1 INTRODUCTION

Chub mackerel Scomber japonicus is a coastal-pelagic species which is widely distributed in the continental shelf of the subtropical and temperate waters of the Pacific, Atlantic, and Indian Oceans and adjacent seas (Collette and Nauen, 1983; Wang et al., 2021). According to the difference in the patterns of seasonal migration and spawning grounds, the chub mackerel in the northwest Pacific Ocean is generally divided into two stocks, i.e., Pacific stock and Tsushima Warm Current stock (Wang et al., 2021). The Tsushima Warm Current stock on which we focused in this study inhabits a wide area from the south East China Sea (ECS) to the northern Japan/East Sea (JES) and also occurs in the Yellow Sea (YS) and Bohai Sea (Shiraishi et al., 2008; Epur, 2009). Correspondingly, chub mackerel spawning grounds are also widely distributed from the southern part of the ECS, west of Kyushu and Tsushima Straight to the western part of the JES (Yukami et al., 2009) and northern part of the JES (Shelekhov et al., 2020) and the spawning grounds also exist in YS and Bohai Sea (Guan, 2008). Nevertheless, the population structure delineation of the Tsushima Warm Current stock is still controversial (Yan et al., 2012). For instance, Hwang and Lee (2005) divided the chub mackerel in the ECS and JES into two stocks, i.e., Tsushima Current stock and East China Sea stock; some Chinese scholars divided the chub mackerel in the ECS and YS into west of East China Sea stock and west of Kyushu stock, but others considered the chub mackerel as a single stock, i.e., East China Sea stock (Yan et al., 2012).

The Tsushima Warm Current stock, that is assumed to be distributed mainly in the ECS (Hiyama et al., 2002; Yasuda et al., 2014), constitutes an important pelagic fishery resource that is mainly exploited by Chinese, Japanese, and Korean light-purse seine fisheries (Yan et al., 2012). The annual total catches of the chub mackerel from Chinese Mainland, the Republic of Korea, and Japan increased since 1979 and reached maximum (1.12×10⁶ t) in 1996, then declined sharply in 1997 and the catches were on a downward trend from 2008 to 2019 (Guan and Ma, 2022). In contrast, the annual catches from Chinese Mainland steadily increased from 1979 (1.12×10⁵ t) to 2008 (5.44×10⁵ t); since 2012, the catch declined obviously and the annual catch was 3.65×10⁵ t in 2019 (Guan and Ma, 2022). Due to the decline of traditional demersal economic species in the ECS and YS, the chub mackerel has become one of the most important commercial fishing target species in China (Wang et al., 2014). In recent years, because the stock assessments of the chub mackerel show the stock is fully exploited, even overexploited (Wang et al., 2014; National Research Institute of Fisheries Science and Saikai National Fisheries Research Institute, 2019; Guan and Ma, 2022), the status of the chub mackerel resource and the potential for its exploitation have been receiving increasing attention (Wang et al., 2014). Since the knowledge of the early life history plays an important role in understanding the biology, ecology, and evolution of marine fishes (Miller and Kendall, 2009) and the early life history of chub mackerel has an important effect on the recruitment of the fish (Sassa and Tsukamoto, 2010; Li, 2012), it is important to study the distribution, growth, and survival rate of chub mackerel larvae and juveniles and their relationships with environmental factors to understand the chub mackerel recruitment and population structure.

An individual-based model (IBM) can be used in combination with three-dimensional marine environmental data to simulate the condition of the fish and its response to the marine environment as well as to other individuals (Phillips et al., 2018). The results of these simulations can be used to investigate the spatial and temporal distribution and evolutionary dynamics of fishery resources and to explore their relationships with the marine environment (Li, 2012; Phillips et al., 2018). Compared with Eulerian and state variable models, IBM can easily incorporate the stochastic and adaptive behaviors and record the state and position of individuals for each time step which can be used to reproduce and track the dynamic evolution of individuals (Phillips et al., 2018). IBM has wide applications in understanding the variation in recruitment (Miller, 2007), population connectivity (Cowen et al., 2006; Nikolic et al., 2020), school behavior (Hemelrijk and Kunz, 2004), and population dynamics (Shin and Cury, 2004; Phillips et al., 2018). However, the simulation of very detailed mechanisms of the movement, physiology and behavior of individuals in IBM lead to high computational cost which make it more difficult to describe population dynamics at lager temporal and spatial scale (Lehodey et al., 2008). At the same time, the complexity and stochasticity of the IBM increase the number of parameters (Lehodey et al., 2008) and make the parameter estimation more difficult (Duboz et al., 2010; Senina et al., 2020).

