The Argentinian shortfin squid, Illex argentinus, is one of the most economically important species in the Southwest Atlantic. It is widely distributed across the Patagonian Shelf and in adjacent oceanic waters, occurring between 22°S and 54°S (Haimovici et al., 1998). In 1997, Chinese fleets started to exploit I. argentinus in the waters bounded by 43°–50°S and 55°–61°W (Lu et al., 2013a). The annual catch of this squid exploited by Chinese squid-jigging vessels ranged from 5 215 t to 99 387 t during 2000 to 2010.

The population structure of I. argentinus is complex and can be divided into three or four stocks based on length at maturity, area, time of spawning, the distribution of early life stages, juveniles and adults (Brunetti et al., 1998; Haimovici et al., 1998). The most abundant winter-hatched population of squid, known as the southern patagonic stock (SPS), is targeted by Chinese squid-jigging fleets (Lu et al., 2013a). The SPS undertakes long-distance migrations between the winter hatching grounds in the region of the northern Patagonian shelf/slope and the summer feeding grounds in the south (Hatanaka, 1998; Haimovici et al., 1998; Arkhipkin, 2000).

Extensive research has been conducted to study the fishery biology, abundance and fishing ground distribution of I. argentinus in recent decades (Arkhipkin, 1993; Arkhipkin and Laptikhovsky, 1994; Haimovici et al., 2014; Rosas-Luis et al., 2014; Waluda et al., 2001, 2008). This research has indicated that squid abundance is significantly affected by the environmental conditions at the spawning grounds. For example, Waluda et al. (2001) found that high squid abundance was associated with a higher proportion of favorable-SST waters within the inferred hatching area in the year preceding recruitment to the fishery.

The Leslie-Delury model (Basson et al., 1996) has rarely been used to analyze catch data of I. argentinus to determine the annual stock size. Traditional age- or length-structured models have had difficulty evaluating the influence of intensive commercial jigging fleets on I. argentinus stock size due to its unique life history. The methods for assessing short-lived species, such as ommatrephid squids, have greatly improved in recent years. Ichii et al. (2006) evaluated the annual biomass of fall cohorts for 1982–1992 on the driftnet fishing grounds using the ASPIC none equilibrium biomass dynamic model (Prager, 1994) and the DeLury depletion model (Hilborn et al., 1993). For the winter-spring cohort of Ommastrephes bartramii, Chen et al. (2008) fit a modified depletion model to the Chinese squid-jigging fisheries data to estimate the squid stock abundance from 2000 to 2005. The annual maximum allowable catch ranged from 80 000 t to 100 000 t and was consistent with estimations by Osako and Murata (1983) for the annual sustainable catch of the western stock. However, as short-lived ecological opportunists, I. argentinus are typically subject to large fluctuations in abundance, responding rapidly to changes in environmental conditions (Waluda et al., 2008). Therefore, environmental variables are considered to be indispensable factors in assessments of I. argentinus stocks.

The environmentally dependent surplus production (EDSP) model evolved from the traditional surplus production model. In surplus production models, fish population dynamics and fishing processes that include natural mortality, growth, recruitment, and fishing mortality are assumed to be a function of a single aggregated measure of biomass (Wang et al., 2014). This approach may be applicable for species with short life cycles and limited availability of age/size composition data (Zhan, 1995). Research also has shown that surplus production models can provide more accurate and precise estimates of management-related quantities than complex models (Wang et al., 2014). Illex argentinus is a short-lived species and highly susceptible to variations in environmental conditions, therefore, the EDSP model tends to be a better method to assess its stock.

In this study, the influence of the environmental factors on the abundance of SPS cohort of I. argentinus are evaluated by analyzing the correlation between the areas occupied by favorable SST on the spawning ground and CPUE. Furthermore, an optimal EDSP model is selected to estimate the stock abundance and reference points, using more informed K and r values for better fishery management.

The parameters r, K and q were considered to be uniform and normal distribution, and prior distribution for the parameters r, K and q were listed in Table 2.

(3) Calculating posterior distribution of parameters

The posterior distribution of parameters of Schaefer models were calculated by the method of Markov Chain Monte Carlo (MCMC). The initial values for the parameters of models in MCMC iterations were set as follows: Intrinsic rate of growth was 1, carrying capacity was 1 500 000 t, and the catchability coefficient was 0.2×10^–5. The number of MCMC iterations was 50 000, the first 10 000 results of iterations were discarded. For the later 40 000 times, we saved the results for every 40 times.

The fishery management reference points including F_MSY (fishing mortality corresponding to MSY), B_MSY (annual biomass corresponding to MSY), F_0.1 and MSY (Table 3) were estimated. The model with the lowest Deviance Information Criterion (DIC) was selected to be the best model.

