and month), spatial (latitude and longitude) and environmental (SST, SSH and Chl-a concentration) factors. The annual nominal CPUE was then compared with the GAM-estimated standardized CPUE from 2003 to 2013. The same variability trends were exhibited between the annual nominal CPUE and the GAM-standardized CPUE (Fig. 2). Large differences occurred in 2007: the nominal CPUE was highest with a value of 5.12 t d–1, while the GAM-standardized CPUE in 2007 was extremely low with a value of 1.16 t d–1. The production and abundance of western winter-spring cohort of O. bartramii fluctuated from year to year: both were high in 2003-2008 and low in 2009-2013 (Fig. 1).

Comparison of surplus production models

According to the samplings in MCMC and the posterior distribution of parameters (r, K, and q) of the four surplus production models (Fig. 3), there were large differences between the posterior distribution of parameters and their prior distributions. The mean posterior values of parameters (r, K, and q) for the four surplus production models were different. The ranges of r, K, and q were 1.71-1.90, 650000-950000 t, and 0.3-0.4×10–5, respectively. The minimum values of r and K occurred in the Ps-EDSP and SP model, and the maximum of r and K occurred in the Pf-model and Ps-Pf-model, respectively. The results suggested that the optimal fitted model was the Ps-EDSP with the minimum DIC value (Table 2).

Table 2. – Summary statistics for the parameters of Schaefer surplus production models of O. bartramii.

Models Parameters
r K 104 q 10–4 DIC
Mean SD Rhat n.eff Mean SD Rhat n.eff Mean SD Rhat n.eff
SP model 1.77 0.65 1.00 580 65 0.17 1.00 1000 0.04 0.002 1.00 1000 55.9
Ps-model 1.71 0.69 1.00 1000 90 0.16 1.00 1000 0.03 0.002 1.00 290 30.7
Pf-model 1.90 0.78 1.00 420 80 0.17 1.00 1000 0.03 0.002 1.00 820 35.8
Ps-Pf-model 1.87 0.77 1.00 1000 95 0.17 1.00 1000 0.03 0.002 1.00 1000 40.1

The MSY and BMSY were 289100 and 325000 t for the SP model, respectively (Table 3). The MSY varied from 210000 to 262500 t and its biomass ranged from 360000 to 450000 t for the Ps-EDSP model (Table 3). For the Pf-EDSP model, the MSY ranged from 245300 to 371600 t, and the BMSY was approximately 400000 t (Table 3). For the Ps-Pf-EDSP model, the MSY was within the range of 254100 to 392400 t, and the BMSY was from 380000 to 475000 t (Table 3).

Table 3. – The fishery management reference points and stock assessment results estimated by the SP model (A), the Ps-model (B), the Pf-model (C) and the Ps-Pf-model (D) in 2003-2013.

Year Biomass (104 t) BMSY (104 t) Blim (104 t) MSY (104 t) Ftar FMSY Ft
A B C D A B C D A B C D A B C D A B C D A B C D A B C D
2003 40.00 40.00 40.00 40.00 32.5 39.95 40.0 42.27 8.12 9.98 10.0 10.57 28.91 23.37 37.16 39.24 0.8 0.78 0.84 0.84 0.88 0.87 0.92 0.93 0.32 0.32 0.32 0.32
2004 54.41 63.56 60.11 63.53 32.5 42.30 40.0 44.65 8.12 10.58 10.0 11.16 28.91 24.68 33.08 36.89 0.8 0.78 0.74 0.74 0.88 0.87 0.82 0.83 0.30 0.26 0.28 0.26
2005 53.52 76.03 63.19 72.30 32.5 43.20 40.0 45.60 8.12 10.80 10.0 11.40 28.91 25.20 26.37 30.05 0.8 0.78 0.60 0.59 0.88 0.87 0.66 0.66 0.29 0.20 0.24 0.21
2006 54.97 63.01 71.76 71.91 32.5 38.70 40.0 40.85 8.12 9.68 10.0 10.21 28.91 22.59 36.04 36.79 0.8 0.78 0.81 0.81 0.88 0.87 0.90 0.90 0.31 0.27 0.23 0.23
2007 53.16 68.44 66.41 70.70 32.5 39.60 40.0 41.80 8.12 9.90 10.0 10.45 28.91 23.10 31.22 32.60 0.8 0.78 0.70 0.70 0.88 0.87 0.78 0.78 0.33 0.26 0.27 0.25
2008 52.70 56.64 63.83 59.61 32.5 36.00 40.0 38.00 8.12 9.00 10.0 9.5 28.91 21.00 26.76 25.40 0.8 0.78 0.60 0.60 0.88 0.87 0.66 0.67 0.31 0.29 0.26 0.28
2009 53.87 68.82 68.37 71.77 32.5 40.05 40.0 42.28 8.12 10.01 10.0 10.56 28.91 23.37 32.70 34.54 0.8 0.78 0.74 0.74 0.88 0.87 0.82 0.82 0.11 0.08 0.08 0.08
2010 64.53 91.14 76.67 90.79 32.5 45.00 40.0 47.50 8.12 11.25 10.0 11.87 28.91 26.25 28.24 33.52 0.8 0.78 0.64 0.64 0.88 0.87 0.70 0.71 0.13 0.09 0.11 0.10
2011 56.70 73.86 71.94 82.64 32.5 43.20 40.0 45.60 8.12 10.80 10.0 11.40 28.91 25.20 24.53 27.94 0.8 0.78 0.55 0.55 0.88 0.87 0.61 0.61 0.15 0.11 0.12 0.10
2012 61.10 71.26 72.50 73.00 32.5 38.71 40.0 40.85 8.12 9.67 10.0 10.21 28.91 22.58 24.90 25.41 0.8 0.78 0.56 0.56 0.88 0.87 0.62 0.62 0.09 0.07 0.07 0.07
2013 62.23 80.74 76.86 82.88 32.5 40.51 40.0 42.75 8.12 10.13 10.0 10.69 28.91 23.63 28.62 30.56 0.8 0.78 0.64 0.64 0.88 0.87 0.70 0.71 0.13 0.10 0.10 0.10