Li (2012) used an IBM to study the spatial distribution and survival rate of chub mackerel in the ECS; subsequently, Li et al. (2014, 2018) investigated the effects of flow fields, the water temperature and a typhoon on the spatial distribution and survival rate of chub mackerel larvae and juveniles. Although an IBM that includes swimming behavior has been proposed (Li, 2012), in most cases, the simulation results are based on the assumption that the chub mackerel larvae and juveniles are not capable of swimming (Li, 2012; Li et al., 2014, 2018). Since the chub mackerel in the ECS are characterized by rapid growth (Mendiola et al., 2009; Yan et al., 2012), ignoring their swimming ability will have a negative impact on the rationality of the results. For example, the simulation results have shown that most juveniles spawned to the northeast of the Taiwan Island are transported into the region to the east of 127°E and recruited into the Tsushima fishing grounds; according to the results, very few juveniles are recruited into the fishing grounds in the Changjiang (Yangtze) River estuary and around the Zhoushan Islands (Li, 2012; Li et al., 2014). These results are inconsistent with the observations (Miao, 1993; Zheng et al., 2003; Zhu et al., 2021) which show there are many juveniles distributed along the coastal area of Zhejiang Province from May to September and these chub mackerels are recruited into Zhoushan Islands fishing ground. Therefore, it is necessary to further develop IBMs to include swimming behavior so that better simulations can be produced.

In this paper, we describe the development of an IBM that can be used to simulate the growth, mortality, and swimming behavior of chub mackerel larvae and juveniles in the ECS based on models that describe their early life history, food and habitat. Using this IBM, we investigated the spatial and temporal distribution of the chub mackerel larvae and juveniles and the spatial and temporal patterns in their growth and survival rates. We also analyzed the relationship of the distribution, growth, and survival rate with the marine environment. This overall aim of the study was to improve our understanding of the recruitment and population structure of chub mackerel in the ECS.

2 MATERIAL AND METHOD

Firstly, we created a coordinate system using non-overlapping unstructured triangular grids in the horizontal direction and hybrid coordinates in the vertical direction over the computational domain and we downloaded the environmental data from website and generated abiotic (irradiance, water temperature, salinity, current velocity, horizontal eddy diffusion, and vertical eddy viscosity) and biotic (ocean primary production) environment over the domain. Secondly the IBM was developed based on the five life stages of chub mackerel early life history, i.e., egg, early larva, late larva, early juvenile, and late juvenile and the knowledge of growth, mortality, and movement for each stage. Then, we generated the locations of the super-individuals of eggs according to the survey of chub mackerel eggs in the ECS and created simulation scenarios. Finally, we combined the super-individuals of eggs with the three-dimensional abiotic and biotic environmental data in the IBM and simulated the spatial distribution, growth, and mortality of the super-individuals. After 90-d simulation, we analyzed the distribution, growth, and survival rate of the super-individuals and presented the results. The followings are the details.

2.1 The coordinate system and environmental data

The computational domain (110°E‒135°E, 15°N‒42°N) was subdivided into 21 419 non-overlapping unstructured triangular cells with 11 260 nodes; the horizontal resolution was in a range of 2.8–44.4 km. Hybrid coordinates corresponding to 55 layers were used in the vertical direction. A σ-coordinate corresponding to 55 uniform layers (a vertical resolution of 5 m or less) was used in the shallower regions (depth less than or equal to 275 m); elsewhere, an s-coordinate corresponding to 50 uniform layers (each with a thickness of 5 m) was used near the surface with the remaining depth covered by the other 5 layers, which were of equal thickness. For details of the placement scheme for the water temperature, current velocity, and other variables, the reader is referred to the Finite Volume Community Ocean Model (FVCOM) user manual (Chen et al., 2013).

Horizontal current velocity, water temperature, salinity, Secchi depth, and ocean primary production data were downloaded from the Copernicus Marine Service website (https://resources.marine.copernicus.eu/products). The vertical current velocity and vertical eddy viscosity were calculated using the global ocean environment forecasting model of Shanghai Ocean University. The temporal and spatial resolution and water depth range of the data are shown in Table 1. The time range of the data used in this study was from March 2020 to October 2020. The environmental data for a node or triangle centroid were obtained using bilinear interpolation.

The horizontal eddy diffusion coefficient, A_h (m²/s), was calculated using Smagorinsky's eddy parameterization method (Chen et al., 2013):

where λ is a constant which was set to 0.005 following the possible range of A_h according to the grids we used (Prof. Changsheng Chen, personal communication), and u_c and v_c are the zonal and meridional components of the ocean current velocity (m/s), respectively. Ω is the area of the individual tracer control element (m²) (Chen et al., 2013).

