Cephalopods are considered to be one of the three major marine fishery resources that are not fully exploited (Chen 1996). Global annual catches of cephalopods have risensteadily over the last fewdecades, with the highest catch being 4.3 million tonnes in 2007 and 4.77 million tonnesin 2014. The annual catches of cephalopods accounted for 3.04-4.75% of the global capture fishery yields (animals) from 1991 to 2012 (FAO 2016).Commercially targeted cephalopods include species of the families Sepiidae, Loliginidae, Ommastrephidae and Octopodidae, with Ommastrephidaehaving the largest proportion (Chen et al. 2012). The Ommastrephidae squid species such as Todarodes pacificus, Ommastrephes bartramii, Nototodarus sloani, Illex argentinus and Dosidicus gigas are commercially important species. O. bartramii, I. argentinus and D. gigas are traditionally targeted by the Chinese squid-jigging fleets, and their annual production reached 400000 to 700000 tonnes in 2013 and 2014.

The neon flying squid O. bartramii is widely distributed in the northwest Pacific Ocean (Murata 1990). The Japanese squid-jigging fleet has commercially exploited this species since 1974, and it was later exploited by South Korea, China and Chinese Taipei (Wang and Chen 2005). The O. bartramii population is composed of 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 (Yatsu 1992, Yatsu et al. 1997). Of these stocks, the western winter-spring cohort has become an important target in the regions of 150-165°E (Chen et al. 2008b). Since 2000, this stock has mainly been captured by China and Chinese Taipei. The western winter-spring cohort migrates from subtropical waters to the subarctic boundary during the first half of the summer and then moves northward into the sub-Arctic domain in August-November. This species matures gradually in autumn and it seems thatit starts the spawning migration in October and November (Murata and Hayase 1993).

The spawning and feeding grounds for the western winter-spring cohort of O. bartramii are located at 20-30°N, 130-170°E and 38-46°N, 150-165°E (Bower 1997, Bower and Ichii 2005). The suitable sea surface temperature (SST) for the spawners ranges from 21 to 25°C during the spawning season (January-April) (Bower 1997, Bower and Ichii 2005) and favourable SSTs for the feeding ground vary between August and November: 15 to 19°C in August, 14 to 18°C in September, 10 to 13°C in October and 12 to 15°C in November (Chen and Tian 2005).

Illex argentinus, the Argentinian shortfin squid, is a major component of commercial squid fisheries in the southwest Atlantic Ocean. I. argentinus is widely distributed across the Patagonian Shelf and adjacent oceanic waters between 22 and 54°S (Wang and Chen 2005, Chen et al 2008b).The population structure of I. argentinus is complex and based on length at maturity, area and timing of spawning, and the distribution of early juveniles and adult life stages, divided into four stocks: the South Patagonia Stock (SPS), the Bonaerensis-Northpatagonia Stock, the Summer Spawning Stock and the Southern Brazil Stock (Hatanaka 1986). The Falkland Islands fishery consists almost exclusively of winter spawners and fishery managers assume that it target a single stock (SPS) south of 45°S (Brunetti and Ivanovic 1992). China (Lu and Chen 2013), Chinese Taipei (Chen and Chiu 2009) and the Falkland Islandshave exploited the SPS cohort of I. argentinus since 2000 (Waluda et al. 1999).

Previous studies from this region suggest that the inferred hatching area (the region where winter-hatched I. argentinus paralarvae are most commonly found) of SPS is found between 32 and 39°S and 49 and 61°W from June to July (a peak hatching season). Waluda et al. (2001a) found that suitable SST for hatching ranges from 16 to 18°C. The species feeds in the waters from 42 to 54°S and 54 to 62°W from January to June, and the preferred SST for feeding is 7 to 14°C (Lu et al. 2013a).