Moreover, the values of Ftar and FMSY in the SP model differed from those in other three models (Table 3). Of the four surplus production models, the indications were that the fishing mortality coefficient of O. bartramii from 2003 to 2013 was much smaller than the values of Ftar and FMSY. Meanwhile, the annual catch of O. bartramii in 2003-2013 was also lower than the value of MSY (Table 3).

The results of the four surplus production models indicated that the biomass and development of the O. bartramii fishery are in a good state at present (Table 3; Fig. 4). The resource of this species was at a high level, with no sign of occurrence of overfishing based on the Ps-EDSP model (Fig. 4).

DISCUSSIONTop

There have been many attempts to explain variation in recruitment based on the relationship between some direct or indirect measures of year-class strength and environmental variables (). The most commonly used environmental variables are temperature, salinity and wind (). Temperature, because it regulates many physiological processes, has been considered to be an important explanatory variable of recruitment in the context of global warming (). Salinity has frequently been used as an indirect measure of nutrient flux, and the physical process by which wind may influence recruitment is thought to be primarily through effects on the egg and larval transportation and distribution (). The significance of these variables identified in this study is consistent with their ecological roles in regulating the squid habitat quality and stock dynamics ().

For a short-lived species, the role of environmental variables in regulating its population dynamics has received much emphasis and comprises an important research topic (, ). Most squid live for less than one year (), and recruitment success is greatly influenced by the physical and biological environmental conditions on the spawning and nursery grounds, which contribute to the variability in the stock abundance (). In addition, the abundance and distribution of squid populations on the fishing ground tend to be greatly affected by oceanographic conditions and respond quickly to changes in the environment (, , , , , , , ). For instance, suggested that about 55% of the variability in recruitment of the Falkland Island Illex argentinus fishery could be explained by variations in the total putative favourable SST areas on the spawning ground during the spawning season. Variability in the abundance of Todarodes pacificus in the Sea of Japan was found to be closely related to changes in their favourable SST areas for paralarvae development (). and suggested that February Ps and August to November Pf could account for about 60% of the variability in O. bartramii abundance between 1995 and 2004. February Ps was the most important factor influencing squid recruitment during the spawning season, and feeding ground Pf during the fishing season also had a strong influence on CPUE. Consequently, the SST is an important environmental indicator for predicting the recruitment of squid (), and should be considered in O. bartramii stock assessment.

In this study, the nominal CPUE in 2007 was extremely high, possibly due to the high concentrated fishing operation along the longitudinal direction during that year. This finding suggests that it is important to obtain the standardized yearly CPUE. Additionally, no significant correlations were identified between yearly CPUE and monthly Ps and Pf. However, and evaluated the influences of SST on the spawning ground on the abundance of O. bartramii. These authors suggested that there was a significant positive relationship between the monthly proportion of favourable SST areas on the spawning ground and CPUE, but this relationship was not consistent with the results of our study. The reasons which caused this difference might be the use of a variety of resource abundance indicators (nominal or standardized CPUE) and different sources of fishery data. Therefore, the average Ps during spawning months and the average Pf during feeding months other than significant Ps and Pf were used to measure the “effective” K and r. The methods for estimating the parameters of the surplus production model can be divided into three types: equilibrium estimators, process-error estimators and observation-error estimators (, ). Each estimator has its own drawback. For example, the assumption of the equilibrium estimators is that they are suitable for applying to a fishery in equilibrium but not for an actual fishery. For process-error estimators, we usually obtain negative values of parameters (r, q) when converting the surplus production equation into a linear form fitted by a linear regression. Bayesian inference has been increasingly used for fisheries in recent years because it provides a systematic approach that explicitly incorporates both uncertainty and risk caused by uncertainty in the analysis (, , , ). Atypical errors should also be noted in the data. Mis-specification of prior distribution and the choice of an inappropriate likelihood function may result in unreliable posterior distribution for parameters in Bayesian inference (, , , ). In this paper, we used Bayesian inference to estimate the parameters of the four surplus production models, and attempted to interpret the data consistently by using standardized CPUE and modifying the yearly catch from 2003 to 2013. We also referred to some previous studies in order to set the prior distribution (normal distribution) of parameters and to select the likelihood function (, ). According to the MCMC results, there were great differences in the posterior distributions of parameters (r, K, q) and prior distributions. It was shown that the fishery data for O. bartramii provided enough information to estimate the parameters in these four surplus production models.