The sea surface irradiance (μmol photons/(m²·s)) was calculated using a simple spectral solar irradiance model using standard atmospheric parameters (Gregg and Carder, 1990), a lunar surface reflection model (Kieffer and Stone, 2005), and a twilight model (Revel and Hignett, 2004).

The underwater irradiance was calculated as

where Z_eu, z, and E₀ are the euphotic zone depth calculated from the Secchi depth (m) multiplied by a factor of 2.7, the water depth (m), and the sea surface irradiance, respectively.

2.2 IBM

The IBM that was developed was based on the five early life stages of chub mackerel (Li et al., 2014) which were divided according to the incubation time of eggs (H), metamorphosis time of larva (Q), age and body length (L). These stages are egg (life stage 1: age < H), early larva (life stage 2: H≤age < 2/3 Q+H), late larva (life stage 3: H+2/3Q≤age < Q+H), early juvenile (life stage 4: Q+H≤age and L < 160 mm), and late juvenile (life stage 5:160 mm≤L < 220 mm). The methods used to determine the growth, mortality, and movement of the eggs, larvae, and juveniles are described below.

2.2.1 Incubation and metamorphosis time

The incubation times of eggs, i.e., H (h), and the metamorphosis time of larva, i.e., Q (d), were calculated as follow (Hunter and Kimbrell, 1980):

where T is the temperature (℃).

2.2.2 Growth

The time step of the model, Δt, was 1 200 s and the chub mackerel age was increased by Δt for one time step. Because we had no information about the growth of eggs, we assumed the initial length of egg (L₀) equaled the length of larva at age 1 d which was generated randomly from a normal distribution using a mean length of 3.1 mm (Go et al., 2020) and a standard deviation of 0.24 mm (Hunter and Kimbrell, 1980) and then the subsequent growth of the eggs was ignored. The growth of the larvae and early juveniles was calculated as follows (Go et al., 2020):

where L_t is the body length (mm) at age t, L_∞ is the asymptotic length (mm), G_t is growth rate (mm/d), Δt₁ is a time interval (d) and ΔL is the increase in body length during the time interval, F is the food index which is calculated by using the density of chub mackerel, water temperature, habitat suitability index, and ocean primary production (see below).

ΔL, the amount by which the late juvenile grows was calculated as:

where k is a growth parameter (/a), Δt₂ is a time interval (a).

For each individual, L_∞ and k were randomly generated from two-dimensional normal distribution. The means, the standard deviations and the correlation coefficient of the distribution that are shown in Table 2 were calculated from values of L_∞ and k given in the literature (Carvalho et al., 2002; Zheng et al., 2003; Cheng and Lin, 2004; Liu et al., 2005; Shiraishi et al., 2008).

The body weight, W_t (g), was calculated from the body length and the weight-length relationship (Cheng and Lin, 2004), i.e., W_t=1.6554e–5L_t^2.9485. The density of chub mackerel at life stage J within a control element, B_J (g/m²), was calculated as

where Φ is a scale factor which we used to control the calculation of density, n∈ Ω denotes the super-individual n contained in the control element, W and N are the body weight and the number of the individual contained in the super-individual.

2.2.3 Mortality

The instantaneous natural mortality rate, M (/d), for the chub mackerel eggs, larvae, and early juveniles was calculated from the empirical relationship given by Pepin (1991) and Bartsch and Coombs (2004):

For the late juveniles, the instantaneous natural mortality rate, M (/a), was calculated according to the empirical relationship given by Gislason et al. (2010):

2.2.4 Habitat suitability index

The habitat suitability index (HSI) was used to evaluate the habitat quality of the chub mackerel. Because the water temperature, salinity, and food are the important environmental factors affecting the spatial distribution of chub mackerel larvae and juveniles (Miao, 1993; Guan, 2008) and irradiance can be used to simulate diel vertical migration (Richards et al., 1996; Yasuda et al., 2018), HSI was defined as

where H_T, H_S, H_L, H_F, and H_O are the water temperature, salinity, irradiance, food, and ocean primary production suitability indexes, respectively. Λ is the maximum value of the HSI and is used to normalize the HSI to the range 0–1.