The role of environmental variables in regulating the dynamics of fish abundance has been a hot topic, in particular for short-lived species such as Ommstrephid squid (Roberts, 1998; Agnew et al., 2002). Most squid have less than 1-year lifespan (Boyle, 1987). With regard to short-lived species, recruitment success is greatly influenced by the physical and biological environmental variables on the spawning and nursery grounds, and contributions to variations in the stock abundance (Sakurai et al., 2000). In addition, the abundance and distribution of squid populations tend to be greatly affected by oceanographic conditions and respond quickly to changes in the environment (Wadley and Lu, 1983; Waluda et al., 1999, 2001; Yatsu et al., 2000; Anderson and Rodhouse, 2001; Rodhouse, 2001; Bazzino et al., 2005). For example, Waluda et al. (2001) suggested that about 55% of the variability in recruitment of the Falkland Island I. argentinus fishery could be explained by variations in the total putative favorable-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 favorable-SST areas for larvae development (Sakurai et al., 2000). Cao (2010) suggested that February P_s and August to November P_f (suitable SST in the presumed feeding grounds during the feeding seasons) could account for about 60% of the variability in O. bartramii abundance between 1995 and 2004, and February P_s was the most important period influencing squid recruitment during the spawning season, and feeding ground P_f during the fishing reason would also play a crucial influence on CPUE. Consequently, sea surface environmental indicators were important to use for predicting the recruitment of squid (Agnew et al., 2002). In this study, I. argentinus was a short-lived species with less than 1-year lifespan, the yearly biomass almost depended on recruitment. Therefore, it was reasonable to consider the environmental indices into the assessment of the I. argentinus stock. However, traditional surplus production model regards the carrying capacity as constant, which was inconsistent with the squid population dynamics. Therefore, we used P_s as an indicator of carrying capacity in this study, which were commonly utilized to evaluate the suitability of habitat on the spawning grounds.

Significant correlations were identified between yearly CPUE and monthly P_s in July, and this result was different from previous findings (Waluda et al., 2001). The reason might be the use of various resources abundance indicators (nominal or standardized CPUE) and different sources of fishery data.

The methods to estimate parameters of surplus production model can be divided into three types including equilibrium estimators, process-error estimators, and observation-error estimators (Polacheck et al., 1993). Each estimator has its own drawbacks. For example, the assumption of equilibrium estimators is appropriate to apply to the fishery in equilibrium state, but it was not suitable for actual fishery. For process-error estimators, we usually obtain negative values of parameters (r, q) when converting surplus production equation into a linear form fitted by linear regression. Bayesian inference is increasingly used to fisheries in recent years, because it provides a systematic approach that explicitly incorporates both uncertainties and risk in the analysis (Hilborn et al., 1993; McAllister et al., 1994; Kinas, 1996; Chen et al., 2000). At the same time, atypical errors should 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 (Berger et al., 1994; Adkison and Peterman, 1996; McAllister and Kirkwood, 1998; Chen et al., 2000). In this study, we used Bayesian inference to estimate the parameters of the two surplus production models under different settings, and we tried to make data consistent with the actual situation by standardizing yearly CPUE. We also referred to some of the previous studies in order to set the prior distribution (uniform and normal distribution) of parameters and to select likelihood function (Cao, 2010; Lu et al., 2013b). According to MCMC results, there were big differences in the posterior distributions of parameters (r, K, q) and prior distributions except the parameter of K under normal distribution. It was shown that fishery data of I. argentinus brought enough information for Bayesian inference.

According to the fishery data (Table 1), annual production of I. argentinus have greatly fluctuated. In this study, the annual catches of I. argentinus were lower than MSY and fishing mortality coefficient were also lower than F_0.1 in EDSP models under two scenarios, it was indicated that the resource of I. argentinus was not overfished. The yearly biomass of I. argentinus in EDSP models under two scenarios were all higher than B_MSY, which suggested that the resource of I. argentinus was at a high level in recent years. The results of this study were optimistic, and we could conclude that the resource of I. argentinus in the Southwest Atlantic did not suffer from overfishing, these findings were basically consistent with the previous results (Cao, 2010; Lu et al., 2013b).

The EDSP models were fitted well than SP models under uniform and normal scenarios by DIC values. It suggested that environmental conditions had significant influences on the parameter of carrying capacity. We obtained the changed values of fishery reference points in models with environmental factors. Those values could be more useful and preventive for managing I. argentinus fishery than fixed reference points.

The uncertainties of the models mainly came from the uncertainty of data collection and model parameters. (1) The catch data were only sourced from three parts included Chinese mainland, Taiwan of China and Falkland Islands in this study. (2) We assumed the biomass in 2003 to be initial resource with the value of 2 500 000 t, this assumption would cause biases on the estimation of biomass of I. argentinus. We also assumed that the standard deviation of CPUE (σ) was equal to 0.2, the effects of \sigma on model selection and resource assessment need to be studied in the future research.

In summary, the EDSP model fitted better than conventional Schaefer surplus model without environmental factors. We also estimated parameters of models and some fishery reference points based on spawning habitat of I. argentinus in Southwest Atlantic. These findings suggested that the environment of habitat should be considered in the squid stock assessment.

The authors thank Chinese distant-water Squid Jigging Technical Group for providing fishery data and information, and NOAA for providing environmental data used in this paper.