Dosidicus gigas, the jumbo flying squid, supports a major fishery in the eastern Pacific Ocean and its range of distributed extends from 37-40°N to 45-47°S, between California and southern Chile, extending westward from the coast to a maximum of 125-140°W at the equator (Nigmatullin et al. 2001). D. gigas fisheries occur off the coast of Peru (Taipe et al. 2001), and Central America (Ichii et al. 2002) and in the Gulf of California, Mexico (Nevárez-Martínez et al. 2000). D. gigas’s population structure is not well defined, but based on individual mantle lengths it may include three stocks: large, medium and small sizes (Argüelles et al. 2001). Small-scale fisheries, particularly off Peru, Chile and Mexico, traditionally exploited these stocks (Nevárez-Martínez et al. 2000, Rocha and Vega 2003). However, since the early 1990s there has been an increase in industrial vessels, largely from East Asia (Japan, Korea and China), fishing off Peru and Central America, with a resulting increase in squid catches from the eastern Pacific Ocean (Ichii et al. 2002). The spawning ground of D. gigas is defined in the region from 5 to 14°N and 85 to 95°W and the favourable SST for spawning is from 24 to 28°C in September. The feeding ground of D. gigas is found from 20°N to 20°S and from 70 to 110°W, based on the distribution of fishing fleets, and the favourable SST is from 17 to 22°C in July (Ichii et al. 2002, Waluda and Rodhouse 2006).

Recent studies suggest that variations in the oceanographic environmental variables, such as SST, sea surface height (SSH), and chlorophyll a (Chl a), play an important role in regulating the distribution and abundance of squid populations (Waluda et al. 2001b, 2006, Chen et al. 2007). Here we focus on SST influencing abundances of ommastrephid squid. For example, Chen et al. (2007) found that the SST rose by 1°C in a La Niña year compared with the normal level, and a higher SST resulted in unfavourable recruitment conditions for O. bartramii. In an El Niño year, however, the SST was almost the same as in a normal year; thereby leading to favourable conditions for recruitment. SST data analyses for I. argentinus showed that variations in the availability of optimum sea temperature for larval development during the spawning season explained about 55% of the recruitment variability (Waluda et al. 2001a). Moreover, D. gigas abundance was strongly influenced by the mesoscale variability linked to the ENSO, with low levels of upwelling during the very strong El Niño leading to low catches of D. gigas off Peru (Waluda et al. 2006).

The majority of ommastrephid squid, such as O. bartramii, I. argentinus and D. gigas, are short-lived species with about aone-year life span, and the biomass of these species in the subsequent year is largely composed of new recruits. As the annual recruitment variability of ommastrephid squid is largely driven by the environment, there is a growing need to incorporate environmental variability in the assessment of ommastrephid stocks. However, to date few studies of ommastrephid stock assessment have included environmental factors.

In this study, we modified a surplus production model by incorporating known environmental factors of spawning and feeding grounds, and then used this model to evaluate the environmental influence on the populations of O. bartramii, I. argentinus and D. gigas. This study shows the importance of including environmental variables in the assessment of squid populationdynamics.

Many studies indicated that variability in marine ecosystems, especially SST, causes inter-annual variability in the ommastrephid squid stocks (Waluda et al. 1999, 2006, Chen et al. 2007), but the inter-annual variability cannot be controlled and predicted effectively. Thus, assessment of ommastrephid squid stocks by incorporating environmental factors is difficult to implement. To our knowledge, there is only one study about assessing the western winter-spring cohort of neon flying squid with Bayesian inferences using SST on spawning ground and feeding ground based on surplus production model, and the model with spawning ground SST was the optimal model (Wang et al. 2015).

The longevity of ommastrephid squids is roughly one year, so the stock of a given year is comprised almost entirely of new recruits (Rosenberg et al. 1990, Pierce and Guerra 1994). It is therefore essential to allow the suitable spawning habitat (for spawners to spawn and the larvae to survive) to ensure a high probability of successful recruitment in the following year. Furthermore, ommastrephid squids are fast-growing species (Boyle and Rodhouse 2005) and a suitable feeding habitat is vital for their growth in stock biomass. Thus, how to measure the habitat of the spawning and feeding grounds when assessing ommastrephid stocks is very important.