The water temperature, salinity, and irradiance suitability indexes were calculated as follows:

where P_{i, 1}, P_{i, 2}, σ_{i, 1}, and σ_{i, 2} are parameters; x represents the variable value and i denotes the type of variable (e.g., water temperature, salinity, or irradiance). The value of the irradiance is transformed by -log₁₀. We assumed the preferred light range was from 1.85e-3, i.e., the light level near the sea surface at dusk or dawn (Revel and Hignett, 2004), to 1.85e-4 μmol photons/(m²·s), i.e., the light level at depth 0.5Z_eu at dusk or dawn. According to the preferred range of water temperature, salinity (Miao, 1993), and light level (we assumed in this study), the parameters values we defined for specific life stage are shown in Table 3 and the parameters for different life stage were set by linear interpolation according to these values.

The food suitability indexes were calculated as following:

where Ψ is an adjustment coefficient of temperature, γ₁ and γ₂ are the daily consumption of food per unit of body weight (0.009 6 g/(g·d)) (Shin and Cury, 2004), W_C1 and W_C2 are the carbon to wet weight ratio of the food (0.12 g C/g), O_pp (g C/(m²·d)) is the ocean primary production, E₁ and E₂ are the efficiency of the conversion from primary production to secondary production and from secondary production to small fish (set as 15% and 10%, respectively).

The ocean primary production suitability index which was used to prevent a large number of larvae and juveniles from entering west Pacific Ocean was defined as

2.2.5 Food index

The food index for chub mackerel larvae was calculated as

where δ₁ and δ₂ are the proportions of the food for chub mackerel larvae and juveniles respectively which both were set to 0.15.

2.2.6 Movement

The chub mackerel swimming speed was calculated based on the body length, habitat suitability index, and ocean current data using a stochastic process. The distance traveled by chub mackerel was then calculated using a modified fourth-order Runge-Kutta time-step scheme (Chen et al., 2013). Further details are given in the following.

Based on the results of Hunter and Kimbrell (1980) and a swimming speed of 1.2 m/s for chub mackerel with a length of 247 mm (Guo et al., 2020), a relationship between body length and swimming speed, V (m/s), for chub mackerel was established:

where φ=1‒HSI.

The zonal (u) and meridional (v) components of the velocity of the chub mackerel were calculated as (Faugeras and Maury, 2007):

where θ is a random number generated from the von Mises distribution. The mean angle (θ_F) and concentration parameter (K_a) of the von Mises distribution were given by

where τ is a parameter set to a value of 15.0.

The vertical speed of the chub mackerel, ω_z, was calculated as:

where R is a random number generated from a normal distribution with a mean of 0 and a standard deviation of 1, and the speed, ω, was calculated as

Here ω_c is the vertical current velocity and α is a parameter set to a value of 0.5.

The spatial distribution of the eggs and larvae is also affected by turbulence and the random displacement in the horizontal (x- and y-) directions was calculated as (Ross and Sharples, 2004; Phillips et al., 2018):

where δt is a time interval (60 s), and R_U and σ are the random number and the standard deviation of the uniform distribution between -1 and 1, respectively.

The random displacement in the vertical direction was given by Visser (1997):

where n is the iteration number, z is the depth and K'_z is the gradient of the vertical eddy viscosity, K (m²/s), at a water depth z, i.e., K'_z=ΔK_z/Δz.

In addition, the vertical distribution of chub mackerel was limited according to the life stage: eggs and larvae were confined to depths of less than 60 m, early juveniles to depths of less than 120 m and late juveniles to depths of less than 300 m. If the depth exceeded these limits, absolute values of the vertical velocities were taken. The computational domain had a closed boundary and individuals moving out of the boundary were symmetrically reflected back into the domain.

2.3 Simulation setting 2.3.1 Spawning ground

According to the surveys of chub mackerel eggs in the ECS (Zheng et al., 2003), we assumed the existence of four spawning grounds along the Chinese coast of the ECS; these were given the labels (coordinates of the centers in brackets) S1 (120.0°E, 24.5°N), S2 (122.5°E, 27°N), S3 (123.75°E, 29.0°N), and S4 (126.0°E, 30.75°N) (Fig. 1).

2.3.2 Eggs locations and release dates

At each spawning ground, 2 000 super-individuals, each containing 10⁹ eggs, were generated (Li et al., 2014). The horizontal location of each super-individual was randomly generated from two normal distributions that had the center point coordinates of the spawning ground as their mean and a standard deviation of 0.75° (Fig. 1). The depth distribution of the super-individuals was assumed to follow a normal distribution with a mean of 10 m and a standard deviation of 5 m (Li, 2012), and the depth of each super-individual corresponded to a random number generated from this normal distribution. It was assumed that the chub mackerel spawned between March and June and that all eggs were released at 00꞉00 hours on the 15^th of each month.