Fishery statistics of the Chinese squid-jigging fleets (Fig. 1) suggest a large fluctuation in annual production of O. bartramii. In this study, the annual catches of O. bartramii are lower than the MSY. The current fishing mortality rates are also lower than Ftar in the four surplus production models, indicating that overfishing does not occur in the O. bartramii fishery (Fig. 4). The yearly biomass of O. bartramii in the four surplus production models is higher than BMSY, suggesting that the resource of O. bartramii is not overfished and has been at a high level of abundance in recent years. Thus, we can conclude that overfishing does not occur and the stock is not overfished for the O. bartramii stock in the northwest Pacific. These findings are basically consistent with the previous results (, ).

The DIC value of the original surplus production model was maximum in the four models, and the fitting level of the surplus production model with environmental factors was higher than that of the models without environmental factors (Table 3). Changes in environmental factors (Ps and Pf) have important impacts on carrying capacity (K) and intrinsic rate of growth (r). The particle-tracking experiment showed that paralarvae and juveniles aged <90 days remained on their spawning grounds and that Chl-a in this habitat, where 21°C<SST<25°C, had a significant positive correlation with the CPUE (), and Ps calculated by average optimal SST (21°C<SST<25°C) on the spawning ground would affect the survival of paralarvae and juveniles. Moreover, SST was the most important environmental factor in the formation of the fishing ground based on the HSI model and the neural network model (, ). Pf is a measure of habitat quality of the fishing ground and would affect individual growth. Hence, environmental conditions, especially Ps and Pf, have significant influences on the spawning, hatching, growth, and even the whole life history of O. bartramii. We considered annual variability of environmental variables in estimating fishery management reference points (MRPs), resulting in temporal differences in reference points, which better reflect temporal changes in the habitat quality than the reference points assumed to be same over time in a traditional stock assessment. This can be useful to help adjust annual regulations in O. bartramii fisheries management.

The development status of the O. bartramii fishery from 2003 to 2013 based on the SP model and the Ps-EDSP model were plotted (Fig. 4). At present, the O. bartramii fishery development is still not fully exploited, and the advantage of the EDSP model is not obvious in this situation. However, with an increased intensity of exploitation, the EDSP model proves to be more conservative as the “B/BMSY” in the Ps-EDSP model tended to be closer to “1” (the threshold of overfishing) than that in the SP model (Fig. 4). In summary, when there was low Ps and Pf, the “effective” r and K decreased, calling for a decline in fishing effort to avoid the overexploitation of O. bartramii resources.

The uncertainty of the models came mainly from (1) uncertainty associated with data because we only included the catch data from the Chinese fishery, although we standardized yearly CPUE and modified yearly catches; and (2) uncertainty of model parameters: we assumed the biomass in 2003 to be an initial value of 400000 t, and this may induce biases in the estimation of biomass of O. bartramii. In addition, we also assumed that the standard deviation of CPUE (σ) was equal to 0.12, and the effects of this assumed σ value on model selection and resource assessment need to be further investigated in future studies.

In summary, an estimated EDSP model fitted the data better than the conventional Schaefer surplus model without environmental factors in estimating the squid stocks. We found that the fishery MRPs largely depended on optimal spawning and feeding habitat areas. These findings suggest that environmental factors on the spawning and feeding grounds should be considered in squid stock assessment and management of O. bartramii in the northwest Pacific.

ACKNOWLEDGEMENTSTop

We thank the Chinese Distant-Water Squid-Jigging Technical Group for providing fishery data and information, and we thank NOAA for providing the environmental data used in this paper. This work was funded by State 863 projects (2012AA092303), the Funding Programme for Outstanding Dissertations at Shanghai Ocean University, the Funding Scheme for Training Young Teachers in Shanghai Colleges and the Shanghai Leading Academic Discipline Project (Fisheries Discipline). Involvement of Y. Chen was supported by SHOU International Centre for Marine Studies and the Shanghai 1000 Talent Programme.

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