This study incorporates the environmental indices (Ps and Pf) to reflect inter-annual variability in environmental conditions of spawning grounds and feeding grounds. On spawning grounds, climate changes and some large-scale or mesoscale oceanographic processes may drive the inter-annual variability of Ps, which can influence the recruitment of ommastrephid squids. For example, ENSO events and the strength of the North Equatorial Current and the Kuroshio Current change Ps to influence O. bartramii recruitment in the northwest Pacific (Chen et al. 2007). The relative strength of the Brazil current and the Falkland current may influence the Ps to affect the recruitment of I. argentinus in the southwest Atlantic (Waluda et al. 1999). ENSO events also strongly influence D. gigas recruitment, as weak upwelling during strong El Niño years lead to very low catches in the southeast Pacific (Waluda and Rodhouse 2006). On feeding grounds, ommastrephid squids are mainly distributed in waters with a suitable SST (Chen et al. 2007), which are mainly located in transition areas, including meandering eddies, frontal zones and so on, yielding highly productive habitats that serve as feeding grounds for ommastrephid squids (Zainuddin et al. 2006). The best surplus production models for the three-ommastrephid stocks (the surplus production model with Ps for O. bartramii and I. argentinus, the surplus production model with Pf for D. gigas) are all models incorporating environmental factors. This is consistent with our hypothesis that considering environmental variability can improve the assessment of ommastrephid squids.

For each modelled ommastrephid stock, the original surplus production model and corresponding best model showed differences in the exploitation status. The O. bartramii fisheries arenot overfished, which was consistent with previous results (Chen et al. 2008a, Wang et al. 2015). Parameters r, K and q based on SP and Ps-EDSP showed little difference, but K in SP model was about 10% less than that in Ps-EDSP model (Table 4). The status for each year based on Ps-EDSP model was closer to the limit (F/F_MSY) than any other based on the SP model (Fig. 6). This finding was similar to the results obtained by different methods modelled by Bayesian inferences (Wang et al. 2015).

For the I. argentinus fishery, status for almost the whole year in the target zone was in a good state. The MSY was about 44×10⁴ t and the results were consistent with Lu et al. (2013b). However, the status of all years based on the SP model was much tight and no differences were found between them relative to the status of all years based on the Ps-EDSP model (Fig. 7). Parameter r in the SP model was about four times that in the Ps-EDSP model, and K in the SP model was about 12% less than that in Ps-EDSP model (Table 5).

For the D. gigas fishery, the development status in the SP and the Pf-EDSP model was similar (Fig. 8), but parameters r and K were about 19 and 26% less than any other one in the Pf-EDSP model, respectively (Table 6).

The improvements in the results through incorporation of environmental factors benefit the assessment and management of ommastrephid squid stocks. For example, one benefit is another method of assessing ommastrephid squid stocks. Because assessment of fished cephalopod stocks is a relatively undeveloped field, only a few methods are currently used, such as fishing and acoustic surveys, egg and larval production estimates, mark-recapture, the Leslie-Delury method and the surplus production model (Boyle and Rodhouse 2005, Wang et al. 2015); even fewer of those methods incorporate environmental variables. The other benefit of incorporating environmental factors into management procedures could be the potential increase in fishing effort when future recruitment is expected to be stable or increasing, and the reduction in fishing effort when future recruitment is expected to be poor (Basson 1999). With the effective forecasting of environmental conditions, the surplus production models developed will allow precautionary approaches for the management of ommastrephid squid fisheries.

The dynamic life history of ommastrephid squids poses challenges for the assessment of stocks. This study shows that considering environmental factors can improve their assessment. Because of the importance of thermal habitat in regulating the dynamics of ommastrephid squids, we suggest that environmental factors such as SST should be considered in the assessment of ommastrephid squid stocks.