2.3.3 Simulation scenario

We considered a series of five simulation scenarios; the swimming behavior, ocean current transport, pattern of egg release, and value of a scale factor, Φ, were different in the different scenarios (Table 4).

In scenario A, the larvae and juveniles did not swim and were passively transported by the ocean current; eggs were released at each spawning ground in each month. Scenario B was similar except that the larvae and juveniles did swim and were unaffected by the current. In scenario C, the larvae and juveniles swam as well as being transported by the current. Scenario D was similar to scenario C except that the value of Φ was set to 0.075 rather than 7.5. Scenario E was similar to scenario C except that the eggs were simultaneously released in all four spawning grounds each month.

2.4 Statistics

In next section, the simulation results corresponding to 90 d after the release of the eggs are analyzed. The survival rate is the number of extant individuals divided by the total initial number of eggs. Because the average body length weighted by the number of surviving individuals was influenced by both survival rate and individual growth and blurred the effect of the habitat conditions on the individual growth, the average body length of the super-individuals was taken as the average juvenile body length. The spatial distribution of the super-individuals, the average body length and the survival rate were determined over a 0.5°×0.5° grid.

3 RESULT 3.1 Spatial distribution

When the larvae and juveniles are only passively transported by the ocean current (scenario A), the juveniles (age 90 d) from different spawning grounds drift eastward or northeastward and are subsequently mainly distributed within the area stretching from the Taiwan Strait to the Tsushima Strait. The further north the spawning ground is, the greater the number of juveniles that entered the JES is (Fig. 2). Compared with the super-individuals spawned in March, more super-individuals spawned in June enter the western Pacific Ocean and the JES (Fig. 2). In the case of June spawning, the number of super-individuals from spawning grounds S1 and S2 in the central southern ECS also increases (Fig. 2e–f), but that from spawning grounds S3 and S4 in the northern ECS and southern YS decreases significantly (Fig. 2g–h).

When it is assumed that the chub mackerel larvae and juveniles do swim but are unaffected by the ocean current (i.e., scenario B), although the super-individuals are found to be spread around their original spawning locations, their spatial distribution varies with the spawning time and spawning ground (Fig. 3). For example, the spatial distribution of the super-individuals spawned at spawning ground S1 in March is much wider than for those spawned at the same spawning ground in June (Fig. 3a & e). In contrast, for the juveniles spawned at spawning ground S4, the opposite is the case (Fig. 3d & h). In addition, under scenario B, hardly any chub mackerel juveniles enter the JES or the western Pacific Ocean (Fig. 3).

For the larvae and juveniles that swim themselves and are also transported by the ocean current (Scenario C), compared with scenario B, there is an obvious eastward or northeastward shift in the spatial distribution of the super-individuals, and the areas where the density of the super-individuals is high also differ significantly (Fig. 4). Under scenario C, there are no or a small number of super-individuals spawned at spawning ground S1, S2, and S3 entering the JES or the western Pacific Ocean (Fig. 4); however, a considerable number of super-individuals spawned at spawning ground S4 still enter the JES (Fig. 4d & h), especially when the spawning time is in June (Fig. 4h).

Because the super-individuals are more concentrated in areas with a high-quality habitat under scenario D than under scenario C (Figs. 4–5), the spatial distribution area of the super-individuals is significantly smaller under scenario D and there is also a substantial reduction in the number of super-individuals entering the region to the east of 127°E (Fig. 5). Compared with scenario C, under scenario E, the area of overlap between super-individuals originating from different spawning grounds is clearly reduced and the areas where the density of super-individuals from different spawning grounds is high coincide less well (Fig. 6).

3.2 Growth

The results in Table 5 show that, in general, under scenarios B and C, there is a gradual decrease in the average juvenile body length as the spawning time moves forward; the trends under scenario A and D are similar when the spawning grounds are S1 and S2 (Table 5). As spawning time moves forward and spawning ground shifts northward, the average body length generally increases. Under scenarios C and B, the average juvenile body length is usually greater than that under scenario A. Compared with scenario B, the average body length of the juveniles spawned at spawning grounds S1, S2, and S4 is greater under scenario C; however, it is generally smaller in the case of the juveniles spawned at spawning ground S3 (Table 5). Among the four scenarios shown here, the average juvenile body length under scenario D is the greatest (Table 5).

The spatial distribution of the average juvenile body length varies with the spawning time and spawning location (Fig. 7). For example, the average body length of the juveniles in the region near Kuroshio or under the influence of the Kuroshio (i.e., the region to the west of Kyushu Island and the southern Tsushima Strait) gradually decreases as the spawning time moves forward (Fig. 7). The juveniles spawned at spawning ground S4 in March have a greater average body length south of 31°N than north of this (Fig. 7d), but spawned in June, the average body length is smaller in the region to the west of Kyushu Island and the Tsushima Strait than in other regions (Fig. 7h).

3.3 Survival rate

For all of the scenarios that have been described, the later the spawning time, the lower the survival rate of the chub mackerel juveniles from spawning grounds S1 and S2; however, in the case of spawning grounds S3 and S4, there is either a steady increase in the survival rate or there is an initial increase followed by a decrease as the spawning time moves forward (Table 6). In the case of March spawning, the juveniles from spawning ground S2 have the highest survival rate, followed by those from S1; the juveniles from the spawning ground S4 have the lowest survival rate. As the spawning time become later, the higher the ranking of the survival rate of the juveniles from the northern spawning grounds and the lower the ranking of those from the southern spawning grounds (Table 6).

The juvenile survival rate under scenarios B and C is higher than that under scenario A. Compared with scenario B, the survival rate of the juveniles from spawning grounds S1 and S2 is higher under scenario C (Table 6). However, whether the survival rate of the juveniles from spawning grounds S3 and S4 is larger under scenario C than under scenario B depends on the spawning time: under scenario C, the juveniles spawned at spawning ground S3 in April have a higher survival rate than under scenario B; however, juveniles spawned at the same spawning ground at other times have a lower survival rate. Of the five scenarios, scenario D has the highest survival rate.

The survival rate of chub mackerel juveniles from spawning grounds S1 and S2 is relatively low in the region near the Kuroshio and to the west of Kyushu Island and gradually decreases as the spawning time becomes later; the region where the survival rate is low also gradually expands shoreward (Fig. 8a, b, e, & f). The survival rate of the juveniles spawned at spawning ground S3 in March is relatively low in the region to the north of 31°N (Fig. 8c), but spawned in June, the region of low survival rates shifts to the west of Kyushu Island and to the region close to the Kuroshio (Fig. 8g). The juveniles spawned at spawning ground S4 in March have a relatively high survival rate in the area around Jeju Island, in the region to the south of this and in the Tsushima Strait (Fig. 8d). As the spawning time becomes later, the survival rate of the juveniles from spawning ground S4 gradually increases in the region outside the Changjiang River estuary and the YS but decreases in the region to the west of Kyushu Island or along the coast near Honshu Island (Fig. 8h).

4 DISCUSSION 4.1 Spatial distribution

As the body length of chub mackerel larvae and juveniles increases rapidly (Mendiola et al., 2009; Yan et al., 2012), their swimming capacity is quickly improved. Correspondingly, the effect of the ocean currents on the spatial distribution of chub mackerel larvae and juveniles is gradually weakened and their spatial distribution depends more on their habitat conditions, i.e., the spatial distribution of chub mackerel larvae and juveniles is related to the quality of their own habitat, but also limited by the neighboring environment. Consequently, when active swimming of chub mackerel larvae and juveniles is simulated, our results show that the juveniles from spawning grounds S1, S2, and S3 scarcely enter the JES or the western Pacific Ocean, which is significantly different from the results of an IBM that did not include the ability to swim (Li et al., 2014). In addition, our results show the overlap areas of the spatial distribution of chub mackerel juveniles spawned at different spawning grounds are obviously reduced under scenario E, which means that a fish population will limit the spatial expansion of the neighboring populations by changing its own habitat condition (e.g., food conditions) and the population spatial structure may be formed.

The delineation of the chub mackerel population structure in the ECS is still controversial (Yan et al., 2012). If the population structure assumption is wrong, it will lead the unit stock assumptions of the current chub mackerel stock assessment models to be violated (Hilborn and Walters, 1992; Wang et al., 2014; National Research Institute of Fisheries Science and Saikai National Fisheries Research Institute, 2019; Guan and Ma, 2022) and have a negative impact on the assessment and management of chub mackerel (Guan et al., 2014). Our results show although most chub mackerel juveniles from spawning ground S1, S2, and S3 are recruited into the fishing ground in the ECS and YS, a significant proportion of juveniles from spawning ground S4 are recruited into the JES fishing ground. Therefore, we speculate there are exchanges between chub mackerel stocks which distribute in the ECS, YS, and JES and we suggest assessing and managing these chub mackerels as a stock. Therefore, in order to understand the chub mackerel population structure and recruitment mechanisms from a holistic perspective and to inform the stock assessment and management of the chub mackerel, we still need a more comprehensive study of the distribution, growth, and survival rate of chub mackerel larvae and juveniles from the spawning ground in the west of Kyushu, Tsushima Straight, eastern part of the JES (Yukami et al., 2009), northern part of the JES (Shelekhov et al., 2020) and YS (Guan, 2008) besides the spawning grounds along the offshore areas of China in the ECS.

4.2 Growth and survival rates

The growth and survival rates of chub mackerel are influenced by the water temperature and prey density (Sassa and Tsukamoto, 2010; Taga et al., 2019), and the prey density is related to the chub mackerel density as well as the ocean primary production. Therefore, the water temperature and ocean primary productivity in the ECS are two important factors affecting the growth and survival rates of chub mackerel as well as the spatial and temporal variations in these rates. Moreover, the influence of the ocean primary production gradually increases as the water temperature rises. In March, the water temperature and ocean primary production are relatively high in the southern ECS and low near to the coast and in the northern ECS. As time moves forward, the water temperature in the ECS rises rapidly and the ocean primary production is restricted or even declines in the regions away from the coast in the southern ECS due to nutrient limitation or the influence of the oligotrophic Kuroshio water, which is characterized by high temperatures and salinity; in contrast, there is a significant increase in the ocean primary production near the coast and in the northern ECS as the low-temperature limitation is weakened or disappears in these regions (Guan et al., 2005). Correspondingly, during the early spawning season (March), the growth and survival rates of juveniles from the southern spawning grounds are relatively high, whereas the survival rate of juveniles from the northern spawning grounds is low (the growth rate is not necessarily low due to the impacts of density-dependent food competition, see below); as the spawning time moves forward, the juvenile growth and survival rates gradually decrease in the regions away from the coast in the southern ECS but increase near the coast and in the northern ECS and YS. As a result, March is more favorable for spawning in the southern ECS, and as time progresses, the spawning grounds nearer the coast or further north in the ECS have higher growth and survival rates. If chub mackerel can not gradually move their spawning grounds toward the coast or further north in the ECS with time and, for example, the chub mackerel continues to spawn in the southern ECS in June, the juvenile growth and survival rate will decline.

An increase in prey density and water temperature is conducive to improving the survival rate of chub mackerel larvae and juveniles; this, in turn, intensifies the competition for food among the larvae and juveniles and inhibits their growth. For example, under scenario C, the juveniles spawned at spawning ground S3 in April have a higher survival rate, but their average body length is relatively small (Table 5). As spawning time moves forward, the variation in the average body length of the juveniles from spawning ground S4 under scenarios C and D also implies that there are effects due to the intense competition for food that results from the high survival rate (Tables 5–6).

The effects of the ocean current transport on the juvenile growth and survival rates vary with the spawning ground and spawning time. In the two southern spawning grounds, the ocean current transport is beneficial to the improvement of the prey conditions for the larvae and juveniles and leads to an increase in the growth and survival rates. However, in the two northern spawning grounds, the effects are related to the spawning time due to the spatial and temporal variability of the water temperature and ocean primary production in the northern ECS (Tables 5–6).

Our results show that although the water temperature and ocean primary production are two important factors influencing the growth and survival rates of chub mackerel and its recruitment, the recruitment mainly depends on the degree to which the temporal and spatial distribution of chub mackerel larvae and juveniles are matched with the suitable water temperature and ocean primary production in the ECS. Therefore, it may be incorrect to draw conclusions about trends in chub mackerel recruitment based on a single ocean environmental factor or several environmental factors in a specific site. This may be one of the reasons why the conclusions drawn by different scholars who have analyzed the relationship between water temperature and chub mackerel recruitment in the ECS are contradictory (Nishida, 1997; Hwang, 1999; Hiyama et al., 2002; Guan et al., 2011).

4.3 Sources of uncertainty

The visualization of the flow fields, water temperature, salinity, and ocean primary production data that were used in this study reveals that these data can correctly reproduce the basic pattern of the marine environment in the ECS and YS, and the results are similar to those in Li et al. (2014) when it is assumed that chub mackerel larvae and juveniles do not have the ability to swim. However, because the maximum temporal resolution of these data is 6 h, it is difficult to use them to analyze the effects of short-term processes such as tides. In addition, the ocean primary production data is monthly and the values are obviously overestimated. Consequently, these data may be unable to accurately reflect the status quo and changes of the environment in the ECS and YS.

The accuracy of marine environmental data affects the forms of the functions and the parameter values used in the IBM as well as the reliability and reasonableness of the simulation results. For example, because of the overestimation of the ocean primary production in the Kuroshio and western Pacific Ocean, the model produces an unreasonable spread of chub mackerel across the Kuroshio; these chub mackerels also enter the western Pacific Ocean. In order to deal with this problem, a suitability index for the ocean primary production was introduced; this increased the complexity of the model and made it more difficult to judge whether the parametric forms of the IBM were reasonable. At present, there is widespread consensus regarding ecosystem-based fisheries management (Pikitch et al., 2004; Lehodey et al., 2008) and to achieve the goal of this approach, more high-quality ocean observation and assimilation data based on numerical ocean models are required. However, it is still a great challenge for fisheries scientists to obtain these high-quality data.

The assumptions made and the forms of the functions and parameter values used in this study need more support from relevant theories and observations to improve the reasonableness and reliability of the model results. Although we included the irradiance suitability index to simulate the diel vertical migration of chub mackerel in order to account for its possible effect on the spatial distribution of chub mackerel during their early life stages, we still do not know whether there are some other behaviors that allow chub mackerel larvae or even eggs to resist ocean currents and thus remain in the better habitats. The relationship between growth and water temperature is theoretically described as a dome-shaped function when prey is abundant and available (Yamashita et al., 2001), and the optimum water temperature for the growth of chub mackerel larvae may be close to or higher than 25 ℃ (Taga et al., 2019). However, the temperature-dependent growth equation for the chub mackerel larvae and juveniles used in this study is a monotonically increasing function which was estimated based on the observations of water temperature with a range of 16.8‒22.1 ℃ (Go et al., 2020). Therefore, whether it is reasonable to use this function still needs to be investigated and verified. Our results also show that the density of larvae and juveniles affects their spatial distribution, growth, and survival rate. Consequently, the number of eggs contained in the super-individual will affect the simulation results, and how to set this number also needs to be investigated. In addition, the parameterization of the IBM was carried out by manual calibration using empirical values or values that were derived from estimates made by external models (Phillips et al., 2018; Senina et al., 2020); these values require further validation and thus are another source of uncertainty in the simulation results. In future, in order to improve the reliability and reasonableness of the IBM simulation results, it will be necessary to use observational data, such as data from egg, larva and juvenile surveys as well as fishery data, to estimate the IBM-related parameters using parameter estimation algorithms such as the genetic strategy algorithm (Duboz et al., 2010).

5 CONCLUSION

In this study, an IBM for chub mackerel that incorporated swimming behavior was developed and then applied to simulate the distribution, growth, and survival rate of chub mackerel larvae and juveniles in the East China Sea based on the three-dimensional ocean environmental data and the assumptions of spawning ground and spawning time.

Although the spatial distribution of chub mackerel juveniles is influenced by ocean currents, as the swimming ability of chub mackerel larvae and juveniles improves with the rapid growth of the fish, the spatial distribution is also heavily restricted by their habitat conditions. This is obviously a different situation from the one in which the ability to swim is not considered. Our results show there are exchanges between chub mackerel stocks which distribute in East China Sea, Yellow Sea, and Japan/East Sea and we suggest assessing and managing these chub mackerels as a stock.

The water temperature and ocean primary production are two important factors affecting the growth and survival of chub mackerel larvae and juveniles. During the early spawning period, the growth and survival rates are mainly restricted by the water temperature; however, as the spawning time moves forward and the water temperature rises, the influence of the ocean primary production is enhanced. Our results also show the growth and survive rate of chub mackerel larvae and juveniles mainly depends on the degree to which the spawning location, spawning time, water temperature, and ocean primary production match rather than on a single environmental factor or several environmental factors in a specific site. In general, when chub mackerel spawns at the southern ECS spawning ground in March, the growth and survival rate of the larvae and juveniles is relatively high; as spawning time moves forward, the higher growth and survival rates would be expected if the chub mackerel can gradually spawn coastward or northward. For specific spawning sites, early or delayed spawning will reduce the survival rate.

There are still large uncertainties associated with the assumptions on which the model was based, the parameter settings and the marine environmental data, all of which affect the structure of the model and the simulation results. To reduce these uncertainties in future studies, more support from ecological theories, numerical computation methods, and observational data is required.

6 DATA AVAILABILITY STATEMENT

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

7 ACKNOWLEDGMENT

We are grateful to Professor Changsheng CHEN from University of Massachusetts Dartmouth for assistance in the development of the IBM and we also thank Dr. Yu ZHANG and Dr. Yuesong LI from Shanghai Ocean University for their help in the data process.